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.
Table with columns: Model, AIME 2026, HMMT 2026, MATH-500, HumanEval+, LiveCodeBench, TACO, Avg| 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},
}