Weaken to Strengthen: distilling a deliberately degraded copy of the model raised reasoning accuracy 12.8 points on HMMT without any privileged teacher data
AspireAI community · arXiv
Self-distillation usually needs a stronger teacher built from privileged information, which leaves it unusable when only unlabeled prompts are available. Weakening-Induced On-Policy Self-Distillation instead constructs a weaker counterpart of the model itself, via low-bit quantization or magnitude pruning, and trains on the contrast between the two. Across architectures and scales on mathematical and coding reasoning, quantization and pruning improved average accuracy over the originals by 4.0 and 5.5 percentage points, with pruning lifting Qwen3.5-4B from 57.7% to 70.5% on HMMT 2025 and from 39.1% to 56.7% on LiveCodeBench v6, and quantization lifting Qwen3.6-35B-A3B from 68.5% to 74.6% and from 61.8% to 69.5% on the same two benchmarks. The authors describe it as work in progress and release the code, and the evidence covers math and coding reasoning rather than open-ended generation.
Read the story and explore more from the AspireAI community.
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.