---
license: apache-2.0
library_name: transformers
pipeline_tag: text-generation
base_model: Qwen/Qwen3.5-2B
language:
  - en
tags:
  - on-policy-distillation
  - cross-tokenizer
  - knowledge-distillation
  - mathematics
  - code
---

# BPM · GLM-Z1-9B → Qwen3.5-2B

[arXiv:2607.22334](https://arxiv.org/abs/2607.22334) · [Project page](https://bpm-opd.github.io/)

Qwen3.5-2B distilled from GLM-Z1-9B-0414 with **BPM** (Byte-Prefix Marginalization), a
cross-tokenizer on-policy distillation method. Forward-KL arm, step 149.

## Results

Every cell is `avg@8 / pass@8`, matching Table 1 of the paper. Sampling: temperature 0.6,
top-p 0.95, top-k 20, 8 samples per prompt, thinking enabled.

| Model | AIME 2026 | HMMT 2026 | MATH-500 | HumanEval+ | LiveCodeBench | TACO | **Avg** |
|---|---|---|---|---|---|---|---|
| GLM-Z1-9B-0414 *(teacher)* | 63.3 / 90.0 | 33.3 / 48.5 | 92.3 / 97.4 | 89.8 / 96.9 | 45.6 / 63.2 | 53.5 / 64.0 | 63.0 / 76.7 |
| Qwen3.5-2B *(base)* | 7.5 / 26.7 | 10.6 / 18.2 | 60.5 / 84.6 | 52.5 / 84.0 | 11.6 / 17.6 | 5.3 / 11.7 | 24.7 / 40.5 |
| SimCT | 15.8 / 30.0 | 12.5 / 27.3 | 58.6 / 89.2 | 50.2 / 78.5 | 12.6 / 23.6 | 8.4 / 21.2 | 26.3 / 45.0 |
| ULD | 17.5 / 40.0 | 12.5 / 24.2 | 81.2 / 94.4 | 66.0 / 88.3 | 15.8 / 25.8 | 12.4 / 27.2 | 34.2 / 50.0 |
| GOLD | 22.1 / 53.3 | 17.4 / 33.3 | 81.8 / 96.4 | 63.0 / 89.0 | 9.0 / 23.6 | 4.8 / 15.5 | 33.0 / 51.9 |
| SeqKD | 23.3 / 50.0 | 14.8 / 27.3 | 74.4 / 93.4 | 60.1 / 87.1 | 20.1 / 31.3 | 16.8 / 34.3 | 34.9 / 53.9 |
| **BPM** | **35.4** / **63.3** | **21.2** / **36.4** | **84.8** / **95.4** | **68.8** / **91.4** | **22.3** / **33.5** | **16.5** / **36.4** | **41.5** / **59.4** |

## Usage

```python
from transformers import AutoModelForCausalLM, AutoTokenizer

tok   = AutoTokenizer.from_pretrained("K1zE/BPM")
model = AutoModelForCausalLM.from_pretrained("K1zE/BPM", dtype="auto", device_map="auto")

msgs = [{"role": "user", "content": "What is the remainder of 7^100 modulo 13?"}]
ids  = tok.apply_chat_template(msgs, add_generation_prompt=True, return_tensors="pt").to(model.device)
print(tok.decode(model.generate(ids, max_new_tokens=2048)[0][ids.shape[-1]:], skip_special_tokens=True))
```

Prompts: [K1zE/BPM](https://huggingface.co/datasets/K1zE/BPM). Research checkpoint, not
instruction-tuned for general use.

## Citation

```bibtex
@misc{wang2026crosstokenizeronpolicydistillationbyteprefix,
      title={Cross-Tokenizer On-Policy Distillation via Byte-Prefix Marginalization}, 
      author={Hao Wang and Kun Yuan and Wenlin Zhong and Minglei Zhang and Han Xiao and Ming Sun and Honggang Qi},
      year={2026},
      eprint={2607.22334},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2607.22334}, 
}
```