README.md

---
language:
- en
- zh
pipeline_tag: text-generation
library_name: transformers
tags:
- xllm
- k2-horizon
- causal-lm
- reasoning
- knowledge-distillation
- vllm
- reinforcement-learning
license: other
license_name: internal-only
license_link: LICENSE
model-index:
- name: K2-Horizon-0.9B
  results:
  - task:
      type: text-generation
      name: Math Reasoning
    dataset:
      name: AIME 2026
      type: aime26
    metrics:
    - type: accuracy
      name: avg@16
      value: 0.485
  - task:
      type: text-generation
      name: Math Reasoning
    dataset:
      name: AIME 2025
      type: aime25
    metrics:
    - type: accuracy
      name: avg@16
      value: 0.390
  - task:
      type: text-generation
      name: Code Generation
    dataset:
      name: HumanEval+
      type: humaneval_plus
    metrics:
    - type: pass@1
      value: 0.799
  - task:
      type: text-generation
      name: Code Generation
    dataset:
      name: MBPP+
      type: mbpp_plus
    metrics:
    - type: pass@1
      value: 0.680
  - task:
      type: text-generation
      name: Code Generation
    dataset:
      name: LiveCodeBench v6
      type: livecodebench_v6
    metrics:
    - type: pass@1
      value: 0.357
  - task:
      type: text-generation
      name: General Knowledge / Reasoning
    dataset:
      name: GPQA-Diamond
      type: gpqa_diamond
    metrics:
    - type: accuracy
      name: avg@16
      value: 0.273
  - task:
      type: text-generation
      name: General Knowledge / Reasoning
    dataset:
      name: MMLU-Pro
      type: mmlu_pro
    metrics:
    - type: accuracy
      value: 0.455
  - task:
      type: text-generation
      name: General Knowledge / Reasoning
    dataset:
      name: BBH
      type: bbh
    metrics:
    - type: accuracy
      name: zero-shot CoT
      value: 0.660
  - task:
      type: text-generation
      name: Tool Use
    dataset:
      name: BFCL v4
      type: bfcl_v4
    metrics:
    - type: accuracy
      name: overall
      value: 0.280
  - task:
      type: text-generation
      name: Instruction Following
    dataset:
      name: IFEval
      type: ifeval
    metrics:
    - type: accuracy
      name: strict-instruction
      value: 0.808
  - task:
      type: text-generation
      name: Math Reasoning
    dataset:
      name: HMMT February 2026
      type: hmmt_feb_2026
    metrics:
    - type: accuracy
      name: avg@16
      value: 0.258
---

# K2-Horizon-0.9B

K2-Horizon-0.9B is a compact, 0.9-billion-parameter reasoning model designed
to combine mathematics, code generation, instruction following, and STEM
knowledge in one checkpoint. It was produced with multi-teacher on-policy
distillation (mOPD), starting from a merge of specialist models and then
learning from three domain teachers under a shared objective.

## Model Details

| Property | Value |
|---|---|
| **Architecture** | `K2HorizonForCausalLM` (`model_type: k2_horizon`) |
| **Parameters** | 1,078,285,824 (released as 0.9B; counted from the safetensors tensors) |
| **Hidden size / layers** | 1,536 / 28 |
| **Attention heads / KV heads** | 32 / 8 |
| **Context length** | 131,072 tokens with YaRN RoPE scaling; original context length 8,192 tokens |
| **Vocabulary size** | 64,256 |
| **Released weight dtype** | BF16 |
| **Format** | Hugging Face safetensors, one weight shard, with custom configuration and modeling code in the repository root |
| **Distillation checkpoint** | Step 249 of a 500-step mOPD run |

The `main` revision publishes `K2HorizonForCausalLM`,
`model_type: k2_horizon`, and matching `configuration_k2_horizon.py` and
`modeling_k2_horizon.py` modules. The Transformers and vLLM preflights below
validate that public contract before loading weights.

### Training Lineage

Training examples were routed to a math-and-code teacher, a STEM teacher, or
an instruction-following teacher through the example's `opd_domain` metadata.
The math-and-code teacher was used as the fallback when no recognized domain
was present.

| Domain | Teacher checkpoint step |
|---|---:|
| Math and code | 2,739 |
| STEM | 499 |
| Instruction following | 1,499 |

The base context window was extended in stages from 8,192 to 40,960 and then
to 131,072 tokens. The `mid1_75k` and `mid2_47k` repository revisions preserve
the corresponding intermediate checkpoints. The distilled release checkpoint
is on `main`; all stages use a vocabulary of 64,256 tokens.

## Model Description

K2-Horizon-0.9B begins with a task-arithmetic merge of three specialist
checkpoints. mOPD then trains that merged student against math-and-code, STEM,
and instruction-following teachers at the same time. The training objective
combines an on-policy distillation loss with a reference-model KL term so the
student can learn specialist behavior while remaining close to the merged base
model.

The resulting checkpoint retains most of the specialist teachers' performance
on the reported math and coding tasks. It also improves every reported IFEval
submetric over the pre-distillation merge. This makes the model useful for
research on compact reasoning models, local inference, distillation, and
task-specific adaptation.

## Model Card Comparison Table

| Benchmark | **K2-Horizon-0.9B** | MiniCPM5-1B | Qwen3.5-0.8B | Qwen3.5-2B |
|---|---:|---:|---:|---:|
| IFEval (strict instruction) | **80.8†** | 80.41‡ | 44.0‡ | 78.6‡ |
| GPQA-Diamond (avg@16) | **27.3†** | 26.26‡ | 11.9‡ | 51.6‡ |
| HMMT February 2026 (avg@16) | **25.8†** | 23.3† | 0.57‡ | 18.56† |
| AIME 2025 (avg@16) | **41.7†** | 40.42‡ | 1.04‡ | 26.46† |
| AIME 2026 (avg@16) | **48.5†** | 40.42‡ | 0.21‡ | 25.42† |
| HumanEval+ (pass@1) | **79.9†** | 65.2† | 26.22† | 42.68† |
| MBPP+ (pass@1) | **68.0†** | 60.6† | 32.8† | 47.09† |
| LiveCodeBench v6 (avg@3) | **37.41†** | 33.52‡ | 5.33‡ | 13.08† |

- **† Local  result.**
- **‡ Published comparison/model-card value; protocol is not necessarily matched.**

## How to Use

K2-Horizon-0.9B emits a reasoning segment before its final answer when the
chat template is used. The template supports `reasoning_effort` values `high`,
`medium`, and `low`, which select the model's full, fast, and faster reasoning
modes respectively.

For a deterministic runtime check, use `temperature=0` and generate 20 to 50
tokens. For general sampled generation, `temperature=0.6` and `top_p=0.95`
reproduce the GPQA evaluation setting and are reasonable starting points.
IFBench used `temperature=0.8`. Long math and coding tasks may require several
thousand output tokens; choose limits from application measurements rather
than treating an evaluation limit as a universal default.

### Option A - vLLM (recommended, native architecture support)

The validated serving image was reconstructed into the following manual
runtime contract:

| Component | Validated value |
|---|---|
| Operating system | Ubuntu 24.04, Linux x86-64 |
| Python | 3.12.13 |
| CUDA toolkit | 12.9 |
| PyTorch | 2.13.0+cu129 |
| Transformers | 5.16.1 |
| Safetensors | 0.8.0 |
| FlashInfer | 0.6.17 |
| Attention backend | vLLM FlashAttention 3; Triton 3.7.1 |
| vLLM | `0.26.1rc1.dev1212`, [PR #53806](https://github.com/vllm-project/vllm/pull/53806) source commit [`d9fd5f11`](https://github.com/vllm-project/vllm/commit/d9fd5f11423a1a5628fe29e7296ceb9de91aac3c) |

That source revision contains the native `K2HorizonForCausalLM` implementation
and the built-in `k2_horizon` reasoning and tool parsers. Other vLLM revisions
have not been validated for this checkpoint. Pin the exact commit until the
integration is available in an upstream release.

Use Linux x86-64 with a CUDA 12.9-compatible NVIDIA driver and Git. The setup
uses vLLM's precompiled extension path while keeping the Python package on the
exact reviewed source commit.

<details>
<summary>Show the pinned vLLM environment setup</summary>

```bash
git clone --filter=blob:none --no-checkout \
  https://github.com/vllm-project/vllm.git
cd vllm
git fetch origin pull/53806/head:refs/remotes/origin/pr-53806
git checkout --detach d9fd5f11423a1a5628fe29e7296ceb9de91aac3c
test "$(git rev-parse HEAD)" = \
  "d9fd5f11423a1a5628fe29e7296ceb9de91aac3c"

python3.12 -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip uv
export UV_LINK_MODE=copy
VLLM_USE_PRECOMPILED=1 uv pip install --upgrade --editable . \
  --torch-backend=auto
uv pip install "transformers==5.16.1" "safetensors==0.8.0"
python -m pip check

python - <<'PY'
from vllm import ModelRegistry
from vllm.reasoning import ReasoningParserManager
from vllm.tool_parsers import ToolParserManager

assert "K2HorizonForCausalLM" in ModelRegistry.get_supported_archs()
assert ReasoningParserManager.get_reasoning_parser("k2_horizon") is not None
assert ToolParserManager.get_tool_parser("k2_horizon") is not None
PY
```

</details>

Download the repository chat template explicitly and start the server with one
GPU. The 8,192-token profile below is a conservative starting point. Increase
`MAX_MODEL_LEN` only after measuring KV-cache capacity; the checkpoint supports
up to 131,072 tokens.

<details>
<summary>Show the vLLM serving command</summary>

```bash
source .venv/bin/activate

export MODEL_ID="IFM/K2-Horizon-0.9B"
export MODEL_REVISION="main"
export MAX_MODEL_LEN=8192
export CHAT_TEMPLATE="$(hf download "$MODEL_ID" chat_template.jinja \
  --revision "$MODEL_REVISION")"

vllm serve "$MODEL_ID" \
  --revision "$MODEL_REVISION" \
  --model-impl vllm \
  --trust-remote-code \
  --dtype bfloat16 \
  --tensor-parallel-size 1 \
  --max-model-len "$MAX_MODEL_LEN" \
  --max-num-seqs 1 \
  --gpu-memory-utilization 0.85 \
  --served-model-name "$MODEL_ID" \
  --chat-template "$CHAT_TEMPLATE" \
  --reasoning-parser k2_horizon \
  --tool-call-parser k2_horizon \
  --enable-auto-tool-choice
```

</details>

The reasoning parser moves `<ifm|think>`, `<ifm|think_fast>`, or
`<ifm|think_faster>` text into the OpenAI-compatible response's
`reasoning_content` field. The tool parser converts generated
`<ifm|tool_call>` blocks into structured tool calls when tools are supplied in
the request.

<details>
<summary>Show an OpenAI-compatible request</summary>

```python
from openai import OpenAI

client = OpenAI(base_url="http://localhost:8000/v1", api_key="unused")
response = client.chat.completions.create(
    model="IFM/K2-Horizon-0.9B",
    messages=[{"role": "user", "content": "What is the square root of 2?"}],
    max_tokens=50,
    temperature=0,
    extra_body={"chat_template_kwargs": {"reasoning_effort": "high"}},
)
message = response.choices[0].message
print(getattr(message, "reasoning_content", None))
print(message.content)
```

</details>

### Option B - plain Transformers (no vLLM, no container)

The checkpoint can also be loaded directly from the Hugging Face repository.
Its `configuration_k2_horizon.py` and `modeling_k2_horizon.py` files are loaded
through `trust_remote_code=True`. Use a clean environment so the direct path
does not inherit vLLM's build dependencies. Transformers 4.57.x is not
compatible with this remote configuration class; use the validated 5.14.1
version below. Transformers may print nonfatal `cache_position` documentation
diagnostics while loading the remote code, but BF16 loading and generation
complete normally.

<details>
<summary>Show the Transformers environment setup</summary>

```bash
python3.12 -m venv .venv-transformers
source .venv-transformers/bin/activate
python -m pip install --upgrade pip
python -m pip install "torch==2.11.0" \
  --index-url https://download.pytorch.org/whl/cu128
python -m pip install \
  "transformers==5.14.1" \
  "safetensors==0.8.0"
python -m pip check
```

</details>

This deterministic sample loads the released weights as BF16 on one CUDA GPU
and generates only 50 tokens, making it suitable as an end-to-end smoke test.

<details>
<summary>Show the Transformers inference example</summary>

```python
import torch
from transformers import AutoModelForCausalLM, AutoTokenizer

MODEL_ID = "IFM/K2-Horizon-0.9B"
REVISION = "main"

tokenizer = AutoTokenizer.from_pretrained(
    MODEL_ID,
    revision=REVISION,
    trust_remote_code=True,
)
model = AutoModelForCausalLM.from_pretrained(
    MODEL_ID,
    revision=REVISION,
    dtype=torch.bfloat16,
    trust_remote_code=True,
).to("cuda").eval()

messages = [{"role": "user", "content": "What is the square root of 2?"}]
inputs = tokenizer.apply_chat_template(
    messages,
    add_generation_prompt=True,
    reasoning_effort="high",
    return_dict=True,
    return_tensors="pt",
)
inputs = {name: value.to(model.device) for name, value in inputs.items()}
inputs.pop("token_type_ids", None)

with torch.inference_mode():
    outputs = model.generate(
        **inputs,
        max_new_tokens=50,
        do_sample=False,
        pad_token_id=tokenizer.pad_token_id,
    )

new_tokens = outputs[0, inputs["input_ids"].shape[-1]:]
print(tokenizer.decode(new_tokens, skip_special_tokens=True))
```

</details>

## Hardware Requirements

The BF16 weights occupy approximately 2.0 GiB. One CUDA GPU is sufficient for
short-context inference; 8 GiB is a practical minimum for a one-request smoke
test, while 16 GiB or more provides useful room for longer prompts and runtime
workspaces. The BF16 KV cache is approximately 0.44 GiB per request at 8,192
tokens and approximately 7 GiB at 131,072 tokens, before allocator, activation,
CUDA-graph, and framework overhead. Start with a short context and one sequence,
then increase context length and concurrency from measured memory headroom.

## Repository Contents

The model repository stores the checkpoint directly at its root. It includes:

- `model.safetensors` and `model.safetensors.index.json`
- `config.json`, `generation_config.json`, and the K2 architecture code
- tokenizer files and three chat-template variants
- `README.md` and `LICENSE`

Use `chat_template.jinja` for ordinary chat and OpenAI-compatible serving.
`chat_template_generation.jinja` and `chat_template_asst_tool_gen.jinja` are
specialized generation and assistant-tool-generation variants.

## Training and Evaluation Provenance

- **Training:** multi-teacher on-policy distillation with OPD loss weight 0.1,
  reference-KL weight 0.01, learning rate `1e-7`, and a 500-step schedule. The
  selected checkpoint is step 249.
- **Evaluation:** the AIME, coding, and instruction-following evaluations used
  the training evaluation path with SGLang as the rollout engine. GPQA-Diamond
  was evaluated with Eval360-V2 at revision `f5081bf`.
- **Export:** the distributed training checkpoint was converted to Hugging Face
  safetensors and checked for tensor parity; all 255 expected weight tensors
  matched. The architecture label was later updated from `XllmForCausalLM` to
  `K2HorizonForCausalLM` without changing the weights.

## Limitations

- AIME 2025 remains below the math-and-code teacher, and AIME results have high
  sampling uncertainty because each benchmark contains only 30 problems.
- GPQA-Diamond is statistically close to the pre-distillation base result, so
  the reported run does not demonstrate a clear STEM improvement.
- Long-horizon tool use remains substantially weaker than single-turn tool
  calling in the BFCL v4 breakdown.
- Benchmark scores depend on prompt templates, reasoning effort, sampling
  parameters, framework versions, and evaluation harness details. Validate the
  model on representative prompts before deployment.
- As with other language models, K2-Horizon-0.9B can produce inaccurate,
  biased, or unsafe text. Applications should use task-specific evaluation,
  input and output controls, monitoring, and human review where appropriate.