Optimising quantization range, transformation and rounding jointly under one output-sensitivity objective beat separate state-of-the-art methods for both channel-wise and block-wise quantization
AspireAI community · arXiv
Low-bit quantization needs three decisions made at once, which range to use, which linear transformation to apply and how to round weights, and existing approaches optimise each independently against local reconstruction objectives that ignore how much the resulting error actually moves downstream predictions. This work derives a Hessian-guided approximation of the output change caused by joint weight and activation quantization, builds a tractable Fisher approximation on top of it, and formulates a unified post-training quantization framework that optimises all three components under a common output-sensitivity objective. The authors report consistent gains over state-of-the-art transformation and rounding methods in both channel-wise and block-wise settings, and state the method remains practical for modern large language models. The paper reports no absolute bits or latency figures in the abstract.
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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.