On-policy distillation (OPD) offers a promising way to transfer reasoning capabilities from stronger teacher models, but applying it to long-context reasoning teachers and short-context students introduces practical challenges, including tokenizer mismatch, teacher-student distribution mismatch, response length explosion, and training instability. In this work, we study this setting by transferring proof-reasoning capabilities from the long-context reasoning model SU-01 to short-context student models. To handle tokenizer differences, we perform OPD in a shared text space and align only tokens that occupy identical text spans under the student and teacher tokenizers. To mitigate the problem of excessive generation length and frequent truncation, we introduce a student reference KL loss and mask the advantages of special termination tokens such as </think> and <|im_end|>. This strategy constrains the student from drifting excessively from its initial policy, thereby mitigating the teacher-student distribution mismatch problem and fostering steady length growth. Experiments on both same-family and different-family student models, including Qwen3, Qwen3.5, Intern-S2, GLM-4.7, Gemma-4, show consistent gains in mathematical reasoning, especially natural-language math proving. Notably, Intern-S2-Preview improves by 21.2 points on ProofBench, reaching 55.2 and surpassing Gemini-2.5-Pro. It also improves on science benchmarks such as HLE and HiPhO, suggesting that OPD transfers reasoning capabilities that generalize beyond the mathematical training domain.
Deepseek's Engram, a conditional memory module, was introduced to trade-off storage versus reasoning in large language models. However, the module relies on token-level $N$-gram hashing for Engram embedding lookup, introducing a tight coupling to the tokenizer used: a model with a different tokenizer would have to train its own Engram embeddings from scratch. To improve the reusability of Engram embeddings, we propose a change to the hashing routine, enabling compatibility between Engram models using different tokenizers. Instead of modelling disjoint $N$-gram spaces, we treat $N$-gram as a method to sample potentially useful byte sequences, from all possible byte sequences across tokens. We replace the XOR-based hashing with the general polynomial hashing with a joint embedding space across $N$. This work investigates the possible trade-offs and shows that this simple substitution produces comparable performance and achieves tokenizer-agnosticism: hash equivalence for byte-equivalent token sequences.