Daily Papers

We propose Infinite-World, a robust interactive world model capable of maintaining coherent visual memory over 1000+ frames in complex real-world environments. While existing world models can be efficiently optimized on synthetic data with perfect ground-truth, they lack an effective training paradigm for real-world videos due to noisy pose estimations and the scarcity of viewpoint revisits. To bridge this gap, we first introduce a Hierarchical Pose-free Memory Compressor (HPMC) that recursively distills historical latents into a fixed-budget representation. By jointly optimizing the compressor with the generative backbone, HPMC enables the model to autonomously anchor generations in the distant past with bounded computational cost, eliminating the need for explicit geometric priors. Second, we propose an Uncertainty-aware Action Labeling module that discretizes continuous motion into a tri-state logic. This strategy maximizes the utilization of raw video data while shielding the deterministic action space from being corrupted by noisy trajectories, ensuring robust action-response learning. Furthermore, guided by insights from a pilot toy study, we employ a Revisit-Dense Finetuning Strategy using a compact, 30-minute dataset to efficiently activate the model's long-range loop-closure capabilities. Extensive experiments, including objective metrics and user studies, demonstrate that Infinite-World achieves superior performance in visual quality, action controllability, and spatial consistency.

Loop closing is a crucial component in SLAM that helps eliminate accumulated errors through two main steps: loop detection and loop pose correction. The first step determines whether loop closing should be performed, while the second estimates the 6-DoF pose to correct odometry drift. Current methods mostly focus on developing robust descriptors for loop closure detection, often neglecting loop pose estimation. A few methods that do include pose estimation either suffer from low accuracy or incur high computational costs. To tackle this problem, we introduce SGLC, a real-time semantic graph-guided full loop closing method, with robust loop closure detection and 6-DoF pose estimation capabilities. SGLC takes into account the distinct characteristics of foreground and background points. For foreground instances, it builds a semantic graph that not only abstracts point cloud representation for fast descriptor generation and matching but also guides the subsequent loop verification and initial pose estimation. Background points, meanwhile, are exploited to provide more geometric features for scan-wise descriptor construction and stable planar information for further pose refinement. Loop pose estimation employs a coarse-fine-refine registration scheme that considers the alignment of both instance points and background points, offering high efficiency and accuracy. Extensive experiments on multiple publicly available datasets demonstrate its superiority over state-of-the-art methods. Additionally, we integrate SGLC into a SLAM system, eliminating accumulated errors and improving overall SLAM performance. The implementation of SGLC will be released at https://github.com/nubot-nudt/SGLC.

Humans possess a remarkable ability to mentally explore and replay 3D environments they have previously experienced. Inspired by this mental process, we present EvoWorld: a world model that bridges panoramic video generation with evolving 3D memory to enable spatially consistent long-horizon exploration. Given a single panoramic image as input, EvoWorld first generates future video frames by leveraging a video generator with fine-grained view control, then evolves the scene's 3D reconstruction using a feedforward plug-and-play transformer, and finally synthesizes futures by conditioning on geometric reprojections from this evolving explicit 3D memory. Unlike prior state-of-the-arts that synthesize videos only, our key insight lies in exploiting this evolving 3D reconstruction as explicit spatial guidance for the video generation process, projecting the reconstructed geometry onto target viewpoints to provide rich spatial cues that significantly enhance both visual realism and geometric consistency. To evaluate long-range exploration capabilities, we introduce the first comprehensive benchmark spanning synthetic outdoor environments, Habitat indoor scenes, and challenging real-world scenarios, with particular emphasis on loop-closure detection and spatial coherence over extended trajectories. Extensive experiments demonstrate that our evolving 3D memory substantially improves visual fidelity and maintains spatial scene coherence compared to existing approaches, representing a significant advance toward long-horizon spatially consistent world modeling.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

Scaling Transformer-based click-through rate (CTR) models by stacking more parameters brings growing computational and storage overhead, creating a widening gap between scaling ambitions and the stringent industrial deployment constraints. We propose LoopCTR, which introduces a loop scaling paradigm that increases training-time computation through recursive reuse of shared model layers, decoupling computation from parameter growth. LoopCTR adopts a sandwich architecture enhanced with Hyper-Connected Residuals and Mixture-of-Experts, and employs process supervision at every loop depth to encode multi-loop benefits into the shared parameters. This enables a train-multi-loop, infer-zero-loop strategy where a single forward pass without any loop already outperforms all baselines. Experiments on three public benchmarks and one industrial dataset demonstrate state-of-the-art performance. Oracle analysis further reveals 0.02--0.04 AUC of untapped headroom, with models trained with fewer loops exhibiting higher oracle ceilings, pointing to a promising frontier for adaptive inference.

Autonomous GUI agents face two fundamental challenges: early stopping, where agents prematurely declare success without verifiable evidence, and repetitive loops, where agents cycle through the same failing actions without recovery. We present VLAA-GUI, a modular GUI agentic framework built around three integrated components that guide the system on when to Stop, Recover, and Search. First, a mandatory Completeness Verifier enforces UI-observable success criteria and verification at every finish step -- with an agent-level verifier that cross-examines completion claims with decision rules, rejecting those lacking direct visual evidence. Second, a mandatory Loop Breaker provides multi-tier filtering: switching interaction mode after repeated failures, forcing strategy changes after persistent screen-state recurrence, and binding reflection signals to strategy shifts. Third, an on-demand Search Agent searches online for unfamiliar workflows by directly querying a capable LLM with search ability, returning results as plain text. We additionally integrate a Coding Agent for code-intensive actions and a Grounding Agent for precise action grounding, both invoked on demand when required. We evaluate VLAA-GUI across five top-tier backbones, including Opus 4.5, 4.6 and Gemini 3.1 Pro, on two benchmarks with Linux and Windows tasks, achieving top performance on both (77.5% on OSWorld and 61.0% on WindowsAgentArena). Notably, three of the five backbones surpass human performance (72.4%) on OSWorld in a single pass. Ablation studies show that all three proposed components consistently improve a strong backbone, while a weaker backbone benefits more from these tools when the step budget is sufficient. Further analysis also shows that the Loop Breaker nearly halves wasted steps for loop-prone models.

Augmenting Large Language Models (LLMs) with external tools enables them to execute complex, multi-step tasks. However, tool learning is hampered by the static synthetic data pipelines where data generation and model training are executed as two separate, non-interactive processes. This approach fails to adaptively focus on a model's specific weaknesses and allows noisy labels to persist, degrading training efficiency. We introduce LoopTool, a fully automated, model-aware data evolution framework that closes this loop by tightly integrating data synthesis and model training. LoopTool iteratively refines both the data and the model through three synergistic modules: (1) Greedy Capability Probing (GCP) diagnoses the model's mastered and failed capabilities; (2) Judgement-Guided Label Verification (JGLV) uses an open-source judge model to find and correct annotation errors, progressively purifying the dataset; and (3) Error-Driven Data Expansion (EDDE) generates new, challenging samples based on identified failures. This closed-loop process operates within a cost-effective, open-source ecosystem, eliminating dependence on expensive closed-source APIs. Experiments show that our 8B model trained with LoopTool significantly surpasses its 32B data generator and achieves new state-of-the-art results on the BFCL-v3 and ACEBench benchmarks for its scale. Our work demonstrates that closed-loop, self-refining data pipelines can dramatically enhance the tool-use capabilities of LLMs.

Individual agent capabilities have advanced rapidly through modular skills and tool integrations, yet multi-agent systems remain constrained by fixed team structures, tightly coupled coordination logic, and session-bound learning. We argue that this reflects a deeper absence: a principled organisational layer that governs how a workforce of agents is assembled, governed, and improved over time, decoupled from what individual agents know. To fill this gap, we introduce OneManCompany (OMC), a framework that elevates multi-agent systems to the organisational level. OMC encapsulates skills, tools, and runtime configurations into portable agent identities called Talents, orchestrated through typed organisational interfaces that abstract over heterogeneous backends. A community-driven Talent Market enables on-demand recruitment, allowing the organisation to close capability gaps and reconfigure itself dynamically during execution. Organisational decision-making is operationalised through an Explore-Execute-Review (E^2R) tree search, which unifies planning, execution, and evaluation in a single hierarchical loop: tasks are decomposed top-down into accountable units and execution outcomes are aggregated bottom-up to drive systematic review and refinement. This loop provides formal guarantees on termination and deadlock freedom while mirroring the feedback mechanisms of human enterprises. Together, these contributions transform multi-agent systems from static, pre-configured pipelines into self-organising and self-improving AI organisations capable of adapting to open-ended tasks across diverse domains. Empirical evaluation on PRDBench shows that OMC achieves an 84.67% success rate, surpassing the state of the art by 15.48 percentage points, with cross-domain case studies further demonstrating its generality.

Automated vulnerability reproduction from CVE descriptions requires generating executable Proof-of-Concept (PoC) exploits and validating them in target environments. This process is critical in software security research and practice, yet remains time-consuming and demands specialized expertise when performed manually. While LLM agents show promise for automating this task, existing approaches often conflate exploring attack directions with fixing implementation details, which leads to unproductive debugging loops when reproduction fails. To address this, we propose CVE2PoC, an LLM-based dual-loop agent framework following a plan-execute-evaluate paradigm. The Strategic Planner analyzes vulnerability semantics and target code to produce structured attack plans. The Tactical Executor generates PoC code and validates it through progressive verification. The Adaptive Refiner evaluates execution results and routes failures to different loops: the Tactical Loop for code-level refinement, while the Strategic Loop for attack strategy replanning. This dual-loop design enables the framework to escape ineffective debugging by matching remediation to failure type. Evaluation on two benchmarks covering 617 real-world vulnerabilities demonstrates that CVE2PoC achieves 82.9% and 54.3% reproduction success rates on SecBench.js and PatchEval, respectively, outperforming the best baseline by 11.3% and 20.4%. Human evaluation confirms that generated PoCs achieve comparable code quality to human-written exploits in readability and reusability.

Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we establish the approximation rate of Looped Transformers by defining the modulus of continuity for sequence-to-sequence functions. This reveals a limitation specific to the looped architecture. That is, the analysis prompts the incorporation of scaling parameters for each loop, conditioned on timestep encoding. Experiments validate the theoretical results, showing that increasing the number of loops enhances performance, with further gains achieved through the timestep encoding.

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive retrofits, which involve substantial computational costs and may compromise pretrained capabilities. To address these limitations, we introduce Looped Depth Up-Scaling (LoopUS), a post-training framework that converts a standard pretrained LLM into a looped architecture. As a key technical contribution, LoopUS recasts the pretrained LLM into an encoder, a looped reasoning block, and a decoder. It operationalizes this latent-refinement architecture through four core components: (1) block decomposition, guided by staged representation dynamics; (2) an input-dependent selective gate to mitigate hidden-state drift; (3) random deep supervision for memory-efficient learning over long recursive horizons; and (4) a confidence head for adaptive early exiting. Collectively, these mechanisms transform a standard non-looped model into a looped form while stabilizing it against both computational bottlenecks and representation collapse. Through stable latent looping, LoopUS improves reasoning-oriented performance without extending the generated traces or requiring recurrent training from scratch. For more details, see https://thrillcrazyer.github.io/LoopUS

We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a bounded observational interface, a canonical toolkit of six closure-changing primitives (P1--P6) is unavoidable. The framework unifies order-theoretic closure operators with dynamics-induced endomaps E_{τ,f} built from a Markov kernel, a coarse-graining lens, and a time scale τ. We introduce a computable total-variation idempotence defect for E_{τ,f}; small retention error implies approximate idempotence and yields stable "objects" packaged at the chosen τ within a fixed lens. For directionality, we define an arrow-of-time functional as the path-space KL divergence between forward and time-reversed trajectories and prove it is monotone under coarse-graining (data processing); we also formalize a protocol-trap audit showing that protocol holonomy alone cannot sustain asymmetry without a genuine affinity in the lifted dynamics. Finally, we prove a finite forcing-style counting lemma: relative to a partition-based theory, definable predicate extensions are exponentially rare, giving a clean anti-saturation mechanism for strict ladder climbing.

We study auto research as a closed empirical loop driven by external measurement. Each submitted trial carries a hypothesis, an executable code edit, an evaluator-owned outcome, and feedback that shapes the next proposal. The output is not a generated paper or a single model checkpoint, but an auditable trajectory of proposals, code diffs, experiments, scores, and failure labels. We instantiate this loop with specialist agents that partition recipe surfaces and share measured lineage across trials. The central empirical finding is that lineage feedback lets agents turn evaluator outcomes, including crashes, budget overruns, size failures, and accuracy-gate misses, into later program-level recipe edits rather than one-shot suggestions. Across 1,197 headline-run trials plus 600 Parameter Golf control trials after one-time setup and launch, humans did not choose proposals, edit recipes, override scores, or repair failed trials during the search. In the three headline runs, the same submitted-trial loop reduces Parameter Golf validation bpb by 0.81%, raises NanoChat-D12 CORE by 38.7%, and reduces CIFAR-10 Airbench96 wallclock by 4.59%, with each task measured by its own external evaluator and legality checks. The trace includes a strict architecture-domain audit of 157 headline-run submissions and program rewrites such as a NanoChat attention-kernel path change. Within this scope the loop autonomously writes code, submits experiments, absorbs feedback, applies and combines known techniques inside each environment, and improves public starting recipes.

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this approach has a major flaw: the loops run one after another, causing inference latency and memory requirements to increase with each added loop. This makes them impractical for fast applications. To solve this problem, we introduce the Parallel Loop Transformer (PLT). PLT is a new architecture that delivers the performance benefits of a deep, looped model but with the low latency of a standard, non-looped model. PLT works using two key techniques. First, Cross-Loop Parallelism (CLP) breaks the sequential dependency by computing different loops for different tokens at the same time, all within a single pass. Second, to prevent memory costs from growing, we use an Efficient Representation Enhancement strategy. This method shares the memory (KV cache) from the first loop with all other loops. It then uses a Gated Sliding-Window Attention (G-SWA) to combine this shared global information with local information, maintaining high accuracy. Our experiments show that PLT achieves the high accuracy of a traditional looped model but with almost no extra latency or memory cost compared to a standard transformer.

We study infinite-horizon average-reward Markov decision processes (AMDPs) in the context of general function approximation. Specifically, we propose a novel algorithmic framework named Local-fitted Optimization with OPtimism (LOOP), which incorporates both model-based and value-based incarnations. In particular, LOOP features a novel construction of confidence sets and a low-switching policy updating scheme, which are tailored to the average-reward and function approximation setting. Moreover, for AMDPs, we propose a novel complexity measure -- average-reward generalized eluder coefficient (AGEC) -- which captures the challenge of exploration in AMDPs with general function approximation. Such a complexity measure encompasses almost all previously known tractable AMDP models, such as linear AMDPs and linear mixture AMDPs, and also includes newly identified cases such as kernel AMDPs and AMDPs with Bellman eluder dimensions. Using AGEC, we prove that LOOP achieves a sublinear mathcal{O}(poly(d, sp(V^*)) Tbeta ) regret, where d and beta correspond to AGEC and log-covering number of the hypothesis class respectively, sp(V^*) is the span of the optimal state bias function, T denotes the number of steps, and mathcal{O} (cdot) omits logarithmic factors. When specialized to concrete AMDP models, our regret bounds are comparable to those established by the existing algorithms designed specifically for these special cases. To the best of our knowledge, this paper presents the first comprehensive theoretical framework capable of handling nearly all AMDPs.

Global climate models (GCMs) are the main tools for understanding and predicting climate change. However, due to limited numerical resolutions, these models suffer from major structural uncertainties; e.g., they cannot resolve critical processes such as small-scale eddies in atmospheric and oceanic turbulence. Thus, such small-scale processes have to be represented as a function of the resolved scales via closures (parametrization). The accuracy of these closures is particularly important for capturing climate extremes. Traditionally, such closures are based on heuristics and simplifying assumptions about the unresolved physics. Recently, supervised-learned closures, trained offline on high-fidelity data, have been shown to outperform the classical physics-based closures. However, this approach requires a significant amount of high-fidelity training data and can also lead to instabilities. Reinforcement learning is emerging as a potent alternative for developing such closures as it requires only low-order statistics and leads to stable closures. In Scientific Multi-Agent Reinforcement Learning (SMARL) computational elements serve a dual role of discretization points and learning agents. We leverage SMARL and fundamentals of turbulence physics to learn closures for prototypes of atmospheric and oceanic turbulence. The policy is trained using only the enstrophy spectrum, which is nearly invariant and can be estimated from a few high-fidelity samples (these few samples are far from enough for supervised/offline learning). We show that these closures lead to stable low-resolution simulations that, at a fraction of the cost, can reproduce the high-fidelity simulations' statistics, including the tails of the probability density functions. The results demonstrate the high potential of SMARL for closure modeling for GCMs, especially in the regime of scarce data and indirect observations.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

Tool-using LLM agents increasingly coordinate real workloads by selecting and chaining third-party tools based on text-visible metadata such as tool names, descriptions, and return messages. We show that this convenience creates a supply-chain attack surface: a malicious MCP tool server can be co-registered alongside normal tools and induce overthinking loops, where individually trivial or plausible tool calls compose into cyclic trajectories that inflate end-to-end tokens and latency without any single step looking abnormal. We formalize this as a structural overthinking attack, distinguishable from token-level verbosity, and implement 14 malicious tools across three servers that trigger repetition, forced refinement, and distraction. Across heterogeneous registries and multiple tool-capable models, the attack causes severe resource amplification (up to 142.4times tokens) and can degrade task outcomes. Finally, we find that decoding-time concision controls do not reliably prevent loop induction, suggesting defenses should reason about tool-call structure rather than tokens alone.

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.

Traditional fixed-depth architectures scale quality by increasing training FLOPs, typically through increased parameterization, at the expense of a higher memory footprint, or data. A potential alternative is looped architectures, which instead increase FLOPs by sending activations through a block of layers in a loop. While promising, existing recipes for training looped architectures can be unstable, suffering from residual explosion and loss spikes. We address these challenges by recasting looping as a nonlinear time-variant dynamical system over the residual stream. Via a linear approximation to this system, we find that instability occurs in existing looped architectures as a result of large spectral norms in their injection parameters. To address these instability issues, we propose Parcae, a novel stable, looped architecture that constrains the spectral norm of the injection parameters via discretization of a negative diagonal parameterization. As a result, Parcae achieves up to 6.3% lower validation perplexity over prior large-scale looped models. Using our stable looped architecture, we investigate the scaling properties of looping as a medium to improve quality by increasing FLOPs in training and test-time. For training, we derive predictable power laws to scale FLOPs while keeping parameter count fixed. Our initial scaling laws suggest that looping and data should be increased in tandem, given a fixed FLOP budget. At test-time, we find that Parcae can use looping to scale compute, following a predictable, saturating exponential decay. When scaled up to 1.3B parameters, we find that Parcae improves CORE and Core-Extended quality by 2.99 and 1.18 points when compared to strong Transformer baselines under a fixed parameter and data budget, achieving a relative quality of up to 87.5% a Transformer twice the size.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

Understanding the topology of decision regions is central to explaining the inner workings of deep neural networks. Prior empirical work has provided evidence that these regions are path connected. We study a stronger topological question: whether closed loops inside a decision region can be contracted without leaving that region. To this end, we propose an iterative quad-mesh filling procedure that constructs a finite-resolution label-preserving surface bounded by a given loop and lying entirely within the same decision region. We further connect this construction to natural Coons patches in order to quantify its deviation from a canonical geometric interpolation of the loop. By evaluating our method across several modern image-classification models, we provide empirical evidence supporting the hypothesis that decision regions in deep neural networks are not only path connected, but also simply connected.

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.

While polyhedral compilers have shown success in implementing advanced code transformations, they still face challenges in selecting the ones that lead to the most profitable speedups. This has motivated the use of machine learning based cost models to guide the search for polyhedral optimizations. State-of-the-art polyhedral compilers have demonstrated a viable proof-of-concept of such an approach. While promising, this approach still faces significant limitations. State-of-the-art polyhedral compilers that use a deep learning cost model only support a small subset of affine transformations, limiting their ability to explore complex code transformations. Furthermore, their applicability does not scale beyond simple programs, thus excluding many program classes from their scope, such as those with non-rectangular iteration domains or multiple loop nests. These limitations significantly impact the generality of such compilers and autoschedulers and put into question the whole approach. In this paper, we introduce LOOPer, the first polyhedral autoscheduler that uses a deep learning based cost model and covers a large space of affine transformations and programs. LOOPer allows the optimization of an extensive set of programs while being effective at applying complex sequences of polyhedral transformations. We implement and evaluate LOOPer and show that it achieves competitive speedups over the state-of-the-art. On the PolyBench benchmarks, LOOPer achieves a geometric mean speedup of 1.84x over Tiramisu and 1.42x over Pluto, two state-of-the-art polyhedral autoschedulers.

AI agents that interact with the real world through tool calls pose fundamental safety challenges: agents might leak private information, cause unintended side effects, or be manipulated through prompt injection. To address these challenges, we propose to put the agent in a programming-language-based "safety harness": instead of calling tools directly, agents express their intentions as code in a capability-safe language: Scala 3 with capture checking. Capabilities are program variables that regulate access to effects and resources of interest. Scala's type system tracks capabilities statically, providing fine-grained control over what an agent can do. In particular, it enables local purity, the ability to enforce that sub-computations are side-effect-free, preventing information leakage when agents process classified data. We demonstrate that extensible agent safety harnesses can be built by leveraging a strong type system with tracked capabilities. Our experiments show that agents can generate capability-safe code with no significant loss in task performance, while the type system reliably prevents unsafe behaviors such as information leakage and malicious side effects.

The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to embed computational effects, evaluation strategies, and control flow operations. The first instalment modelled sequential higher-order computation with global store, input/output, probabilities, and non-determinism, and embedded both the call-by-name and call-by-value lambda-calculus, as well as Moggi's computational metalanguage and Levy's call-by-push-value. The present paper extends the calculus from sequential to branching and looping control flow. This allows the faithful embedding of a minimal but complete imperative language, including conditionals, exception handling, and iteration, as well as constants and algebraic data types. The calculus is defined through a simple operational semantics, extending the (simplified) Krivine machine for the lambda-calculus with multiple operand stacks to model effects and a continuation stack to model sequential, branching, and looping computation. It features a confluent reduction relation and a system of simple types that guarantees termination of the machine and strong normalization of reduction (in the absence of iteration). These properties carry over to the embedded imperative language, providing a unified functional-imperative model of computation that supports simple types, a direct and intuitive operational semantics, and a confluent reduction semantics.

We measure how much one extra recurrence is worth to a looped (depth-recurrent) language model, in equivalent unique parameters. From an iso-depth sweep of 116 pretraining runs across recurrence counts r in {1, 2, 4, 8} spanning {sim}50times in training compute, we fit a joint scaling law L = E + A,(N_once + r^φ N_rec)^{-α} + B,D^{-β} and recover a new recurrence-equivalence exponent φ= 0.46. Intuitively, φ tells us whether looping a block r times is equivalent in validation loss to r unique blocks of a non-looped model (full equivalence, φ{=}1) or to a single block run repeatedly with no capacity gain (φ{=}0). Our φ= 0.46 sits in between, so each additional recurrence predictably increases validation loss at matched training compute. For example, at r{=}4 a 410M looped model performs on par with a 580M non-looped model, but incurs the training cost of a 1B non-looped one. We demonstrate the utility of φ as a measurement tool on two probes. Truncated backpropagation lowers φ to 0.38, indicating that the loop mechanism is poorly trained under truncation, even though validation loss decreases. Conversely, hyperconnections raise φ to 0.65, a genuine capacity gain. Our method applies to any looped LM and separates true loop improvements from token-budget gains.

Interactive digital agents (IDAs) leverage APIs of stateful digital environments to perform tasks in response to user requests. While IDAs powered by instruction-tuned large language models (LLMs) can react to feedback from interface invocations in multi-step exchanges, they have not been trained in their respective digital environments. Prior methods accomplish less than half of tasks in sophisticated benchmarks such as AppWorld. We present a reinforcement learning (RL) approach that trains IDAs directly in their target environments. We formalize this training as a partially observable Markov decision process and derive LOOP, a data- and memory-efficient variant of proximal policy optimization. LOOP uses no value network and maintains exactly one copy of the underlying LLM in memory, making its implementation straightforward and as memory-efficient as fine-tuning a single LLM. A 32-billion-parameter agent trained with LOOP in the AppWorld environment outperforms the much larger OpenAI o1 agent by 9 percentage points (15% relative). To our knowledge, this is the first reported application of RL to IDAs that interact with a stateful, multi-domain, multi-app environment via direct API calls. Our analysis sheds light on the effectiveness of RL in this area, showing that the agent learns to consult the API documentation, avoid unwarranted assumptions, minimize confabulation, and recover from setbacks.

The ARC-AGI benchmark series serves as a critical measure of few-shot generalization on novel tasks, a core aspect of intelligence. The ARC Prize 2025 global competition targeted the newly released ARC-AGI-2 dataset, which features greater task complexity compared to its predecessor. The Kaggle competition attracted 1,455 teams and 15,154 entries, with the top score reaching 24% on the ARC-AGI-2 private evaluation set. Paper submissions nearly doubled year-over-year to 90 entries, reflecting the growing research interest in fluid intelligence and abstract reasoning. The defining theme of 2025 is the emergence of the refinement loop -- a per-task iterative program optimization loop guided by a feedback signal. Refinement loops come in a variety of forms, in particular evolutionary program synthesis approaches and application-layer refinements to commercial AI systems. Such refinement loops are also possible in weight space, as evidenced by zero-pretraining deep learning methods which are now achieving competitive performance with remarkably small networks (7M parameters). In parallel, four frontier AI labs (Anthropic, Google DeepMind, OpenAI, and xAI) reported ARC-AGI performance in public model cards in 2025, establishing ARC-AGI as an industry standard benchmark for AI reasoning. However, our analysis indicates that current frontier AI reasoning performance remains fundamentally constrained to knowledge coverage, giving rise to new forms of benchmark contamination. In this paper, we survey the top-performing methods, examine the role of refinement loops in AGI progress, discuss knowledge-dependent overfitting, and preview ARC-AGI-3, which introduces interactive reasoning challenges that require exploration, planning, memory, goal acquisition, and alignment capabilities.

Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. Hypergraphs generalize graphs by modeling higher-order relationships among multiple entities, enabling richer representations but introducing significant computational challenges. In this work, we extend the Loop Transformer architecture's neural algorithmic reasoning capability to simulate hypergraph algorithms, addressing the gap between neural networks and combinatorial optimization over hypergraphs. Specifically, we propose a novel degradation mechanism for reducing hypergraphs to graph representations, enabling the simulation of graph-based algorithms, such as Dijkstra's shortest path. Furthermore, we introduce a hyperedge-aware encoding scheme to simulate hypergraph-specific algorithms, exemplified by Helly's algorithm. We establish theoretical guarantees for these simulations, demonstrating the feasibility of processing high-dimensional and combinatorial data using Loop Transformers. This work highlights the potential of Transformers as general-purpose algorithmic solvers for structured data.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This parameter efficiency comes at a cost, as looped models lack the storage capacity of deeper models which use unique weights per layer. In this work, we investigate transformer models that feature both adaptive per-layer looping, where each transformer block learns to iterate its hidden state via a learned halting mechanism, and gated memory banks, that provide additional learned storage. We find that looping primarily benefits mathematical reasoning, while memory banks help recover performance on commonsense tasks compared to parameter and FLOP matched models. Combining both mechanisms yields a model that outperforms an iso-FLOP baseline, with three times the number of layers, across math benchmarks. Analysis of model internals reveals layer specialization: early layers learn to loop minimally and access memory sparingly, while later layers do both more heavily.

Tool-use capability is a fundamental component of LLM agents, enabling them to interact with external systems through structured function calls. However, existing research exhibits inconsistent interaction representations, largely overlooks the structural distribution of tool-use trajectories, and relies on incompatible evaluation benchmarks. We present UniToolCall, a unified framework for tool learning that standardizes the entire pipeline from toolset construction and dataset generation to evaluation. The framework curates a large tool pool of 22k+ tools and constructs a hybrid training corpus of 390k+ instances by combining 10 standardized public datasets with structurally controlled synthetic trajectories. It explicitly models diverse interaction patterns, including single-hop vs. multi-hop and single-turn vs. multi-turn, while capturing both serial and parallel execution structures. To support coherent multi-turn reasoning, we further introduce an Anchor Linkage mechanism that enforces cross-turn dependencies. Furthermore, we convert 7 public benchmarks into a unified Query--Action--Observation--Answer (QAOA) representation with fine-grained evaluation at the function-call, turn, and conversation levels. Experiments show that fine-tuning Qwen3-8B on our dataset substantially improves tool-use performance. Under the distractor-heavy Hybrid-20 setting, achieves 93.0% single-turn Strict Precision, outperforming commercial models including GPT, Gemini, and Claude.

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

Discovering causal regularities and applying them to build functional systems--the discovery-to-application loop--is a hallmark of general intelligence, yet evaluating this capacity has been hindered by the vast complexity gap between scientific discovery and real-world engineering. We introduce SciCrafter, a Minecraft-based benchmark that operationalizes this loop through parameterized redstone circuit tasks. Agents must ignite lamps in specified patterns (e.g., simultaneously or in timed sequences); scaling target parameters substantially increases construction complexity and required knowledge, forcing genuine discovery rather than reliance on memorized solutions. Evaluating frontier models including GPT-5.2, Gemini-3-Pro, and Claude-Opus-4.5 under a general-purpose code agent scaffold, we find that all plateau at approximately 26% success rate. To diagnose these failures, we decompose the loop into four capacities--knowledge gap identification, experimental discovery, knowledge consolidation, and knowledge application--and design targeted interventions whose marginal contributions serve as proxies for corresponding gaps. Our analysis reveals that although the general knowledge application capability still remains as the biggest gap across all models, for frontier models the knowledge gap identification starts to become a major hurdle--indicating the bottleneck is shifting from solving problems right to raising the right problems for current AI. We release SciCrafter as a diagnostic probe for future research on AI systems that navigate the full discovery-to-application loop.

Large language models have achieved striking results in interactive theorem proving, particularly in Lean. However, most benchmarks for LLM-based proof automation are drawn from mathematics in the Mathlib ecosystem, whereas proofs in software verification are developed inside definition-rich codebases with substantial project-specific libraries. We introduce VeriSoftBench, a benchmark of 500 Lean 4 proof obligations drawn from open-source formal-methods developments and packaged to preserve realistic repository context and cross-file dependencies. Our evaluation of frontier LLMs and specialized provers yields three observations. First, provers tuned for Mathlib-style mathematics transfer poorly to this repository-centric setting. Second, success is strongly correlated with transitive repository dependence: tasks whose proofs draw on large, multi-hop dependency closures are less likely to be solved. Third, providing curated context restricted to a proof's dependency closure improves performance relative to exposing the full repository, but nevertheless leaves substantial room for improvement. Our benchmark and evaluation suite are released at https://github.com/utopia-group/VeriSoftBench.

Bold claims about AI's role in science-from "AGI will cure all diseases" to promises of radically accelerated discovery-raise a central epistemic question: do large language models (LLMs) truly generate new knowledge, or do they merely remix memorized fragments? We propose unlearning-as-ablation as a falsifiable probe of constructive scientific discovery. The idea is to systematically remove a target result together with its forget-closure (supporting lemmas, paraphrases, and multi-hop entailments) and then evaluate whether the model can re-derive the result from only permitted axioms and tools. Success would indicate generative capability beyond recall; failure would expose current limits. Unlike prevailing motivations for unlearning-privacy, copyright, or safety-our framing repositions it as an epistemic probe for AI-for-Science. We outline a minimal pilot in mathematics and algorithms to illustrate feasibility, and sketch how the same approach could later be extended to domains such as physics or chemistry. This is a position paper: our contribution is conceptual and methodological, not empirical. We aim to stimulate discussion on how principled ablation tests could help distinguish models that reconstruct knowledge from those that merely retrieve it, and how such probes might guide the next generation of AI-for-Science benchmarks.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10\% of the parameter count.

We present SuperCoder2.0, an advanced autonomous system designed to enhance software development through artificial intelligence. The system combines an AI-native development approach with intelligent agents to enable fully autonomous coding. Key focus areas include a retry mechanism with error output traceback, comprehensive code rewriting and replacement using Abstract Syntax Tree (ast) parsing to minimize linting issues, code embedding technique for retrieval-augmented generation, and a focus on localizing methods for problem-solving rather than identifying specific line numbers. The methodology employs a three-step hierarchical search space reduction approach for code base navigation and bug localization:utilizing Retrieval Augmented Generation (RAG) and a Repository File Level Map to identify candidate files, (2) narrowing down to the most relevant files using a File Level Schematic Map, and (3) extracting 'relevant locations' within these files. Code editing is performed through a two-part module comprising CodeGeneration and CodeEditing, which generates multiple solutions at different temperature values and replaces entire methods or classes to maintain code integrity. A feedback loop executes repository-level test cases to validate and refine solutions. Experiments conducted on the SWE-bench Lite dataset demonstrate SuperCoder2.0's effectiveness, achieving correct file localization in 84.33% of cases within the top 5 candidates and successfully resolving 34% of test instances. This performance places SuperCoder2.0 fourth globally on the SWE-bench leaderboard. The system's ability to handle diverse repositories and problem types highlights its potential as a versatile tool for autonomous software development. Future work will focus on refining the code editing process and exploring advanced embedding models for improved natural language to code mapping.

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering a promising alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on the Ouro architecture across multiple model scales. Results demonstrate that LoopRPT consistently improves per-step representation quality, achieving Pareto dominance in accuracy-computation trade-offs. Notably, significant gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Code production is now a commodity; the bottleneck is knowing what to build and proving it works. We present the Kitchen Loop, a framework for autonomous, self-evolving software built on a unified trust model: (1) a specification surface enumerating what the product claims to support; (2) 'As a User x 1000', where an LLM agent exercises that surface as a synthetic power user at 1,000x human cadence; (3) Unbeatable Tests, ground-truth verification the code author cannot fake; and (4) Drift Control, continuous quality measurement with automated pause gates. We validate across two production systems over 285+ iterations, producing 1,094+ merged pull requests with zero regressions detected by the regression oracle (methodology in Section 6.1). We observe emergent properties at scale: multi-iteration self-correction chains, autonomous infrastructure healing, and monotonically improving quality gates. The primitives are not new; our contribution is their composition into a production-tested system with the operational discipline that makes long-running autonomous evolution safe.

Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic unification: looped and depth-grown models exhibit convergent depth-wise signatures, including increased reliance on late layers and recurring patterns aligned with the looped or grown block. These shared signatures support the view that their gains stem from a common form of iterative computation. Building on this connection, we show that the two techniques are adaptable and composable: applying inference-time looping to the middle blocks of a depth-grown model improves accuracy on some reasoning primitives by up to 2times, despite the model never being trained to loop. Both approaches also adapt better than the baseline when given more in-context examples or additional supervised fine-tuning data. Additionally, depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy cooldown mixtures, which can be further boosted by adapting a middle block to loop. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Large Language Models have demonstrated remarkable capabilities in code generation, yet they often struggle with complex programming tasks that require deep algorithmic reasoning. While process supervision through learned reward models shows promise in guiding reasoning steps, it requires expensive training data and suffers from unreliable evaluation. We propose Outcome-Refining Process Supervision, a novel paradigm that treats outcome refinement itself as the process to be supervised. Our framework leverages concrete execution signals to ground the supervision of reasoning steps, while using tree-structured exploration to maintain multiple solution trajectories simultaneously. Experiments demonstrate that our approach enables even smaller models to achieve high success accuracy and performance metrics on competitive programming tasks, creates more reliable verification than traditional reward models without requiring training PRMs. Our approach achieves significant improvements across 5 models and 3 datasets: an average of 26.9% increase in correctness and 42.2% in efficiency. The results suggest that providing structured reasoning space with concrete verification signals is crucial for solving complex programming tasks. We open-source all our code and data at: https://github.com/zhuohaoyu/ORPS

Large Language Models (LLMs) have shown impressive performance across a wide array of tasks involving both structured and unstructured textual data. Recent results on various benchmarks for code generation, repair, or completion suggest that certain models have programming abilities comparable to or even surpass humans. In this work, we demonstrate that high performance on such benchmarks does not correlate to humans' innate ability to understand structural control flow in code. To this end, we extract solutions from the HumanEval benchmark, which the relevant models perform strongly on, and trace their execution path using function calls sampled from the respective test set. Using this dataset, we investigate the ability of seven state-of-the-art LLMs to match the execution trace and find that, despite their ability to generate semantically identical code, they possess limited ability to trace execution paths, especially for longer traces and specific control structures. We find that even the top-performing model, Gemini, can fully and correctly generate only 47% of HumanEval task traces. Additionally, we introduce a subset for three key structures not contained in HumanEval: Recursion, Parallel Processing, and Object-Oriented Programming, including concepts like Inheritance and Polymorphism. Besides OOP, we show that none of the investigated models achieve an accuracy over 5% on the relevant traces. Aggregating these specialized parts with HumanEval tasks, we present Benchmark CoCoNUT: Code Control Flow for Navigation Understanding and Testing, which measures a model's ability to trace execution of code upon relevant calls, including advanced structural components. We conclude that current LLMs need significant improvement to enhance code reasoning abilities. We hope our dataset helps researchers bridge this gap.

Tool-using automation systems, from scripts and CI bots to agentic assistants, fail in recurring patterns. Common failures include unsafe side effects, invalid arguments, uncontrolled retries, and leakage of sensitive outputs. Many mitigations are model-centric and prompt-dependent, so they are brittle and do not generalize to non-LLM callers. We present Policy-First Tooling, a model-agnostic permission layer that mediates tool invocation through explicit constraints, risk-aware gating, recovery controls, and auditable explanations. The paper contributes a compact policy DSL, a runtime enforcement architecture with actionable rationale and fix hints, and a reproducible benchmark based on trace replay with controlled fault and misuse injection. In 225 controlled runs across five policy packs and three fault profiles, stricter packs improve violation prevention from 0.000 in P0 to 0.681 in P4, while task success drops from 0.356 to 0.067. Retry amplification decreases from 3.774 in P0 to 1.378 in P4, and leakage recall reaches 0.875 under injected secret outputs. These results make safety to utility trade-offs explicit and measurable.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

We study the right to be forgotten (GDPR Art. 17) for large language models and frame unlearning as a reproducible systems problem. Our approach treats training as a deterministic program and logs a minimal per-microbatch record (ordered ID hash, RNG seed, learning-rate value, optimizer-step counter, and accumulation boundary). Under a pinned stack and deterministic kernels, replaying the training tail while filtering only the forget closure yields the same parameters as training on the retain set (bit-identical in the training dtype) when preconditions hold. To meet latency and availability constraints, we add complementary paths: (i) exact reverts of recent steps via micro-checkpoints or dense per-step deltas, (ii) cohort-scoped adapter deletion when the base is frozen, and (iii) a curvature-guided anti-update followed by a short retain-tune, audit-gated with escalation to exact replay. We report storage/latency budgets and a toy artifact validating mechanics; in a controlled run that satisfies the preconditions we demonstrate byte-identical equality of model and optimizer states.

We reformulate the problem of supervised learning as learning to learn with two nested loops (i.e. learning problems). The inner loop learns on each individual instance with self-supervision before final prediction. The outer loop learns the self-supervised task used by the inner loop, such that its final prediction improves. Our inner loop turns out to be equivalent to linear attention when the inner-loop learner is only a linear model, and to self-attention when it is a kernel estimator. For practical comparison with linear or self-attention layers, we replace each of them in a transformer with an inner loop, so our outer loop is equivalent to training the architecture. When each inner-loop learner is a neural network, our approach vastly outperforms transformers with linear attention on ImageNet from 224 x 224 raw pixels in both accuracy and FLOPs, while (regular) transformers cannot run.

LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet existing RLMs depend on an open-ended read-eval-print loop (REPL) in which the model generates arbitrary control code, making execution difficult to verify, predict, and analyse. We introduce λ-RLM, a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in λ-calculus. It executes a compact library of pre-verified combinators and uses neural inference only on bounded leaf subproblems, turning recursive reasoning into a structured functional program with explicit control flow. We show that λ-RLM admits formal guarantees absent from standard RLMs, including termination, closed-form cost bounds, controlled accuracy scaling with recursion depth, and an optimal partition rule under a simple cost model. Empirically, across four long-context reasoning tasks and nine base models, λ-RLM outperforms standard RLM in 29 of 36 model-task comparisons, improves average accuracy by up to +21.9 points across model tiers, and reduces latency by up to 4.1x. These results show that typed symbolic control yields a more reliable and efficient foundation for long-context reasoning than open-ended recursive code generation. The complete implementation of λ-RLM, is open-sourced for the community at: https://github.com/lambda-calculus-LLM/lambda-RLM.

The Functional Machine Calculus (Heijltjes 2022) is an extension of the lambda-calculus that preserves confluent reduction and typed termination, while enabling both call-by-name and call-by-value reduction behaviour and encoding the computational effects of mutable higher-order store, input/output, and probabilistic computation. In this note the calculus is extended to capture exception handling and loop constructs.

Recent advancements in large language models (LLMs) have greatly improved code generation, specifically at the function level. For instance, GPT-4 has achieved an 88.4% pass rate on HumanEval. However, this draws into question the adequacy of existing benchmarks in thoroughly assessing function-level code generation capabilities. Our study analyzed two common benchmarks, HumanEval and MBPP, and found that these might not thoroughly evaluate LLMs' code generation capacities due to limitations in quality, difficulty, and granularity. To resolve this, we introduce the Mostly Hard Python Problems (MHPP) dataset, consisting of 140 unique human-curated problems. By focusing on the combination of natural language and code reasoning, MHPP gauges LLMs' abilities to comprehend specifications and restrictions, engage in multi-step reasoning, and apply coding knowledge effectively. Initial evaluations of 22 LLMs using MHPP showed many high-performing models on HumanEval failed to achieve similar success on MHPP. Moreover, MHPP highlighted various previously undiscovered limitations within various LLMs, leading us to believe that it could pave the way for a better understanding of LLMs' capabilities and limitations. Dataset and code are available at https://github.com/SparksofAGI/MHPP.

Besides natural language processing, transformers exhibit extraordinary performance in solving broader applications, including scientific computing and computer vision. Previous works try to explain this from the expressive power and capability perspectives that standard transformers are capable of performing some algorithms. To empower transformers with algorithmic capabilities and motivated by the recently proposed looped transformer (Yang et al., 2024; Giannou et al., 2023), we design a novel transformer block, dubbed Algorithm Transformer (abbreviated as AlgoFormer). Compared with the standard transformer and vanilla looped transformer, the proposed AlgoFormer can achieve significantly higher expressiveness in algorithm representation when using the same number of parameters. In particular, inspired by the structure of human-designed learning algorithms, our transformer block consists of a pre-transformer that is responsible for task pre-processing, a looped transformer for iterative optimization algorithms, and a post-transformer for producing the desired results after post-processing. We provide theoretical evidence of the expressive power of the AlgoFormer in solving some challenging problems, mirroring human-designed algorithms. Furthermore, some theoretical and empirical results are presented to show that the designed transformer has the potential to be smarter than human-designed algorithms. Experimental results demonstrate the empirical superiority of the proposed transformer in that it outperforms the standard transformer and vanilla looped transformer in some challenging tasks.

Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive manual annotation, limiting their scale, or risk measuring memorization rather than genuine reasoning. To address this, we introduce an automated pipeline named A2RBench, encompassing generation, expansion, evaluation, and analysis. Specifically, in the generation stage, LLMs create diverse tasks demanding genuine reasoning; in the expansion stage, LLMs reuse validated rules and expand new input spaces to generate task variations, achieving scaling. However, such a process may cause hallucinations. To eliminate it, we further establish a theoretical framework and prove that programmatic verification--testing whether the inverse operation perfectly reverses the forward operation (cycle consistency)--guarantees a unique solution. Through extensive evaluations on mainstream LLMs, we find: (1) Current LLMs exhibit fundamental deficiencies in abstract reasoning, with top models significantly underperforming humans on a representative subset (39.8% vs. 68.5%). (2) Current LLMs fall far short of 2D and 1D in the complexity of generated 3D tasks, revealing their lack of understanding of high-dimensional tasks. (3) Counterintuitively, inputs with higher information complexity can simplify the reasoning process.

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC derives from the lambda-calculus by taking the standard operational perspective of a call-by-name stack machine as primary, and introducing two natural generalizations. One, "locations", introduces multiple stacks, which each may represent an effect and so enable effect operators to be encoded into the abstraction and application constructs of the calculus. The second, "sequencing", is known from kappa-calculus and concatenative programming languages, and introduces the imperative notions of "skip" and "sequence". This enables the encoding of reduction strategies, including call-by-value lambda-calculus and monadic constructs. The encoding of effects into generalized abstraction and application means that standard results from the lambda-calculus may carry over to effects. The main result is confluence, which is possible because encoded effects reduce algebraically rather than operationally. Reduction generates the familiar algebraic laws for state, and unlike in the monadic setting, reader/writer effects combine seamlessly. A system of simple types confers termination of the machine.

The agent--tool interaction loop is a critical attack surface for modern Large Language Model (LLM) agents. Existing denial-of-service (DoS) attacks typically function at the user-prompt or retrieval-augmented generation (RAG) context layer and are inherently single-turn in nature. This limitation restricts cost amplification and diminishes stealth in goal-oriented workflows. To address these issues, we proposed a stealthy, multi-turn economic DoS attack at the tool layer under the Model Context Protocol (MCP). By simply editing text-visible fields and implementing a template-driven return policy, our malicious server preserves function signatures and the terminal benign payload while steering agents into prolonged, verbose tool-calling chains. We optimize these text-only edits with Monte Carlo Tree Search (MCTS) to maximize cost under a task-success constraint. Across six LLMs on ToolBench and BFCL benchmarks, our attack yields trajectories over 60K tokens, increases per-query cost by up to 658 times, raises energy by 100 to 560 times, and pushes GPU key-value (KV) cache occupancy to 35--74%. Standard prompt filters and output trajectory monitors seldom detect these attacks, highlighting the need for defenses that safeguard agentic processes rather than focusing solely on final outcomes. We will release the code soon.

Large language models have shown remarkable reasoning abilities and scaling laws suggest that large parameter count, especially along the depth axis, is the primary driver. In this work, we make a stronger claim -- many reasoning problems require a large depth but not necessarily many parameters. This unlocks a novel application of looped models for reasoning. Firstly, we show that for many synthetic reasoning problems like addition, p-hop induction, and math problems, a k-layer transformer looped L times nearly matches the performance of a kL-layer non-looped model, and is significantly better than a k-layer model. This is further corroborated by theoretical results showing that many such reasoning problems can be solved via iterative algorithms, and thus, can be solved effectively using looped models with nearly optimal depth. Perhaps surprisingly, these benefits also translate to practical settings of language modeling -- on many downstream reasoning tasks, a language model with k-layers looped L times can be competitive to, if not better than, a kL-layer language model. In fact, our empirical analysis reveals an intriguing phenomenon: looped and non-looped models exhibit scaling behavior that depends on their effective depth, akin to the inference-time scaling of chain-of-thought (CoT) reasoning. We further elucidate the connection to CoT reasoning by proving that looped models implicitly generate latent thoughts and can simulate T steps of CoT with T loops. Inspired by these findings, we also present an interesting dichotomy between reasoning and memorization, and design a looping-based regularization that is effective on both fronts.

We introduce {rm C{small LEVER}}, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, {rm C{small LEVER}} avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use {rm C{small LEVER}} to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

The goal of decompilation is to convert compiled low-level code (e.g., assembly code) back into high-level programming languages, enabling analysis in scenarios where source code is unavailable. This task supports various reverse engineering applications, such as vulnerability identification, malware analysis, and legacy software migration. The end-to-end decompile method based on large langauge models (LLMs) reduces reliance on additional tools and minimizes manual intervention due to its inherent properties. However, previous end-to-end methods often lose critical information necessary for reconstructing control flow structures and variables when processing binary files, making it challenging to accurately recover the program's logic. To address these issues, we propose the ReF Decompile method, which incorporates the following innovations: (1) The Relabelling strategy replaces jump target addresses with labels, preserving control flow clarity. (2) The Function Call strategy infers variable types and retrieves missing variable information from binary files. Experimental results on the Humaneval-Decompile Benchmark demonstrate that ReF Decompile surpasses comparable baselines and achieves state-of-the-art (SOTA) performance of 61.43%.

Continuous-time neural processes are performant sequential decision-makers that are built by differential equations (DE). However, their expressive power when they are deployed on computers is bottlenecked by numerical DE solvers. This limitation has significantly slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show it is possible to closely approximate the interaction between neurons and synapses -- the building blocks of natural and artificial neural networks -- constructed by liquid time-constant networks (LTCs) efficiently in closed-form. To this end, we compute a tightly-bounded approximation of the solution of an integral appearing in LTCs' dynamics, that has had no known closed-form solution so far. This closed-form solution substantially impacts the design of continuous-time and continuous-depth neural models; for instance, since time appears explicitly in closed-form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared to differential equation-based counterparts. More importantly, in contrast to ODE-based continuous networks, closed-form networks can scale remarkably well compared to other deep learning instances. Lastly, as these models are derived from liquid networks, they show remarkable performance in time series modeling, compared to advanced recurrent models.

Agentic systems increasingly rely on reusable procedural capabilities, a.k.a., agentic skills, to execute long-horizon workflows reliably. These capabilities are callable modules that package procedural knowledge with explicit applicability conditions, execution policies, termination criteria, and reusable interfaces. Unlike one-off plans or atomic tool calls, skills operate (and often do well) across tasks. This paper maps the skill layer across the full lifecycle (discovery, practice, distillation, storage, composition, evaluation, and update) and introduces two complementary taxonomies. The first is a system-level set of seven design patterns capturing how skills are packaged and executed in practice, from metadata-driven progressive disclosure and executable code skills to self-evolving libraries and marketplace distribution. The second is an orthogonal representation times scope taxonomy describing what skills are (natural language, code, policy, hybrid) and what environments they operate over (web, OS, software engineering, robotics). We analyze the security and governance implications of skill-based agents, covering supply-chain risks, prompt injection via skill payloads, and trust-tiered execution, grounded by a case study of the ClawHavoc campaign in which nearly 1{,}200 malicious skills infiltrated a major agent marketplace, exfiltrating API keys, cryptocurrency wallets, and browser credentials at scale. We further survey deterministic evaluation approaches, anchored by recent benchmark evidence that curated skills can substantially improve agent success rates while self-generated skills may degrade them. We conclude with open challenges toward robust, verifiable, and certifiable skills for real-world autonomous agents.

Training modern neural networks is increasingly fragile, with rare but severe destabilizing updates often causing irreversible divergence or silent performance degradation. Existing optimization methods primarily rely on preventive mechanisms embedded within the optimizer, offering limited ability to detect and recover from instability once it occurs. We introduce a supervisory runtime stability framework that treats optimization as a controlled stochastic process. By isolating an innovation signal derived from secondary measurements, such as validation probes, the framework enables automatic detection and recovery from destabilizing updates without modifying the underlying optimizer. We provide theoretical runtime safety guarantees that formalize bounded degradation and recovery. Our implementation incurs minimal overhead and is compatible with memory-constrained training settings.

The popularity and widespread use of pruning and quantization is driven by the severe resource constraints of deploying deep neural networks to environments with strict latency, memory and energy requirements. These techniques achieve high levels of compression with negligible impact on top-line metrics (top-1 and top-5 accuracy). However, overall accuracy hides disproportionately high errors on a small subset of examples; we call this subset Compression Identified Exemplars (CIE). We further establish that for CIE examples, compression amplifies existing algorithmic bias. Pruning disproportionately impacts performance on underrepresented features, which often coincides with considerations of fairness. Given that CIE is a relatively small subset but a great contributor of error in the model, we propose its use as a human-in-the-loop auditing tool to surface a tractable subset of the dataset for further inspection or annotation by a domain expert. We provide qualitative and quantitative support that CIE surfaces the most challenging examples in the data distribution for human-in-the-loop auditing.

The advancement of machine learning for compiler optimization, particularly within the polyhedral model, is constrained by the scarcity of large-scale, public performance datasets. This data bottleneck forces researchers to undertake costly data generation campaigns, slowing down innovation and hindering reproducible research learned code optimization. To address this gap, we introduce LOOPerSet, a new public dataset containing 28 million labeled data points derived from 220,000 unique, synthetically generated polyhedral programs. Each data point maps a program and a complex sequence of semantics-preserving transformations (such as fusion, skewing, tiling, and parallelism)to a ground truth performance measurement (execution time). The scale and diversity of LOOPerSet make it a valuable resource for training and evaluating learned cost models, benchmarking new model architectures, and exploring the frontiers of automated polyhedral scheduling. The dataset is released under a permissive license to foster reproducible research and lower the barrier to entry for data-driven compiler optimization.

We present Turn, a compiled, actor-based programming language -- statically typed for schema inference, dynamically typed at the value level -- for agentic software: programs that reason and act autonomously by delegating inference to large language models (LLMs). Existing approaches augment general-purpose languages with frameworks, encoding critical invariants (bounded context, typed inference output, credential isolation, durable state) as application-level conventions rather than language guarantees. Turn introduces five language-level constructs that address this gap. Cognitive Type Safety makes LLM inference a typed primitive: the compiler generates a JSON Schema from a struct definition and the VM validates model output before binding. The confidence operator enables deterministic control flow gated on model certainty. Turn's actor-based process model, derived from Erlang, gives each agent an isolated context window, persistent memory, and mailbox. A capability-based identity system returns opaque, unforgeable handles from the VM host, ensuring raw credentials never enter agent memory. Finally, compile-time schema absorption (use schema::<protocol>) synthesizes typed API bindings from external specifications at compile time; the openapi adapter is shipped with graphql, fhir, and mcp in active development. We describe the language design, type rules, schema semantics, and a Rust-based bytecode VM, and evaluate Turn against representative agentic workloads. Turn is open source at https://github.com/ekizito96/Turn.

Critiques are important for enhancing the performance of Large Language Models (LLMs), enabling both self-improvement and constructive feedback for others by identifying flaws and suggesting improvements. However, evaluating the critique capabilities of LLMs presents a significant challenge due to the open-ended nature of the task. In this work, we introduce a new benchmark designed to assess the critique capabilities of LLMs. Unlike existing benchmarks, which typically function in an open-loop fashion, our approach employs a closed-loop methodology that evaluates the quality of corrections generated from critiques. Moreover, the benchmark incorporates features such as self-critique, cross-critique, and iterative critique, which are crucial for distinguishing the abilities of advanced reasoning models from more classical ones. We implement this benchmark using eight challenging reasoning tasks. We have several interesting findings. First, despite demonstrating comparable performance in direct chain-of-thought generation, classical LLMs significantly lag behind the advanced reasoning-based model o1-mini across all critique scenarios. Second, in self-critique and iterative critique settings, classical LLMs may even underperform relative to their baseline capabilities. We hope that this benchmark will serve as a valuable resource to guide future advancements. The code and data are available at https://github.com/tangzhy/RealCritic.

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of T inputs and produces, after receiving each input, an accurate output on the obtained inputs. In contrast, a batch algorithm receives the data as one batch and produces a single output. We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are widely studied and used in the batch model, we show that the worst case error of every continual release algorithm is tilde Omega(T^{1/3}) times larger than that of the best batch algorithm. Previous work shows only a polylogarithimic (in T) gap between the worst case error achievable in these two models; further, for many problems, including the summation of binary attributes, the polylogarithmic gap is tight (Dwork et al., 2010; Chan et al., 2010). Our results show that problems closely related to summation -- specifically, those that require selecting the largest of a set of sums -- are fundamentally harder in the continual release model than in the batch model. Our lower bounds assume only that privacy holds for streams fixed in advance (the "nonadaptive" setting). However, we provide matching upper bounds that hold in a model where privacy is required even for adaptively selected streams. This model may be of independent interest.

We present CRUXEval (Code Reasoning, Understanding, and eXecution Evaluation), a benchmark consisting of 800 Python functions (3-13 lines). Each function comes with an input-output pair, leading to two natural tasks: input prediction and output prediction. First, we propose a generic recipe for generating our execution benchmark which can be used to create future variation of the benchmark. Second, we evaluate twenty code models on our benchmark and discover that many recent high-scoring models on HumanEval do not show the same improvements on our benchmark. Third, we show that simple CoT and fine-tuning schemes can improve performance on our benchmark but remain far from solving it. The best setup, GPT-4 with chain of thought (CoT), achieves a pass@1 of 75% and 81% on input and output prediction, respectively. In contrast, Code Llama 34B achieves a pass@1 of 50% and 46% on input and output prediction, highlighting the gap between open and closed source models. As no model is close to acing CRUXEval, we provide examples of consistent GPT-4 failures on simple programs as a lens into its code reasoning capabilities and areas for improvement.

This work introduces a general code generation framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent code language models with infilling capabilities can perform self-infilling: whereas infilling operations aim to fill in the middle based on a predefined prefix and suffix, self-infilling sequentially generates both such surrounding context and the infilled content. We utilize this feature to develop an infilling-augmented decoding process that facilitates non-monotonic generation. This approach allows for postponing the generation of uncertain code snippets until a definitive suffix is established, leading to improved control over the generation sequence. In addition, it facilitates a looping mechanism, which can iteratively update and synchronize each piece of generation in a cyclic manner. Extensive experiments are conducted to demonstrate that our proposed decoding process is effective in enhancing regularity and quality across several code generation benchmarks.

Intermediate Representations (IRs) play a critical role in compiler design and program analysis, yet their comprehension by Large Language Models (LLMs) remains underexplored. In this paper, we present an explorative empirical study evaluating the capabilities of six state-of-the-art LLMs: GPT-4, GPT-3, DeepSeek, Gemma 2, Llama 3, and Code Llama, in understanding IRs. Specifically, we assess model performance across four core tasks: control flow graph reconstruction, decompilation, code summarization, and execution reasoning. While LLMs exhibit competence in parsing IR syntax and identifying high-level structures, they consistently struggle with instruction-level reasoning, especially in control flow reasoning, loop handling, and dynamic execution. Common failure modes include misinterpreting branching instructions, omitting critical operations, and relying on heuristic reasoning rather than precise instruction-level logic. Our findings highlight the need for IR-specific enhancements in LLM design. We recommend fine-tuning on structured IR datasets and integrating control-flow-sensitive architectures to improve model effectiveness. All experimental data and source code are publicly available at

We address the problem of runtime trajectory anomaly detection, a critical capability for enabling trustworthy LLM agents. Current safety measures predominantly focus on static input/output filtering. However, we argue that ensuring LLM agents reliability requires auditing the intermediate execution process. In this work, we formulate the task of Trajectory Anomaly Detection. The goal is not merely detection, but precise error localization. This capability is essential for enabling efficient rollback-and-retry. To achieve this, we construct TrajBench, a dataset synthesized via a perturb-and-complete strategy to cover diverse procedural anomalies. Using this benchmark, we investigate the capability of models in process supervision. We observe that general-purpose LLMs, even with zero-shot prompting, struggle to identify and localize these anomalies. This reveals that generalized capabilities do not automatically translate to process reliability. To address this, we propose TrajAD, a specialized verifier trained with fine-grained process supervision. Our approach outperforms baselines, demonstrating that specialized supervision is essential for building trustworthy agents.

As large language models (LLMs) increasingly integrate native code interpreters, they enable powerful real-time execution capabilities, substantially expanding their utility. However, such integrations introduce potential system-level cybersecurity threats, fundamentally different from prompt-based vulnerabilities. To systematically evaluate these interpreter-specific risks, we propose CIRCLE (Code-Interpreter Resilience Check for LLM Exploits), a simple benchmark comprising 1,260 prompts targeting CPU, memory, and disk resource exhaustion. Each risk category includes explicitly malicious ("direct") and plausibly benign ("indirect") prompt variants. Our automated evaluation framework assesses not only whether LLMs refuse or generates risky code, but also executes the generated code within the interpreter environment to evaluate code correctness, simplifications made by the LLM to make the code safe, or execution timeouts. Evaluating 7 commercially available models from OpenAI and Google, we uncover significant and inconsistent vulnerabilities. For instance, evaluations show substantial disparities even within providers - OpenAI's o4-mini correctly refuses risky requests at 7.1%, notably higher rates compared to GPT-4.1 at 0.5%. Results particularly underscore that indirect, socially-engineered prompts substantially weaken model defenses. This highlights an urgent need for interpreter-specific cybersecurity benchmarks, dedicated mitigation tools (e.g., guardrails), and clear industry standards to guide safe and responsible deployment of LLM interpreter integrations. The benchmark dataset and evaluation code are publicly released to foster further research.

Template mining is one of the foundational tasks to support log analysis, which supports the diagnosis and troubleshooting of large scale Web applications. This paper develops a human-in-the-loop template mining framework to support interactive log analysis, which is highly desirable in real-world diagnosis or troubleshooting of Web applications but yet previous template mining algorithms fails to support it. We formulate three types of light-weight user feedbacks and based on them we design three atomic human-in-the-loop template mining algorithms. We derive mild conditions under which the outputs of our proposed algorithms are provably correct. We also derive upper bounds on the computational complexity and query complexity of each algorithm. We demonstrate the versatility of our proposed algorithms by combining them to improve the template mining accuracy of five representative algorithms over sixteen widely used benchmark datasets.

Recursive (looped) Transformers decouple computational depth from parameter depth by repeatedly applying shared layers, providing an explicit architectural primitive for iterative refinement and latent reasoning. However, early looped Transformers often underperform non-recursive baselines of equal compute. While recent literature has introduced more effective recursion mechanisms to mitigate this gap, existing architectures still operate at a fixed, full-token resolution, neglecting the potential efficiency of computing over compressed latent representations. In this paper, we propose SpiralFormer, a looped Transformer that executes recurrence under a multi-resolution recursion schedule. We provide probing evidence that multi-resolution recursion enables the model to learn hierarchical dependencies by inducing iteration-wise functional specialization across different scales. Empirically, SpiralFormer achieves better parameter and compute efficiency than both looped and non-looped baselines across model scales from 160M to 1.4B, establishing sequence resolution as a potential axis for scaling recursive architectures.

Pre-trained code language models have achieved promising performance in code generation and improved the programming efficiency of human developers. However, their self-refinement capability is typically overlooked by the existing evaluations of code LMs, which focus only on the accuracy of the one-time prediction. For the cases when code LMs fail to implement the correct program, developers actually find it hard to debug and fix the faulty prediction since it is not written by the developers themselves. Unfortunately, our study reveals that code LMs cannot efficiently self-refine their faulty generations as well. In this paper, we propose CYCLE framework, learning to self-refine the faulty generation according to the available feedback, such as the execution results reported by the test suites. We evaluate CYCLE on three popular code generation benchmarks, HumanEval, MBPP, and APPS. The results reveal that CYCLE successfully maintains, sometimes improves, the quality of one-time code generation, while significantly improving the self-refinement capability of code LMs. We implement four variants of CYCLE with varied numbers of parameters across 350M, 1B, 2B, and 3B, and the experiments show that CYCLE consistently boosts the code generation performance, by up to 63.5%, across benchmarks and varied model sizes. We also notice that CYCLE outperforms code LMs that have 3times more parameters in self-refinement.

We introduce self-invoking code generation, a new task designed to evaluate the progressive reasoning and problem-solving capabilities of LLMs. In this task, models are presented with a base problem and a related, more complex problem. They must solve the base problem and then utilize its solution to address the more complex one. This work features three key contributions. First, we propose a general recipe for generating more challenging versions of existing benchmarks, resulting in three new benchmarks: HumanEval Pro, MBPP Pro, and BigCodeBench-Lite Pro, specifically designed to assess LLMs on self-invoking code generation. Second, from the analysis of experimental results over twenty LLMs on our benchmarks, we have two important observations: (i) Most LLMs excel in traditional code generation benchmarks like HumanEval and MBPP, but their performance declines on self-invoking tasks. For example, o1-mini achieves 96.2% pass@1 on HumanEval but only 76.2% on HumanEval Pro. (ii) On self-invoking code generation task, the instruction-tuned models demonstrate only marginal improvements compared to the base models. Third, we disclose the types of failure modes that exist in our evaluation results. All these results underscore the need for further advancements in self-invoking code generation tasks and provide a new direction for future research on enhancing LLMs' code reasoning capabilities.

In recent years, the application of large language models (LLMs) to code-related tasks has gained significant attention. However, existing evaluation benchmarks often focus on limited scenarios, such as code generation or completion, which do not reflect the diverse challenges developers face in real-world contexts. To address this, we introduce ComplexCodeEval, a benchmark designed to assess LCMs in various development tasks, including code generation, completion, API recommendation, and test case generation. It includes 3,897 Java samples and 7,184 Python samples from high-star GitHub repositories, each annotated with function signatures, docstrings, and API references to simulate real development environments. Our experiments across ten LCMs reveal that context improves performance and that data leakage can lead to overestimation, highlighting the need for more accurate evaluations.

Reinforcement Learning with Verifiable Rewards(RLVR) has emerged as a powerful framework for enhancing the reasoning capabilities of large language models (LLMs). However, existing approaches such as Group Relative Policy Optimization (GRPO) and its variants, while effective on reasoning benchmarks, struggle with agentic tasks that require iterative decision-making. We introduce MURPHY, a multi-turn RLVR framework that incorporates execution feedback directly into training, extending GRPO to optimize over multi-turn trajectories where models iteratively refine solutions. MURPHY combines a feedback conditioned rollout tree with trajectory-level credit assignment, and uses pruning to reduce the cost of multi-turn optimization. Evaluations on code generation benchmarks with two model families show that MURPHY consistently improves multi-iteration performance, achieving up to an 8% absolute gain in pass@1 over compute-matched GRPO baselines, and outperforming the prior leading method that incorporates multi-turn execution feedback.

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed signals, such as random or inverted rewards. This raises a fundamental question: do such improvements reflect genuine reasoning, or are they merely artifacts of overfitting to benchmark-specific patterns? To answer this question, we adopt an evaluation-centric perspective and highlight two critical shortcomings in existing protocols. First, benchmark contamination arises because test problems are publicly available, thereby increasing the risk of data leakage. Second, evaluation fragility results from reliance on single-instance assessments, which are sensitive to stochastic outputs and fail to capture reasoning consistency. These limitations suggest the need for a new evaluation paradigm that can probe reasoning ability beyond memorization and one-off success. As response, we propose VAR-MATH, a symbolic evaluation framework that converts fixed numerical problems into parameterized templates and requires models to solve multiple instantiations of each. This design enforces consistency across structurally equivalent variants, mitigates contamination, and enhances robustness through bootstrapped metrics. We apply VAR-MATH to transform three popular benchmarks, AMC23, AIME24, and AIME25, into their symbolic counterparts, VAR-AMC23, VAR-AIME24, and VAR-AIME25. Experimental results show substantial performance drops for RL-trained models on these variabilized benchmarks, especially for smaller models, with average declines of 47.9\% on AMC23, 58.8\% on AIME24, and 72.9\% on AIME25. These findings indicate that some existing RL methods rely on superficial heuristics and fail to generalize beyond specific numerical forms.

Looped Language Models (LoopLMs) perform multi-step latent reasoning prior to token generation and outperform conventional LLMs on reasoning benchmarks at smaller parameter budgets. However, attempts to further improve LoopLM reasoning with reinforcement learning have failed - standard objectives such as Group Relative Policy Optimization (GRPO) only assign credit to the final latent state, creating a fundamental mismatch with the model's internal computation. To resolve this, we introduce RLTT (Reward Latent Thought Trajectories), a reinforcement learning framework which distributes reward across the full latent reasoning trajectory. RLTT provides dense, trajectory-level credit assignment without relying on external verifiers and can directly replace GRPO with negligible overhead. Across extensive experiments with Ouro-2.6B-Thinking under identical training and inference conditions, RLTT yields substantial improvements over GRPO on challenging mathematical reasoning benchmarks, improving accuracy by +14.4% on MATH-500, +16.6% on AIME24, and +10.0% on BeyondAIME. Despite being trained exclusively on mathematics, RLTT also transfers effectively to non-mathematical reasoning benchmarks, demonstrating the effectiveness of trajectory-level credit assignment for reinforcement learning in LoopLMs.

While enabling large language models to implement function calling (known as APIs) can greatly enhance the performance of LLMs, function calling is still a challenging task due to the complicated relations between different APIs, especially in a context-learning setting without fine-tuning. This paper proposes a simple yet controllable target-driven approach called Reverse Chain to empower LLMs with capabilities to use external APIs with only prompts. Given that most open-source LLMs have limited tool-use or tool-plan capabilities, LLMs in Reverse Chain are only employed to implement simple tasks, e.g., API selection and argument completion, and a generic rule is employed to implement a controllable multiple functions calling. In this generic rule, after selecting a final API to handle a given task via LLMs, we first ask LLMs to fill the required arguments from user query and context. Some missing arguments could be further completed by letting LLMs select another API based on API description before asking user. This process continues until a given task is completed. Extensive numerical experiments indicate an impressive capability of Reverse Chain on implementing multiple function calling. Interestingly enough, the experiments also reveal that tool-use capabilities of the existing LLMs, e.g., ChatGPT, can be greatly improved via Reverse Chain.

RL training of multi-turn LLM agents is inherently unstable, and reasoning quality directly determines task performance. Entropy is widely used to track reasoning stability. However, entropy only measures diversity within the same input, and cannot tell whether reasoning actually responds to different inputs. In RAGEN-2, we find that even with stable entropy, models can rely on fixed templates that look diverse but are input-agnostic. We call this template collapse, a failure mode invisible to entropy and all existing metrics. To diagnose this failure, we decompose reasoning quality into within-input diversity (Entropy) and cross-input distinguishability (Mutual Information, MI), and introduce a family of mutual information proxies for online diagnosis. Across diverse tasks, mutual information correlates with final performance much more strongly than entropy, making it a more reliable proxy for reasoning quality. We further explain template collapse with a signal-to-noise ratio (SNR) mechanism. Low reward variance weakens task gradients, letting regularization terms dominate and erase cross-input reasoning differences. To address this, we propose SNR-Aware Filtering to select high-signal prompts per iteration using reward variance as a lightweight proxy. Across planning, math reasoning, web navigation, and code execution, the method consistently improves both input dependence and task performance.

In this paper we present a novel solution that combines the capabilities of Large Language Models (LLMs) with Formal Verification strategies to verify and automatically repair software vulnerabilities. Initially, we employ Bounded Model Checking (BMC) to locate the software vulnerability and derive a counterexample. The counterexample provides evidence that the system behaves incorrectly or contains a vulnerability. The counterexample that has been detected, along with the source code, are provided to the LLM engine. Our approach involves establishing a specialized prompt language for conducting code debugging and generation to understand the vulnerability's root cause and repair the code. Finally, we use BMC to verify the corrected version of the code generated by the LLM. As a proof of concept, we create ESBMC-AI based on the Efficient SMT-based Context-Bounded Model Checker (ESBMC) and a pre-trained Transformer model, specifically gpt-3.5-turbo, to detect and fix errors in C programs. Our experimentation involved generating a dataset comprising 1000 C code samples, each consisting of 20 to 50 lines of code. Notably, our proposed method achieved an impressive success rate of up to 80% in repairing vulnerable code encompassing buffer overflow and pointer dereference failures. We assert that this automated approach can effectively incorporate into the software development lifecycle's continuous integration and deployment (CI/CD) process.

Reliable evaluation is essential for developing and deploying large language models, yet in practice it often requires substantial manual effort: practitioners must identify appropriate benchmarks, reproduce heterogeneous evaluation codebases, configure dataset schema mappings, and interpret aggregated metrics. To address these challenges, we present One-Eval, an agentic evaluation system that converts natural-language evaluation requests into executable, traceable, and customizable evaluation workflows. One-Eval integrates (i) NL2Bench for intent structuring and personalized benchmark planning, (ii) BenchResolve for benchmark resolution, automatic dataset acquisition, and schema normalization to ensure executability, and (iii) Metrics \& Reporting for task-aware metric selection and decision-oriented reporting beyond scalar scores. The system further incorporates human-in-the-loop checkpoints for review, editing, and rollback, while preserving sample evidence trails for debugging and auditability. Experiments show that One-Eval can execute end-to-end evaluations from diverse natural-language requests with minimal user effort, supporting more efficient and reproducible evaluation in industrial settings. Our framework is publicly available at https://github.com/OpenDCAI/One-Eval.

Multi-agent systems (MAS) have emerged as a promising paradigm for solving complex tasks. Recent work has explored self-evolving MAS that automatically optimize agent capabilities or communication topologies. However, existing methods either learn a topology that remains fixed at inference time or adapt only the topology or capability during inference. We empirically and theoretically show that effective test-time evolution requires jointly adapting both axes, but on different time scales: capabilities should update rapidly to handle emerging subtasks, while the topology should evolve more slowly to preserve coordination stability. We then introduce TacoMAS, a test-time co-evolution framework for dynamic MAS. TacoMAS formulates MAS inference as a task of online graph adaptation, where nodes represent agents with role-specific capabilities and edges define their communication topology. During inference, a fast capability loop updates agent expertise using trajectory-level feedback, while a slow meta-LLM-driven topology loop performs agents' birth-death operations on MAS, including edge edit, agent addition, and agent removal. We further show that this fast-slow design drives MAS evolution toward a task-conditioned stable equilibrium. Experiments on four benchmarks demonstrate that TacoMAS outperforms nearly 20 multi-agent baselines, achieving an average improvement of 13.3% over the strongest baseline. The codes are released at https://github.com/chenxu2-gif/TacoMAS-MultiAgent.

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot vectors and cannot be propagated across steps, forcing subsequent steps to operate with limited information. To mitigate this problem, we introduce Loopholing, a novel and simple mechanism that preserves this information via a deterministic latent pathway, leading to Loopholing Discrete Diffusion Models (LDDMs). Trained efficiently with a self-conditioning strategy, LDDMs achieve substantial gains-reducing generative perplexity by up to 61% over prior baselines, closing (and in some cases surpassing) the gap with autoregressive models, and producing more coherent text. Applied to reasoning tasks, LDDMs also improve performance on arithmetic benchmarks such as Countdown and Game of 24. These results also indicate that loopholing mitigates idle steps and oscillations, providing a scalable path toward high-quality non-autoregressive text generation.

Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes. In many settings, surgery exhibits practical space overheads, while its time overhead remains a bottleneck at O(d) syndrome rounds per operation. In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead (O(1)) and near-constant space overhead (O(1)). The reduced time overhead is a result of amortization, as we show, following the formulation by Cowtan et al. (arXiv:2510.14895), that performing d surgery operations in O(d) time is fault tolerant. Our gadgets combine the strengths of different approaches to fault-tolerant logical operations: they partially retain the flexibility of surgery while achieving overheads comparable to transversal gates. Consequently, they are well-suited for near-term experimental realization and demonstrate new possibilities in the design of gadgets for fast logical computation.

LLMs demonstrate strong performance on code benchmarks, yet round-trip code execution reveals limitations in their ability to maintain consistent reasoning across forward and backward execution. We present RoundTripCodeEval (RTCE), a comprehensive benchmark consisting of four distinct code execution reasoning tasks designed to rigorously test round-trip consistency. RTCE provides an execution-free, exact-match evaluation of bijection fidelity, assessing whether models preserve a consistent one-to-one mapping between encoding and decoding operations across various algorithms and directions. We systematically evaluate state-of-the-art Code-LLMs using zero-shot prompting, supervised fine-tuning on execution traces, and self-reflection mechanisms. Each yields modest improvements, but none closes the gap, indicating that current LLMs struggle with true round-trip consistency, which demonstrates that they lack the internal coherence required for trustworthy code reasoning. RTCE surfaces several new and previously unmeasured insights that are not captured by existing I/O-prediction, execution-reasoning, or round-trip natural-language benchmarks. We will release the code and the dataset upon acceptance.

We present an end-to-end reconfigurable algorithmic pipeline for solving a famous problem in knot theory using a noisy digital quantum computer, namely computing the value of the Jones polynomial at the fifth root of unity within additive error for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we implement and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The practical tools provided in this work allow for precise resource estimation to identify near-term quantum advantage for a meaningful quantum-native problem in knot theory.

State-of-the-art large language models (LLMs) are now claiming remarkable supported context lengths of 256k or even more. In contrast, the average context lengths of mainstream benchmarks are insufficient (5k-21k), and they suffer from potential knowledge leakage and inaccurate metrics, resulting in biased evaluation. This paper introduces LV-Eval, a challenging long-context benchmark with five length levels (16k, 32k, 64k, 128k, and 256k) reaching up to 256k words. LV-Eval features two main tasks, single-hop QA and multi-hop QA, comprising 11 bilingual datasets. The design of LV-Eval has incorporated three key techniques, namely confusing facts insertion, keyword and phrase replacement, and keyword-recall-based metric design. The advantages of LV-Eval include controllable evaluation across different context lengths, challenging test instances with confusing facts, mitigated knowledge leakage, and more objective evaluations. We evaluate 10 LLMs on LV-Eval and conduct ablation studies on the techniques used in LV-Eval construction. The results reveal that: (i) Commercial LLMs generally outperform open-source LLMs when evaluated within length levels shorter than their claimed context length. However, their overall performance is surpassed by open-source LLMs with longer context lengths. (ii) Extremely long-context LLMs, such as Yi-6B-200k, exhibit a relatively gentle degradation of performance, but their absolute performances may not necessarily be higher than those of LLMs with shorter context lengths. (iii) LLMs' performances can significantly degrade in the presence of confusing information, especially in the pressure test of "needle in a haystack". (iv) Issues related to knowledge leakage and inaccurate metrics introduce bias in evaluation, and these concerns are alleviated in LV-Eval. All datasets and evaluation codes are released at: https://github.com/infinigence/LVEval.

LLM-based coding agents can localize bugs, generate patches, and run tests with diminishing human oversight, yet the scaffolding code that surrounds the language model (the control loop, tool definitions, state management, and context strategy) remains poorly understood. Existing surveys classify agents by abstract capabilities (tool use, planning, reflection) that cannot distinguish between architecturally distinct systems, and trajectory studies observe what agents do without examining the scaffold code that determines why. This paper presents a source-code-level architectural taxonomy derived from analysis of 13 open-source coding agent scaffolds at pinned commit hashes. Each agent is characterized across 12 dimensions organized into three layers: control architecture, tool and environment interface, and resource management. The analysis reveals that scaffold architectures resist discrete classification: control strategies range from fixed pipelines to Monte Carlo Tree Search, tool counts range from 0 to 37, and context compaction spans seven distinct strategies. Five loop primitives (ReAct, generate-test-repair, plan-execute, multi-attempt retry, tree search) function as composable building blocks that agents layer in different combinations; 11 of 13 agents compose multiple primitives rather than relying on a single control structure. Dimensions converge where external constraints dominate (tool capability categories, edit formats, execution isolation) and diverge where open design questions remain (context compaction, state management, multi-model routing). All taxonomic claims are grounded in file paths and line numbers, providing a reusable reference for researchers studying agent behavior and practitioners designing new scaffolds.

Formal specification is essential for rigorous program verification, yet writing correct specifications remains costly and difficult to automate. Although large language models (LLMs) and agents have shown promising progress, their true capabilities and failure modes remain unclear. We present the first systematic and contamination-aware study of LLM- and agent-based formal specification generation for C programs. We introduce LiveFMBench, a continuously evolving benchmark of 630 ACSL (ANSI/ISO C Specification Language)-annotated C programs, including 360 newly collected cases designed to mitigate data leakage. Using this benchmark, we evaluate direct prompting with different sampling sizes, reasoning-enabled (thinking mode) inference, the agentic pipeline, and perform a fine-grained failure analysis. Experimental results reveal that naive evaluation substantially overestimates performance because models under direct prompting may exhibit unfaithful behaviors, such as deceiving automated provers or ignoring code-context constraints; after excluding such cases, the true specification generation accuracy drops by approximately 20\%. We further find that both increased sampling and thinking mode significantly improve success rates, with smaller models benefiting more from thinking mode. Agentic pipelines are particularly effective under low sampling budgets and on harder datasets. Failure analysis further shows that incorrect loop invariants are the dominant error type, while agentic pipelines notably reduce assertion errors. These results expose fundamental limitations in current LLM-based approaches and suggest they remain far from replacing human-authored formal specifications. We release LiveFMBench at https://huggingface.co/datasets/fm-universe/Live-FM-Bench and all evaluation artifacts to support future research.

Neural networks are increasingly deployed in safety- and mission-critical pipelines, yet many verification and analysis results are produced outside the programming environment that defines and runs the model. This separation creates a semantic gap between the executed network and the analyzed artifact, so guarantees can hinge on implicit conventions such as operator semantics, tensor layouts, preprocessing, and floating-point corner cases. We introduce TorchLean, a framework in the Lean 4 theorem prover that treats learned models as first-class mathematical objects with a single, precise semantics shared by execution and verification. TorchLean unifies (1) a PyTorch-style verified API with eager and compiled modes that lower to a shared op-tagged SSA/DAG computation-graph IR, (2) explicit Float32 semantics via an executable IEEE-754 binary32 kernel and proof-relevant rounding models, and (3) verification via IBP and CROWN/LiRPA-style bound propagation with certificate checking. We validate TorchLean end-to-end on certified robustness, physics-informed residual bounds for PINNs, and Lyapunov-style neural controller verification, alongside mechanized theoretical results including a universal approximation theorem. These results demonstrate a semantics-first infrastructure for fully formal, end-to-end verification of learning-enabled systems.

Equipping LLM agents with reusable skills derived from past experience has become a popular and successful approach for tackling complex and long-horizon tasks. However, such lessons are often encoded as textual guidance that remains largely advisory, lacking explicit mechanisms for when and how to intervene in the agent loop. To bridge the gap, we introduce HASP(Harnessing LLM Agents with Skill Programs), a new framework that upgrades skills into executable Program Functions (PFs). Rather than offering passive advice, PFs act as executable guardrails that activate on failure-prone states and modify the next action or inject corrective context. HASP is highly modular: it can be applied at inference time for direct agent-loop intervention, during post-training to provide structured supervision, or for self-improvement by evolving validated, teacher-reviewed PFs. Empirically, HASP drives substantial gains compared to both training-free and training-based methods on web-search, math reasoning, and coding tasks. For example, on web-search reasoning, inference-time PFs alone improve the average performance by 25% compared to (multi-loop) ReAct Agent, while post-training and controlled evolution achieve a 30.4% gain over Search-R1. To provide deeper insights into HASP, our mechanism analysis reveals how PFs trigger and intervene, how skills are internalized, and the requirement for stable skill library evolution.

Information systems generate a large volume of event log data during business operations, much of which consists of low-value and redundant information. When performance predictions are made directly from these logs, the accuracy of the predictions can be compromised. Researchers have explored methods to simplify and compress these data while preserving their valuable components. Most existing approaches focus on reducing the dimensionality of the data by eliminating redundant and irrelevant features. However, there has been limited investigation into the efficiency of execution both before and after event log simplification. In this paper, we present a prediction point selection algorithm designed to avoid the simplification of all points that function similarly. We select sequences or self-loop structures to form a simplifiable segment, and we optimize the deviation between the actual simplifiable value and the original data prediction value to prevent over-simplification. Experiments indicate that the simplified event log retains its predictive performance and, in some cases, enhances its predictive accuracy compared to the original event log.

LLM-powered coding agents, which operate in iterative loops (turns) to solve software engineering tasks, are becoming increasingly powerful. However, their practical deployment is hindered by significant and unpredictable costs. This challenge arises from a combination of factors: quadratically growing token counts with each turn, the high price of models, the large number of turns required for real-world tasks, and the tendency of agents to take inefficient or unnecessary actions. While existing research focuses on optimizing individual turns, the strategic control of the total number of turns remains an underexplored area for managing agent performance and cost. To address this gap, we conduct a comprehensive empirical study on SWE-bench using three state-of-the-art models and evaluate the impact of three distinct turn-control strategies: an unrestricted baseline, a fixed-turn limit with reminders, and a novel dynamic-turn strategy that grants extensions on-demand. Our findings first reveal a fundamental trade-off in the unrestricted setting, where no single model excels across performance, cost, and turn efficiency. We then show that a fixed-turn limit, specifically at the 75th percentile of the baseline, serves as a "sweet spot", substantially reducing costs (by 24%-68%) with minimal impact on solve rates. Most significantly, the dynamic-turn strategy consistently outperforms fixed-limit approaches, achieving comparable or better solve rates while further reducing costs by an additional 12%-24% by intelligently allocating resources only to tasks that need them. This work provides the first systematic analysis of turn-control strategies, offering simple yet effective guidelines for developers to balance cost and efficacy. We demonstrate that dynamic resource allocation is a superior, easy-to-implement approach for deploying powerful yet economically viable coding agents.

We present egglog, a fixpoint reasoning system that unifies Datalog and equality saturation (EqSat). Like Datalog, it supports efficient incremental execution, cooperating analyses, and lattice-based reasoning. Like EqSat, it supports term rewriting, efficient congruence closure, and extraction of optimized terms. We identify two recent applications--a unification-based pointer analysis in Datalog and an EqSat-based floating-point term rewriter--that have been hampered by features missing from Datalog but found in EqSat or vice-versa. We evaluate egglog by reimplementing those projects in egglog. The resulting systems in egglog are faster, simpler, and fix bugs found in the original systems.

Retrieval-Augmented Generation (RAG) systems are increasingly evolving into agentic architectures where large language models autonomously coordinate multi-step reasoning, dynamic memory management, and iterative retrieval strategies. Despite rapid industrial adoption, current research lacks a systematic understanding of Agentic RAG as a sequential decision-making system, leading to highly fragmented architectures, inconsistent evaluation methodologies, and unresolved reliability risks. This Systematization of Knowledge (SoK) paper provides the first unified framework for understanding these autonomous systems. We formalize agentic retrieval-generation loops as finite-horizon partially observable Markov decision processes, explicitly modeling their control policies and state transitions. Building upon this formalization, we develop a comprehensive taxonomy and modular architectural decomposition that categorizes systems by their planning mechanisms, retrieval orchestration, memory paradigms, and tool-invocation behaviors. We further analyze the critical limitations of traditional static evaluation practices and identify severe systemic risks inherent to autonomous loops, including compounding hallucination propagation, memory poisoning, retrieval misalignment, and cascading tool-execution vulnerabilities. Finally, we outline key doctoral-scale research directions spanning stable adaptive retrieval, cost-aware orchestration, formal trajectory evaluation, and oversight mechanisms, providing a definitive roadmap for building reliable, controllable, and scalable agentic retrieval systems.

Large language models (LLMs) have achieved remarkable progress in code understanding tasks. However, they demonstrate limited performance in vulnerability detection and struggle to distinguish vulnerable code from patched code. We argue that LLMs lack understanding of security specifications -- the expectations about how code should behave to remain safe. When code behavior differs from these expectations, it becomes a potential vulnerability. However, such knowledge is rarely explicit in training data, leaving models unable to reason about security flaws. We propose VulInstruct, a specification-guided approach that systematically extracts security specifications from historical vulnerabilities to detect new ones. VulInstruct constructs a specification knowledge base from two perspectives: (i) General specifications from high-quality patches across projects, capturing fundamental safe behaviors; and (ii) Domain-specific specifications from repeated violations in particular repositories relevant to the target code. VulInstruct retrieves relevant past cases and specifications, enabling LLMs to reason about expected safe behaviors rather than relying on surface patterns. We evaluate VulInstruct under strict criteria requiring both correct predictions and valid reasoning. On PrimeVul, VulInstruct achieves 45.0% F1-score (32.7% improvement) and 37.7% recall (50.8% improvement) compared to baselines, while uniquely detecting 24.3% of vulnerabilities -- 2.4x more than any baseline. In pair-wise evaluation, VulInstruct achieves 32.3% relative improvement. VulInstruct also discovered a previously unknown high-severity vulnerability (CVE-2025-56538) in production code, demonstrating practical value for real-world vulnerability discovery. All code and supplementary materials are available at https://github.com/zhuhaopku/VulInstruct-temp.

Advanced compiler technology is crucial for enabling machine learning applications to run on novel hardware, but traditional compilers fail to deliver performance, popular auto-tuners have long search times and expert-optimized libraries introduce unsustainable costs. To address this, we developed LoopTune, a deep reinforcement learning compiler that optimizes tensor computations in deep learning models for the CPU. LoopTune optimizes tensor traversal order while using the ultra-fast lightweight code generator LoopNest to perform hardware-specific optimizations. With a novel graph-based representation and action space, LoopTune speeds up LoopNest by 3.2x, generating an order of magnitude faster code than TVM, 2.8x faster than MetaSchedule, and 1.08x faster than AutoTVM, consistently performing at the level of the hand-tuned library Numpy. Moreover, LoopTune tunes code in order of seconds.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present a learning framework based on neural networks that exploit rotational symmetries in the closure terms to learn accurate closure models directly from kinetic simulations. The data-driven closures demonstrate excellent a-priori predictions comparable to the state-of-the-art Bingham closure. We provide a systematic comparison between different neural network architectures and demonstrate that nonlocal effects can be safely ignored to model the closure terms. We develop an active learning strategy that enables accurate prediction of the closure terms across the entire parameter space using a single neural network without the need for retraining. We also propose a data-efficient training procedure based on time-stepping constraints and a differentiable pseudo-spectral solver, which enables the learning of stable closures suitable for a-posteriori inference. The coarse-grained simulations equipped with data-driven closure models faithfully reproduce the mean velocity statistics, scalar order parameters, and velocity power spectra observed in simulations of the kinetic theory. Our differentiable framework also facilitates the estimation of parameters in coarse-grained descriptions conditioned on data.

Interactive agent benchmarks face a tension between scalable construction and realistic workflow evaluation. Hand-authored tasks are expensive to extend and revise, while static prompt evaluation misses failures that only appear when agents operate over persistent state. Existing interactive benchmarks have advanced agent evaluation significantly, but most initialize tasks from clean state and do not systematically test how agents handle pre-existing partial, stale, or conflicting artifacts. We present ClawForge, a generator-backed benchmark framework for executable command-line workflows under state conflict. The framework compiles scenario templates, grounded slots, initialized state, reference trajectories, and validators into reproducible task specifications, and evaluates agents step by step over persistent workflow surfaces using normalized end state and observable side effects rather than exact trajectory matching. We instantiate this framework as the ClawForge-Bench (17 scenarios, 6 ability categories). Results across seven frontier models show that the best model reaches only 45.3% strict accuracy, wrong-state replacement remains below 17\% for all models, and the widest model separation (17% to 90%) is driven by whether agents inspect existing state before acting. Partial-credit and step-efficiency analyses further reveal that many failures are near-miss closures rather than early breakdowns, and that models exhibit qualitatively different failure styles under state conflict.

Automated code generation is gaining significant importance in intelligent computer programming and system deployment. However, current approaches often face challenges in computational efficiency and lack robust mechanisms for code parsing and error correction. In this work, we propose a novel framework, PyCapsule, with a simple yet effective two-agent pipeline and efficient self-debugging modules for Python code generation. PyCapsule features sophisticated prompt inference, iterative error handling, and case testing, ensuring high generation stability, safety, and correctness. Empirically, PyCapsule achieves up to 5.7% improvement of success rate on HumanEval, 10.3% on HumanEval-ET, and 24.4% on BigCodeBench compared to the state-of-art methods. We also observe a decrease in normalized success rate given more self-debugging attempts, potentially affected by limited and noisy error feedback in retention. PyCapsule demonstrates broader impacts on advancing lightweight and efficient code generation for artificial intelligence systems.

Large language models store all learned knowledge in a single, fixed weight vector. Teaching a model new capabilities requires modifying those same weights, inevitably degrading previously acquired knowledge. This fundamental limitation, known as catastrophic forgetting, has resisted principled solutions for decades. Existing approaches treat weights as immutable artifacts that must be protected through techniques like regularization heuristics, replay buffers, or isolated adapter modules. The problem is none of these provide a structural guarantee against forgetting. In this work, we propose Non-Interfering Weight Fields (NIWF), a framework that replaces the fixed weight paradigm with a learned function that generates weight configurations on demand from a continuous capability coordinate space. After training on a task, we commit the occupied coordinate region by snapshotting the fields outputs on anchor points to enforce a functional lock during all future training. We validate NIWF on sequential instructionfollowing and code generation tasks using Mistral-7B, demonstrating zero forgetting on committed tasks with competitive perplexity on new tasks. The framework introduces the notion of software-like versioning for neural network intelligence, where capabilities can be committed, extended, composed, and rolled back without retraining.

Software vulnerabilities are increasing at an alarming rate. However, manual patching is both time-consuming and resource-intensive, while existing automated vulnerability repair (AVR) techniques remain limited in effectiveness. Recent advances in large language models (LLMs) have opened a new paradigm for AVR, demonstrating remarkable progress. To examine the capability of LLMs in AVR, several vulnerability benchmarks have been proposed recently. However, they still suffer from key limitations of outdated vulnerabilities, limited language coverage, unreliable patch validation, and insufficient reproducibility. To overcome these challenges, we introduce PATCHEVAL, a multilingual benchmark for Go, JavaScript, and Python, languages for which existing benchmarks remain unexplored. PATCHEVAL curates a dataset of 1,000 vulnerabilities drawn from CVEs reported between 2015 and 2025, covering 65 distinct CWEs. A subset of 230 CVEs is further equipped with runtime sandbox environments, enabling patch verification through both security tests and functionality tests. To provide a systematic comparison of LLM-based vulnerability repair, we evaluate a series of state-of-the-art LLMs and agents, presenting an in-depth analysis that empirically yields key insights to guide future research in AVR.

Large Reasoning Models (LRMs) have significantly advanced beyond traditional Large Language Models (LLMs) with their exceptional logical reasoning capabilities, yet these improvements introduce heightened safety risks. When subjected to jailbreak attacks, their ability to generate more targeted and organized content can lead to greater harm. Although some studies claim that reasoning enables safer LRMs against existing LLM attacks, they overlook the inherent flaws within the reasoning process itself. To address this gap, we propose the first jailbreak attack targeting LRMs, exploiting their unique vulnerabilities stemming from the advanced reasoning capabilities. Specifically, we introduce a Chaos Machine, a novel component to transform attack prompts with diverse one-to-one mappings. The chaos mappings iteratively generated by the machine are embedded into the reasoning chain, which strengthens the variability and complexity and also promotes a more robust attack. Based on this, we construct the Mousetrap framework, which makes attacks projected into nonlinear-like low sample spaces with mismatched generalization enhanced. Also, due to the more competing objectives, LRMs gradually maintain the inertia of unpredictable iterative reasoning and fall into our trap. Success rates of the Mousetrap attacking o1-mini, Claude-Sonnet and Gemini-Thinking are as high as 96%, 86% and 98% respectively on our toxic dataset Trotter. On benchmarks such as AdvBench, StrongREJECT, and HarmBench, attacking Claude-Sonnet, well-known for its safety, Mousetrap can astonishingly achieve success rates of 87.5%, 86.58% and 93.13% respectively. Attention: This paper contains inappropriate, offensive and harmful content.

Large language models perform strongly on benchmarks in mathematical reasoning, coding and document analysis, suggesting a broad ability to follow instructions. However, it remains unclear whether such success reflects general logical competence, repeated application of learned procedures, or pattern matching that mimics rule execution. We investigate this question by introducing Stable Counting Capacity, an assay in which models count repeated symbols until failure. The assay removes knowledge dependencies, semantics and ambiguity from evaluation, avoids lexical and tokenization confounds, and provides a direct measure of procedural reliability beyond standard knowledge-based benchmarks. Here we show, across more than 100 model variants, that stable counting capacity remains far below advertised context limits. Model behavior is consistent neither with open-ended logic nor with stable application of a learned rule, but instead with use of a finite set of count-like internal states, analogous to counting on fingers. Once this resource is exhausted, the appearance of rule following disappears and exact execution collapses into guessing, even with additional test-time compute. These findings show that fluent performance in current language models does not guarantee general, reliable rule following.

Most programmers make mistakes when writing code. Some of these mistakes are small and require few edits to the original program -- a class of errors recently termed last mile mistakes. These errors break the flow for experienced developers and can stump novice programmers. Existing automated repair techniques targeting this class of errors are language-specific and do not easily carry over to new languages. Transferring symbolic approaches requires substantial engineering and neural approaches require data and retraining. We introduce RING, a multilingual repair engine powered by a large language model trained on code (LLMC) such as Codex. Such a multilingual engine enables a flipped model for programming assistance, one where the programmer writes code and the AI assistance suggests fixes, compared to traditional code suggestion technology. Taking inspiration from the way programmers manually fix bugs, we show that a prompt-based strategy that conceptualizes repair as localization, transformation, and candidate ranking, can successfully repair programs in multiple languages with minimal effort. We present the first results for such a multilingual repair engine by evaluating on 6 different languages and comparing performance to language-specific repair engines. We show that RING can outperform language-specific repair engines for three of these languages.

Code generation plays a crucial role in various tasks, such as code auto-completion and mathematical reasoning. Previous work has proposed numerous methods to enhance code generation performance, including integrating feedback from the compiler. Inspired by this, we present ReflectionCoder, a novel approach that effectively leverages reflection sequences constructed by integrating compiler feedback to improve one-off code generation performance. Furthermore, we propose reflection self-distillation and dynamically masked distillation to effectively utilize these reflection sequences. Extensive experiments on three benchmarks, i.e., HumanEval (+), MBPP (+), and MultiPl-E, demonstrate that models fine-tuned with our method achieve state-of-the-art performance. Notably, ReflectionCoder-DeepSeek-Coder-33B reaches pass@1 of 82.9 (76.8) on HumanEval (+) and 84.1 (72.0) on MBPP (+), on par with GPT-3.5-Turbo and Claude-3-opus, and surpasses early GPT-4. Beyond the code domain, we believe this approach can benefit other domains that focus on final results and require long reasoning paths. Code and data are available at https://github.com/SenseLLM/ReflectionCoder.

LLM architecture research generally aims to maximize model quality subject to fixed compute/latency budgets. However, many applications of interest such as edge and on-device deployment are further constrained by the model's memory footprint, thus motivating parameter-efficient architectures for language modeling. This paper describes a simple architecture that improves the parameter-efficiency of LLMs. Our architecture makes use of looped Transformers as a core primitive, which reuse Transformer layers across depth and are thus more parameter-efficient than ordinary (depth-matched) Transformers. We organize the looped Transformer into three blocks--begin, middle, and end blocks--where each block itself consists of multiple Transformer layers, and only the middle block is applied recurrently across depth. We augment the looped middle block with hyper-connections (Xie et al., 2026), which expand the residual stream into matrix-valued residual streams. Hyper-connections are applied only after each loop, and therefore add minimal new parameters and compute cost. Across various model scales, we find that our Hyper-Connected Looped Transformer (Hyperloop Transformer) is able to outperform depth-matched Transformer and mHC Transformer baselines despite using approximately 50% fewer parameters. The outperformance persists through post-training weight quantization, thus positioning Hyperloop Transformers as an attractive architecture for memory-efficient language modeling.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

Context: Bugs in code are inevitable and can lead to severe consequences, ranging from security vulnerabilities to operational failures. Debugging software remains challenging despite advances in testing and verification, often requiring extensive manual effort. Learning-based automated program repair (APR) has shown promise in reducing the time, effort, and cost of manually fixing bugs. However, existing techniques face several challenges, including language-dependent strategies, limited bug context utilization, and difficulties in handling bugs that span multiple locations in the code. Objective: This paper introduces MultiMend, a learning-based APR approach designed to improve repair performance on multiple programming languages with language-independent context augmentation and multi-hunk patch generation. Method: MultiMend fine-tunes a pre-trained encoder-decoder transformer model (CodeT5) to generate bug-fixing patches. It embeds source code lines and applies retrieval-augmented generation to augment the buggy context with relevant lines during patch generation. The approach systematically constructs patches for multi-hunk bugs to reduce the needed patch validations. We evaluate MultiMend on four benchmarks with four programming languages and compare it with state-of-the-art methods. Results: Experimental results show that MultiMend achieves competitive effectiveness and efficiency against compared tools. Across all benchmarks, MultiMend fixes 2,077 bugs, of which 1,455 are identical to the developer's patch, and 106 are for multi-hunk bugs. Both context augmentation and multi-hunk patch generation positively contribute to the results. Conclusion: MultiMend shows promising performance across benchmarks. The findings highlight its applicability to real-world software maintenance and its potential to reduce manual debugging efforts.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-by-name stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. The second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. The key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. These embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. The equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.

Large Language Models (LLMs) have shown remarkable aptitude in code generation but still struggle on challenging programming tasks. Self-repair -- in which the model debugs and fixes mistakes in its own code -- has recently become a popular way to boost performance in these settings. However, only very limited studies on how and when self-repair works effectively exist in the literature, and one might wonder to what extent a model is really capable of providing accurate feedback on why the code is wrong when that code was generated by the same model. In this paper, we analyze GPT-3.5 and GPT-4's ability to perform self-repair on APPS, a challenging dataset consisting of diverse coding challenges. To do so, we first establish a new evaluation strategy dubbed pass@t that measures the pass rate of the tasks against the total number of tokens sampled from the model, enabling a fair comparison to purely sampling-based approaches. With this evaluation strategy, we find that the effectiveness of self-repair is only seen in GPT-4. We also observe that self-repair is bottlenecked by the feedback stage; using GPT-4 to give feedback on the programs generated by GPT-3.5 and using expert human programmers to give feedback on the programs generated by GPT-4, we unlock significant performance gains.