Daily Papers

We present HelaBERT, a family of two BERT-based masked language models pre-trained from scratch on approximately 1 billion tokens of Sinhala text sourced from MADLAD-400, CulturaX, and a custom corpus comprising news articles, Sinhala Wikipedia, and web crawl data. HelaBERT-Small (~23.3M parameters, 6 layers) and HelaBERT-Large (~110M parameters, 12 layers) both use a SentencePiece Unigram tokenizer (vocabulary size 32,000) tailored to Sinhala's agglutinative morphology and complex script. We evaluate both models on four downstream Sinhala text classification tasks: news category classification, news source classification, sentiment analysis, and writing style classification, using 5 independent seed runs with stratified 80/20 train/test splits. We additionally propose a dual pooling classification head and evaluate it systematically across all four tasks, finding consistent improvements on sentiment analysis and a moderate gain on news category classification for HelaBERT-Small, while the standard [CLS]-linear head remains competitive on news source classification, a headline-level task with short average input length. We release both models to support further research in Sinhala NLP.

The two-stage fine-tuning (FT) method, linear probing (LP) then fine-tuning (LP-FT), outperforms linear probing and FT alone. This holds true for both in-distribution (ID) and out-of-distribution (OOD) data. One key reason for its success is the preservation of pre-trained features, achieved by obtaining a near-optimal linear head during LP. However, despite the widespread use of large language models, there has been limited exploration of more complex architectures such as Transformers. In this paper, we analyze the training dynamics of LP-FT for classification tasks on the basis of the neural tangent kernel (NTK) theory. Our analysis decomposes the NTK matrix into two components. This decomposition highlights the importance of the linear head norm alongside the prediction accuracy at the start of the FT stage. We also observe a significant increase in the linear head norm during LP, which stems from training with the cross-entropy (CE) loss. This increase in the linear head norm effectively reduces changes in learned features. Furthermore, we find that this increased norm can adversely affect model calibration, which can be corrected using temperature scaling. Additionally, we extend our analysis with the NTK to the low-rank adaptation (LoRA) method and validate its effectiveness. Our experiments using a Transformer-based model on multiple natural language processing datasets confirm our theoretical analysis. Our study demonstrates the effectiveness of LP-FT for fine-tuning language models. Code is available at https://github.com/tom4649/lp-ft_ntk.

Despite significant advancements in Large Vision Language Models (LVLMs), a gap remains, particularly regarding their interpretability and how they locate and interpret textual information within images. In this paper, we explore various LVLMs to identify the specific heads responsible for recognizing text from images, which we term the Optical Character Recognition Head (OCR Head). Our findings regarding these heads are as follows: (1) Less Sparse: Unlike previous retrieval heads, a large number of heads are activated to extract textual information from images. (2) Qualitatively Distinct: OCR heads possess properties that differ significantly from general retrieval heads, exhibiting low similarity in their characteristics. (3) Statically Activated: The frequency of activation for these heads closely aligns with their OCR scores. We validate our findings in downstream tasks by applying Chain-of-Thought (CoT) to both OCR and conventional retrieval heads and by masking these heads. We also demonstrate that redistributing sink-token values within the OCR heads improves performance. These insights provide a deeper understanding of the internal mechanisms LVLMs employ in processing embedded textual information in images.

While the Transformer architecture dominates many fields, its quadratic self-attention complexity hinders its use in large-scale applications. Linear attention offers an efficient alternative, but its direct application often degrades performance, with existing fixes typically re-introducing computational overhead through extra modules (e.g., depthwise separable convolution) that defeat the original purpose. In this work, we identify a key failure mode in these methods: global context collapse, where the model loses representational diversity. To address this, we propose Multi-Head Linear Attention (MHLA), which preserves this diversity by computing attention within divided heads along the token dimension. We prove that MHLA maintains linear complexity while recovering much of the expressive power of softmax attention, and verify its effectiveness across multiple domains, achieving a 3.6\% improvement on ImageNet classification, a 6.3\% gain on NLP, a 12.6\% improvement on image generation, and a 41\% enhancement on video generation under the same time complexity.

Multi-Head Attention (MHA) is the core computational primitive underlying modern Large Language Models (LLMs). However, MHA suffers from a fundamental linear scaling limitation: H attention heads produce exactly H independent attention matrices, with no communication between heads during attention computation. This becomes problematic for multi-step reasoning, where correct answers depend on aggregating evidence from multiple parts of the context and composing latent token-to-token relations over a chain of intermediate inferences. To address this, we propose Interleaved Head Attention (IHA), which enables cross-head mixing by constructing P pseudo-heads per head (typically P=H), where each pseudo query/key/value is a learned linear combination of all H original queries, keys and values respectively. Interactions between pseudo-query and pseudo-key heads induce up to P^2 attention patterns per head with modest parameter overhead O(H^2P). We provide theory showing improved efficiency in terms of number of parameters on the synthetic Polynomial task (IHA uses Θ(kn^2) parameters vs. Θ(kn^2) for MHA) and on the synthetic order-sensitive CPM-3 task (IHA uses lceilN_{max}rceil heads vs. N_{max} for MHA). On real-world benchmarks, IHA improves Multi-Key retrieval on RULER by 10-20% (4k-16k) and, after fine-tuning for reasoning on OpenThoughts, improves GSM8K by 5.8% and MATH-500 by 2.8% (Majority Vote) over full attention.

Linear attention reduces the quadratic cost of softmax attention by maintaining a recurrent fast-weight state, but it consistently lags on in-context retrieval and long-context tasks. Existing remedies act on the write side of memory through gating, delta updates, or kernel feature maps, but the read step is left unchanged: every past key contributes additively to the output, so useful targets are diluted by the bulk of stored vectors. We borrow one specific piece of softmax's geometry to construct a cheap read-time contraction of the query. A second-order Taylor expansion of the softmax log-partition at the isotropic-attention point gives a local quadratic model whose curvature coincides with the running key covariance, a quantity that can be maintained with the same recurrent/chunkwise mechanism as the linear-attention state. The associated linear operator contracts the query along the high-density directions of memory before it reads the state. We call this mechanism Curvature-Conditioned Query (CCQ). CCQ modifies only the read step and is composable with any linear-attention backbone. Attached to GLA and Gated DeltaNet, it improves perplexity, zero-shot downstream accuracy, S-NIAH retrieval at and beyond the training context, length-extrapolation perplexity from 4K to 20K, and LongBench accuracy, at small extra cost.

Linear attention is an efficient attention mechanism that has recently emerged as a promising alternative to conventional softmax attention. With its ability to process tokens in linear computational complexities, linear attention, in theory, can handle sequences of unlimited length without sacrificing speed, i.e., maintaining a constant training speed for various sequence lengths with a fixed memory consumption. However, due to the issue with cumulative summation (cumsum), current linear attention algorithms cannot demonstrate their theoretical advantage in a causal setting. In this paper, we present Lightning Attention-2, the first linear attention implementation that enables linear attention to realize its theoretical computational benefits. To achieve this, we leverage the thought of tiling, separately handling the intra-block and inter-block components in linear attention calculation. Specifically, we utilize the conventional attention computation mechanism for the intra-blocks and apply linear attention kernel tricks for the inter-blocks. A tiling technique is adopted through both forward and backward procedures to take full advantage of the GPU hardware. We implement our algorithm in Triton to make it IO-aware and hardware-friendly. Various experiments are conducted on different model sizes and sequence lengths. Lightning Attention-2 retains consistent training and inference speed regardless of input sequence length and is significantly faster than other attention mechanisms. The source code is available at https://github.com/OpenNLPLab/lightning-attention.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

Linear Sequence Modeling (LSM) like linear attention, state space models and linear RNNs, and Mixture-of-Experts (MoE) have recently emerged as significant architectural improvements. In this paper, we introduce Linear-MoE, a production-level system for modeling and training large-scale models that integrate LSM with MoE. Linear-MoE leverages the advantages of both LSM modules for linear-complexity sequence modeling and MoE layers for sparsely activation, aiming to offer high performance with efficient training. The Linear-MoE system comprises: 1) Modeling subsystem, which provides a unified framework supporting all instances of LSM. and 2) Training subsystem, which facilitates efficient training by incorporating various advanced parallelism technologies, particularly Sequence Parallelism designed for Linear-MoE models. Additionally, we explore hybrid models that combine Linear-MoE layers with standard Transformer-MoE layers with its Sequence Parallelism to further enhance model flexibility and performance. Evaluations on two model series, A0.3B-2B and A1B-7B, demonstrate Linear-MoE achieves efficiency gains while maintaining competitive performance on various benchmarks, showcasing its potential as a next-generation foundational model architecture. Code: https://github.com/OpenSparseLLMs/Linear-MoE.

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem we must look at the articulated decisions in entirety. If we could capture the actions of non-linear units for a particular input, we would be able to replay the whole system back and forth as if it was always linear. It would also reveal the actions of non-linearities because the resulting linear system, a Linear Interpreter, depends on the input image. We introduce a hooking layer, called a LinearScope, which allows us to run the network and the linear interpreter in parallel. Its implementation is simple, flexible and efficient. From here we can make many curious inquiries: how do these linear systems look like? When the rows and columns of the transformation matrix are images, how do they look like? What type of basis do these linear transformations rely on? The answers depend on the problems presented, through which we take a tour to some popular architectures used for classification, super-resolution (SR) and image-to-image translation (I2I). For classification we observe that popular networks use a pixel-wise vote per class strategy and heavily rely on bias parameters. For SR and I2I we find that CNNs use wavelet-type basis similar to the human visual system. For I2I we reveal copy-move and template-creation strategies to generate outputs.

While linear attention reduces the quadratic complexity of standard Transformers to linear time, it often lags behind in expressivity due to the removal of softmax normalization. This omission eliminates global competition, a critical mechanism that enables models to sharply focus on relevant information amidst long-context noise. In this work, we propose Softmax Linear Attention (SLA), a framework designed to restore this competitive selection without sacrificing efficiency. By lifting the softmax operation from the token level to the head level, SLA leverages attention heads as coarse semantic slots, applying a competitive gating mechanism to dynamically select the most relevant subspaces. This reintroduces the ``winner-take-all'' dynamics essential for precise retrieval and robust long-context understanding. Distinct from prior methods that focus on refining local kernel functions, SLA adopts a broader perspective by exploiting the higher-level multi-head aggregation structure. Extensive experiments demonstrate that SLA consistently enhances state-of-the-art linear baselines (RetNet, GLA, GDN) across language modeling and long-context benchmarks, particularly in challenging retrieval scenarios where it significantly boosts robustness against noise, validating its capability to restore precise focus while maintaining linear complexity.

Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We empirically compare standard Principal Component Analysis (PCA) with its sparse variant (SPCA) as front-end feature extractors for downstream classifiers, and we complement these experiments with a theoretical analysis. On the theory side, we derive exact robustness certificates for linear heads applied to SPCA features: for both ell_infty and ell_2 threat models (binary and multiclass), the certified radius grows as the dual norms of W^top u shrink, where W is the projection and u the head weights. We further show that for general (non-linear) heads, sparsity reduces operator-norm bounds through a Lipschitz composition argument, predicting lower input sensitivity. Empirically, with a small non-linear network after the projection, SPCA consistently degrades more gracefully than PCA under strong white-box and black-box attacks while maintaining competitive clean accuracy. Taken together, the theory identifies the mechanism (sparser projections reduce adversarial leverage) and the experiments verify that this benefit persists beyond the linear setting. Our code is available at https://github.com/killian31/SPCARobustness.

In this technical report, we present the Ring-linear model series, specifically including Ring-mini-linear-2.0 and Ring-flash-linear-2.0. Ring-mini-linear-2.0 comprises 16B parameters and 957M activations, while Ring-flash-linear-2.0 contains 104B parameters and 6.1B activations. Both models adopt a hybrid architecture that effectively integrates linear attention and softmax attention, significantly reducing I/O and computational overhead in long-context inference scenarios. Compared to a 32 billion parameter dense model, this series reduces inference cost to 1/10, and compared to the original Ring series, the cost is also reduced by over 50%. Furthermore, through systematic exploration of the ratio between different attention mechanisms in the hybrid architecture, we have identified the currently optimal model structure. Additionally, by leveraging our self-developed high-performance FP8 operator library-linghe, overall training efficiency has been improved by 50%. Benefiting from the high alignment between the training and inference engine operators, the models can undergo long-term, stable, and highly efficient optimization during the reinforcement learning phase, consistently maintaining SOTA performance across multiple challenging complex reasoning benchmarks.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Time series forecasting (TSF) is critical in domains like energy, finance, healthcare, and logistics, requiring models that generalize across diverse datasets. Large pre-trained models such as Chronos and Time-MoE show strong zero-shot (ZS) performance but suffer from high computational costs. In this work, We introduce Super-Linear, a lightweight and scalable mixture-of-experts (MoE) model for general forecasting. It replaces deep architectures with simple frequency-specialized linear experts, trained on resampled data across multiple frequency regimes. A lightweight spectral gating mechanism dynamically selects relevant experts, enabling efficient, accurate forecasting. Despite its simplicity, Super-Linear matches state-of-the-art performance while offering superior efficiency, robustness to various sampling rates, and enhanced interpretability. The implementation of Super-Linear is available at https://github.com/azencot-group/SuperLinear{https://github.com/azencot-group/SuperLinear}

In large language models built upon the Transformer architecture, recent studies have shown that inter-head interaction can enhance attention performance. Motivated by this, we propose Multi-head Explicit Attention (MEA), a simple yet effective attention variant that explicitly models cross-head interaction. MEA consists of two key components: a Head-level Linear Composition (HLC) module that separately applies learnable linear combinations to the key and value vectors across heads, thereby enabling rich inter-head communication; and a head-level Group Normalization layer that aligns the statistical properties of the recombined heads. MEA shows strong robustness in pretraining, which allows the use of larger learning rates that lead to faster convergence, ultimately resulting in lower validation loss and improved performance across a range of tasks. Furthermore, we explore the parameter efficiency of MEA by reducing the number of attention heads and leveraging HLC to reconstruct them using low-rank "virtual heads". This enables a practical key-value cache compression strategy that reduces KV-cache memory usage by 50% with negligible performance loss on knowledge-intensive and scientific reasoning tasks, and only a 3.59% accuracy drop for Olympiad-level mathematical benchmarks.

Transformer-based Large Language Models (LLMs) are the state-of-the-art for natural language tasks. Recent work has attempted to decode, by reverse engineering the role of linear layers, the internal mechanisms by which LLMs arrive at their final predictions for text completion tasks. Yet little is known about the specific role of attention heads in producing the final token prediction. We propose Attention Lens, a tool that enables researchers to translate the outputs of attention heads into vocabulary tokens via learned attention-head-specific transformations called lenses. Preliminary findings from our trained lenses indicate that attention heads play highly specialized roles in language models. The code for Attention Lens is available at github.com/msakarvadia/AttentionLens.

Recent works show we can linearize large language models (LLMs) -- swapping the quadratic attentions of popular Transformer-based LLMs with subquadratic analogs, such as linear attention -- avoiding the expensive pretraining costs. However, linearizing LLMs often significantly degrades model quality, still requires training over billions of tokens, and remains limited to smaller 1.3B to 7B LLMs. We thus propose Low-rank Linear Conversion via Attention Transfer (LoLCATs), a simple two-step method that improves LLM linearizing quality with orders of magnitudes less memory and compute. We base these steps on two findings. First, we can replace an LLM's softmax attentions with closely-approximating linear attentions, simply by training the linear attentions to match their softmax counterparts with an output MSE loss ("attention transfer"). Then, this enables adjusting for approximation errors and recovering LLM quality simply with low-rank adaptation (LoRA). LoLCATs significantly improves linearizing quality, training efficiency, and scalability. We significantly reduce the linearizing quality gap and produce state-of-the-art subquadratic LLMs from Llama 3 8B and Mistral 7B v0.1, leading to 20+ points of improvement on 5-shot MMLU. Furthermore, LoLCATs does so with only 0.2% of past methods' model parameters and 0.4% of their training tokens. Finally, we apply LoLCATs to create the first linearized 70B and 405B LLMs (50x larger than prior work). When compared with prior approaches under the same compute budgets, LoLCATs significantly improves linearizing quality, closing the gap between linearized and original Llama 3.1 70B and 405B LLMs by 77.8% and 78.1% on 5-shot MMLU.

Transformers face quadratic complexity and memory issues with long sequences, prompting the adoption of linear attention mechanisms using fixed-size hidden states. However, linear models often suffer from limited recall performance, leading to hybrid architectures that combine linear and full attention layers. Despite extensive hybrid architecture research, the choice of linear attention component has not been deeply explored. We systematically evaluate various linear attention models across generations - vector recurrences to advanced gating mechanisms - both standalone and hybridized. To enable this comprehensive analysis, we trained and open-sourced 72 models: 36 at 340M parameters (20B tokens) and 36 at 1.3B parameters (100B tokens), covering six linear attention variants across five hybridization ratios. Benchmarking on standard language modeling and recall tasks reveals that superior standalone linear models do not necessarily excel in hybrids. While language modeling remains stable across linear-to-full attention ratios, recall significantly improves with increased full attention layers, particularly below a 3:1 ratio. Our study highlights selective gating, hierarchical recurrence, and controlled forgetting as critical for effective hybrid models. We recommend architectures such as HGRN-2 or GatedDeltaNet with a linear-to-full ratio between 3:1 and 6:1 to achieve Transformer-level recall efficiently. Our models are open-sourced at https://huggingface.co/collections/m-a-p/hybrid-linear-attention-research-686c488a63d609d2f20e2b1e.

Linear-attention and state-space language models compress the prefix into a fixed-size recurrent state, yielding O(1) memory at the cost of a lossy exact memory: when many key--value associations compete, earlier facts are overwritten and needle recall degrades. Inspired by Complementary Learning Systems, we give linear attention a hippocampal complement. HOLA (Hippocampal Linear Attention) keeps the usual delta-rule state as a compressive memory and adds a bounded exact KV cache, forming a semiparametric test-time memory: the state models linearly compressible structure, while the cache stores associations that should not be forced through that state. The cache writes without a learned eviction module, keeping tokens with large beta * ||e||, the prediction residual actually committed to the state; a decoupled RMSNorm-gamma cache read then turns these exact KV pairs into sharp retrieval rather than soft averaging. At 340M parameters trained on 15B SlimPajama tokens, HOLA lowers Wikitext perplexity from 27.32 to 22.92 (-16.1%), below a full-attention Transformer++ (26.88), and improves LAMBADA perplexity from 30.95 to 30.26. It also achieves the best linear in-context retrieval and remains much more robust than GDN or a matched HOLA+recency cache on RULER needle-in-a-haystack recall out to 32k tokens (16x its training length).

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Linear attention reduces the quadratic cost of softmax attention to O(T), but its memory state grows as O(T) in Frobenius norm, causing progressive interference between stored associations. We introduce Variational Linear Attention (VLA), which reframes the memory update as an online regularised least-squares problem with an adaptive penalty matrix maintained via the Sherman-Morrison rank-1 formula. We prove that normalising the write direction to unit length gives the recurrence Jacobian spectral norm exactly 1 for all sequence lengths and head dimensions (Proposition 2), and that the state norm is self-limiting under bounded inputs (Proposition 1). Empirically, VLA reduces |S_t|_F by 109times relative to standard linear attention at T{=}1{,}000, achieves near-perfect exact-match accuracy on multi-query associative recall within the effective per-head memory regime (n_pairs < d_h), maintaining substantially higher retrieval performance than DeltaNet and standard linear attention under increasing memory load, and maintains 62\% accuracy at the per-head capacity boundary. A Triton-fused kernel achieves 14times speedup over sequential Python and O(T) scaling, crossing below softmax attention latency at approximately 43\,000 tokens.

Linear probes are widely used in interpretability research and often compared by cosine similarity. The Mahalanobis cosine similarity (MCS) between two directions, which reweights the inner product by test data covariance, is a natural task-aware refinement. Ying et al. (2026) report that a probe's MCS to a reference probe trained on the out-of-distribution (OOD) data near-perfectly linearly predicts the probe's OOD AUROC (R^2 = 0.98). Here, we extend this empirical finding across models, layers, and concept domains, and prove this general phenomenon in closed form: For balanced classes whose projections are Gaussian, OOD AUROC and MCS to the reference probe are linear because both are sigmoid-shaped functions of the probe's signal-to-noise ratio (SNR) on the test data. The theory also predicts when this linearity fails, which we verify empirically. MCS offers a theoretically grounded and empirically effective alternative to Euclidean cosine similarity for comparing linear probes.

In-context learning (ICL) in large language models (LLMs) is a striking phenomenon, yet its underlying mechanisms remain only partially understood. Previous work connects linear self-attention (LSA) to gradient descent (GD), this connection has primarily been established under simplified conditions with zero-mean Gaussian priors and zero initialization for GD. However, subsequent studies have challenged this simplified view by highlighting its overly restrictive assumptions, demonstrating instead that under conditions such as multi-layer or nonlinear attention, self-attention performs optimization-like inference, akin to but distinct from GD. We investigate how multi-head LSA approximates GD under more realistic conditions specifically when incorporating non-zero Gaussian prior means in linear regression formulations of ICL. We first extend multi-head LSA embedding matrix by introducing an initial estimation of the query, referred to as the initial guess. We prove an upper bound on the number of heads needed for ICL linear regression setup. Our experiments confirm this result and further observe that a performance gap between one-step GD and multi-head LSA persists. To address this gap, we introduce yq-LSA, a simple generalization of single-head LSA with a trainable initial guess yq. We theoretically establish the capabilities of yq-LSA and provide experimental validation on linear regression tasks, thereby extending the theory that bridges ICL and GD. Finally, inspired by our findings in the case of linear regression, we consider widespread LLMs augmented with initial guess capabilities, and show that their performance is improved on a semantic similarity task.

Linear attentions have shown potential for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2) "finetuned-conversion" of task-specific Transformers into linear versions that recover task performance, and (3) "pretrained-conversion" of Transformers such as large language models into linear versions finetunable on downstream tasks. However, linear attentions often underperform standard softmax attention in quality. To close this performance gap, we find prior linear attentions lack key properties of softmax attention tied to good performance: low-entropy (or "spiky") weights and dot-product monotonicity. We further observe surprisingly simple feature maps that retain these properties and match softmax performance, but are inefficient to compute in linear attention. We thus propose Hedgehog, a learnable linear attention that retains the spiky and monotonic properties of softmax attention while maintaining linear complexity. Hedgehog uses simple trainable MLPs to produce attention weights mimicking softmax attention. Experiments show Hedgehog recovers over 99% of standard Transformer quality in train-from-scratch and finetuned-conversion settings, outperforming prior linear attentions up to 6 perplexity points on WikiText-103 with causal GPTs, and up to 8.7 GLUE score points on finetuned bidirectional BERTs. Hedgehog also enables pretrained-conversion. Converting a pretrained GPT-2 into a linear attention variant achieves state-of-the-art 16.7 perplexity on WikiText-103 for 125M subquadratic decoder models. We finally turn a pretrained Llama-2 7B into a viable linear attention Llama. With low-rank adaptation, Hedgehog-Llama2 7B achieves 28.1 higher ROUGE-1 points over the base standard attention model, where prior linear attentions lead to 16.5 point drops.

Linearizing pretrained large language models (LLMs) primarily relies on intra-layer hybrid attention mechanisms to alleviate the quadratic complexity of standard softmax attention. Existing methods perform token routing based on sliding-window partitions, resulting in position-based selection and fails to capture token-specific global importance. Meanwhile, linear attention further suffers from distribution shift caused by learnable feature maps that distort pretrained feature magnitudes. Motivated by these limitations, we propose STILL, an intra-layer hybrid linearization framework for efficiently linearizing LLMs. STILL introduces a Self-Saliency Score with strong local-global consistency, enabling accurate token selection using sliding-window computation, and retains salient tokens for sparse softmax attention while summarizing the remaining context via linear attention. To preserve pretrained representations, we design a Norm-Preserved Feature Map (NP-Map) that decouples feature direction from magnitude and reinjects pretrained norms. We further adopt a unified training-inference architecture with chunk-wise parallelization and delayed selection to improve hardware efficiency. Experiments show that STILL matches or surpasses the original pretrained model on commonsense and general reasoning tasks, and achieves up to a 86.2% relative improvement over prior linearized attention methods on long-context benchmarks.

Transformers with linear recurrent modeling offer linear-time training and constant-memory inference. Despite their demonstrated efficiency and performance, pretraining such non-standard architectures from scratch remains costly and risky. The linearization of large language models (LLMs) transforms pretrained standard models into linear recurrent structures, enabling more efficient deployment. However, current linearization methods typically introduce additional feature map modules that require extensive fine-tuning and overlook the gating mechanisms used in state-of-the-art linear recurrent models. To address these issues, this paper presents Liger, short for Linearizing LLMs to gated recurrent structures. Liger is a novel approach for converting pretrained LLMs into gated linear recurrent models without adding extra parameters. It repurposes the pretrained key matrix weights to construct diverse gating mechanisms, facilitating the formation of various gated recurrent structures while avoiding the need to train additional components from scratch. Using lightweight fine-tuning with Low-Rank Adaptation (LoRA), Liger restores the performance of the linearized gated recurrent models to match that of the original LLMs. Additionally, we introduce Liger Attention, an intra-layer hybrid attention mechanism, which significantly recovers 93\% of the Transformer-based LLM at 0.02\% pre-training tokens during the linearization process, achieving competitive results across multiple benchmarks, as validated on models ranging from 1B to 8B parameters. Code is available at https://github.com/OpenSparseLLMs/Linearization.

In commonly used sub-quadratic complexity modules, linear attention benefits from simplicity and high parallelism, making it promising for image synthesis tasks. However, the architectural design and learning strategy for linear attention remain underexplored in this field. In this paper, we offer a suite of ready-to-use solutions for efficient linear diffusion Transformers. Our core contributions include: (1) Simplified Linear Attention using few heads, observing the free-lunch effect of performance without latency increase. (2) Weight inheritance from a fully pre-trained diffusion Transformer: initializing linear Transformer using pre-trained diffusion Transformer and loading all parameters except for those related to linear attention. (3) Hybrid knowledge distillation objective: using a pre-trained diffusion Transformer to help the training of the student linear Transformer, supervising not only the predicted noise but also the variance of the reverse diffusion process. These guidelines lead to our proposed Linear Diffusion Transformer (LiT), an efficient text-to-image Transformer that can be deployed offline on a laptop. Experiments show that in class-conditional 256*256 and 512*512 ImageNet benchmark LiT achieves highly competitive FID while reducing training steps by 80% and 77% compared to DiT. LiT also rivals methods based on Mamba or Gated Linear Attention. Besides, for text-to-image generation, LiT allows for the rapid synthesis of up to 1K resolution photorealistic images. Project page: https://techmonsterwang.github.io/LiT/.

This paper reveals a novel linear characteristic exclusive to transformer decoders, including models such as GPT, LLaMA, OPT, BLOOM and others. We analyze embedding transformations between sequential layers, uncovering a near-perfect linear relationship (Procrustes similarity score of 0.99). However, linearity decreases when the residual component is removed due to a consistently low output norm of the transformer layer. Our experiments show that removing or linearly approximating some of the most linear blocks of transformers does not affect significantly the loss or model performance. Moreover, in our pretraining experiments on smaller models we introduce a cosine-similarity-based regularization, aimed at reducing layer linearity. This regularization improves performance metrics on benchmarks like Tiny Stories and SuperGLUE and as well successfully decreases the linearity of the models. This study challenges the existing understanding of transformer architectures, suggesting that their operation may be more linear than previously assumed.

This paper introduces FaceLiVT, a lightweight yet powerful face recognition model that integrates a hybrid Convolution Neural Network (CNN)-Transformer architecture with an innovative and lightweight Multi-Head Linear Attention (MHLA) mechanism. By combining MHLA alongside a reparameterized token mixer, FaceLiVT effectively reduces computational complexity while preserving competitive accuracy. Extensive evaluations on challenging benchmarks; including LFW, CFP-FP, AgeDB-30, IJB-B, and IJB-C; highlight its superior performance compared to state-of-the-art lightweight models. MHLA notably improves inference speed, allowing FaceLiVT to deliver high accuracy with lower latency on mobile devices. Specifically, FaceLiVT is 8.6 faster than EdgeFace, a recent hybrid CNN-Transformer model optimized for edge devices, and 21.2 faster than a pure ViT-Based model. With its balanced design, FaceLiVT offers an efficient and practical solution for real-time face recognition on resource-constrained platforms.

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

Large language models are increasingly deployed as agents, but reliable agentic behavior requires more than next-token prediction. At inference time, it is preferred that an agent can decide whether to proceed with its current reasoning, defer to a stronger model, request additional information, invoke external tools, or abstain under the given setup. Existing approaches address these decisions through prompt-level routing, external orchestration, or task-specific fine-tuning, which primarily rely on input-side signals, and are often costly and difficult to maintain as model backbones evolve. We ask whether such control decisions can be inferred directly from a model's latent generation process. We introduce Multi-Head Latent Control, a lightweight layer that reads hidden-state trajectories from a frozen LLM or VLM to produce deployment-time control signals. A Capability Head predicts whether the current model can solve the instance or should defer to a stronger collaborator, while a Resolution Head predicts appropriate resolution decision Clarification, Tool Use, Abstention, or Direct Answering. Both heads are trained only on latent traces from the same frozen LLM backbone, enabling post hoc adaptation without modifying the model. Across language and vision-language settings, Multi-Head Latent Control consistently improves the quality-cost tradeoff of multi-model systems, enabling early handoff from partial generations and more accurate intervention decisions. In routed execution (small + large model), it reduces large-model usage by up to 90.7 percent on AndroidWorld and 27-53 percent on average across benchmarks, while retaining most of large-model performance. Additionally, the learned control signals improve tool-use decision quality, yielding up to +158 percent relative score gain and 65.5 percent fewer missed-required tool calls.

Large language models (LLMs) have achieved impressive performance in numerous domains but often struggle to process lengthy inputs effectively and efficiently due to limited length generalization and attention's quadratic computational demands. Many sought to mitigate this by restricting the attention window within the pre-trained length. However, these methods introduce new issues such as ignoring the middle context and requiring additional training. To address these problems, we propose LongHeads, a training-free framework that enhances LLM's long context ability by unlocking multi-head attention's untapped potential. Instead of allowing each head to attend to the full sentence, which struggles with generalizing to longer sequences due to out-of-distribution (OOD) issues, we allow each head to process in-distribution length by selecting and attending to important context chunks. To this end, we propose a chunk selection strategy that relies on the inherent correlation between the query and the key representations, efficiently distributing context chunks to different heads. In this way, each head ensures it can effectively process attended tokens within the trained length, while different heads in different layers can collectively process longer contexts. LongHeads works efficiently in linear time, fits seamlessly with many LLMs that use relative positional encoding. Our extensive empirical analyses verify LongHeads's efficacy in extending the usable context window for existing models, showcasing its promise for enhancing long text understanding.

In this work we present successor heads: attention heads that increment tokens with a natural ordering, such as numbers, months, and days. For example, successor heads increment 'Monday' into 'Tuesday'. We explain the successor head behavior with an approach rooted in mechanistic interpretability, the field that aims to explain how models complete tasks in human-understandable terms. Existing research in this area has found interpretable language model components in small toy models. However, results in toy models have not yet led to insights that explain the internals of frontier models and little is currently understood about the internal operations of large language models. In this paper, we analyze the behavior of successor heads in large language models (LLMs) and find that they implement abstract representations that are common to different architectures. They form in LLMs with as few as 31 million parameters, and at least as many as 12 billion parameters, such as GPT-2, Pythia, and Llama-2. We find a set of 'mod-10 features' that underlie how successor heads increment in LLMs across different architectures and sizes. We perform vector arithmetic with these features to edit head behavior and provide insights into numeric representations within LLMs. Additionally, we study the behavior of successor heads on natural language data, identifying interpretable polysemanticity in a Pythia successor head.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

The interest in linear complexity models for large language models is on the rise, although their scaling capacity remains uncertain. In this study, we present the scaling laws for linear complexity language models to establish a foundation for their scalability. Specifically, we examine the scaling behaviors of three efficient linear architectures. These include TNL, a linear attention model with data-independent decay; HGRN2, a linear RNN with data-dependent decay; and cosFormer2, a linear attention model without decay. We also include LLaMA as a baseline architecture for softmax attention for comparison. These models were trained with six variants, ranging from 70M to 7B parameters on a 300B-token corpus, and evaluated with a total of 1,376 intermediate checkpoints on various downstream tasks. These tasks include validation loss, commonsense reasoning, and information retrieval and generation. The study reveals that existing linear complexity language models exhibit similar scaling capabilities as conventional transformer-based models while also demonstrating superior linguistic proficiency and knowledge retention.

We present Lightning Attention, the first linear attention implementation that maintains a constant training speed for various sequence lengths under fixed memory consumption. Due to the issue with cumulative summation operations (cumsum), previous linear attention implementations cannot achieve their theoretical advantage in a casual setting. However, this issue can be effectively solved by utilizing different attention calculation strategies to compute the different parts of attention. Specifically, we split the attention calculation into intra-blocks and inter-blocks and use conventional attention computation for intra-blocks and linear attention kernel tricks for inter-blocks. This eliminates the need for cumsum in the linear attention calculation. Furthermore, a tiling technique is adopted through both forward and backward procedures to take full advantage of the GPU hardware. To enhance accuracy while preserving efficacy, we introduce TransNormerLLM (TNL), a new architecture that is tailored to our lightning attention. We conduct rigorous testing on standard and self-collected datasets with varying model sizes and sequence lengths. TNL is notably more efficient than other language models. In addition, benchmark results indicate that TNL performs on par with state-of-the-art LLMs utilizing conventional transformer structures. The source code is released at github.com/OpenNLPLab/TransnormerLLM.

Existing head pose estimation (HPE) mainly focuses on single person with pre-detected frontal heads, which limits their applications in real complex scenarios with multi-persons. We argue that these single HPE methods are fragile and inefficient for Multi-Person Head Pose Estimation (MPHPE) since they rely on the separately trained face detector that cannot generalize well to full viewpoints, especially for heads with invisible face areas. In this paper, we focus on the full-range MPHPE problem, and propose a direct end-to-end simple baseline named DirectMHP. Due to the lack of datasets applicable to the full-range MPHPE, we firstly construct two benchmarks by extracting ground-truth labels for head detection and head orientation from public datasets AGORA and CMU Panoptic. They are rather challenging for having many truncated, occluded, tiny and unevenly illuminated human heads. Then, we design a novel end-to-end trainable one-stage network architecture by joint regressing locations and orientations of multi-head to address the MPHPE problem. Specifically, we regard pose as an auxiliary attribute of the head, and append it after the traditional object prediction. Arbitrary pose representation such as Euler angles is acceptable by this flexible design. Then, we jointly optimize these two tasks by sharing features and utilizing appropriate multiple losses. In this way, our method can implicitly benefit from more surroundings to improve HPE accuracy while maintaining head detection performance. We present comprehensive comparisons with state-of-the-art single HPE methods on public benchmarks, as well as superior baseline results on our constructed MPHPE datasets. Datasets and code are released in https://github.com/hnuzhy/DirectMHP.

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear transformers and identify two key issues that lead to such performance gaps: 1) unbounded gradients in the attention computation adversely impact the convergence of linear transformer models; 2) attention dilution which trivially distributes attention scores over long sequences while neglecting neighbouring structures. To address these issues, we first identify that the scaling of attention matrices is the devil in unbounded gradients, which turns out unnecessary in linear attention as we show theoretically and empirically. To this end, we propose a new linear attention that replaces the scaling operation with a normalization to stabilize gradients. For the issue of attention dilution, we leverage a diagonal attention to confine attention to only neighbouring tokens in early layers. Benefiting from the stable gradients and improved attention, our new linear transformer model, transNormer, demonstrates superior performance on text classification and language modeling tasks, as well as on the challenging Long-Range Arena benchmark, surpassing vanilla transformer and existing linear variants by a clear margin while being significantly more space-time efficient. The code is available at https://github.com/OpenNLPLab/Transnormer .

Constructing vivid 3D head avatars for given subjects and realizing a series of animations on them is valuable yet challenging. This paper presents GaussianHead, which models the actional human head with anisotropic 3D Gaussians. In our framework, a motion deformation field and multi-resolution tri-plane are constructed respectively to deal with the head's dynamic geometry and complex texture. Notably, we impose an exclusive derivation scheme on each Gaussian, which generates its multiple doppelgangers through a set of learnable parameters for position transformation. With this design, we can compactly and accurately encode the appearance information of Gaussians, even those fitting the head's particular components with sophisticated structures. In addition, an inherited derivation strategy for newly added Gaussians is adopted to facilitate training acceleration. Extensive experiments show that our method can produce high-fidelity renderings, outperforming state-of-the-art approaches in reconstruction, cross-identity reenactment, and novel view synthesis tasks. Our code is available at: https://github.com/chiehwangs/gaussian-head.