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Beyond Scalar Sensitivity: Activation-Aware Mixed-Precision LLM Quantization with Cross-Layer Refinement

arXiv · AI, language, vision and robotics · article · Sep 22, 2026 · UTC

Mixed-precision weight quantization is commonly formulated as a Multiple-Choice Knapsack Problem (MCKP), yet existing solvers rely on scalar sensitivity proxies that collapse each weight matrix's Hessian into a single number and treat every module independently. We prove that even the optimal scalar proxy incurs multiplicative distortion up to $\sqrt{κ(\mathbf{A})κ(\mathbf{B})}$ relative to the full activation-aware quadratic, where $κ(\mathbf{A})$ and $κ(\mathbf{B})$ denote the condition numbers of the input- and output-side Hessian factors. This bound varies from $10^1$ to $10^{13}$ for typi

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