Teacher-written segments in on-policy distillation made no measurable difference
AspireAI community · arXiv
Some on-policy distillation methods insert teacher-written segments - bridges - into student responses, and the methods disagree on how to train on those tokens. This paper compares no loss, forward KL and reverse KL on identical trajectories, with Qwen3-1.7B as student and Qwen3-4B-Instruct-2507 as teacher, separating gradients by which model wrote each token. The result is a well-designed null: under short training runs and BF16 inference, pre-specified tests detected no added accuracy benefit from teacher text as context or as a training target. A one-paragraph bridge after the student's first paragraph is about 2.7% of the tokens and contributes a small gradient nearly orthogonal to the student-token gradient, and the three loss treatments gave statistically equivalent accuracy within a plus or minus 5 percentage-point margin. An exploratory pilot suggested a benefit that a pre-specified replication did not confirm. The authors bound the finding themselves: BF16 inference rounds away most small weight changes, and in exact FP32 the replication models frequently hit the response-length limit.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.