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. 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}, 
}