Distilling reasoning by copying the teacher's token path wastes most of the signal, because intermediate steps are locally under-specified
AspireAI community · arXiv (cs.LG)
Reasoning distillation usually frames the job as trajectory imitation, but global correctness does not uniquely determine each intermediate move. Validity-calibrated distillation instead compares the student's and teacher's proposed next-step actions under the same prefix and uses their relative local validity to modulate the strength of the update, treating distillation as local learning-signal allocation rather than path alignment. The authors report that this beats strong distillation baselines across math, code and instruction-following benchmarks. The honest limit: the abstract frames the win as coming from locally calibrated allocation of learning signal rather than rigid imitation, without a single headline accuracy figure.
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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.