BPM · GLM-Z1-9B → Qwen3.5-2B

arXiv:2607.22334 · Project page

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

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. Research checkpoint, not instruction-tuned for general use.

Citation

@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}, 
}
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