Scalable Kronecker-Fisher Approximation: Efficient Hessian Analysis for Billion-Parameter Language Models Compression
cs.LG, cs.AI, cs.CL
Submitted: 2026-09-02
Updated: 2026-09-02
License: http://creativecommons.org/licenses/by/4.0/
The gist: In this paper, we propose a scalable Kronecker-based approximation that captures cross-layer interactions without storing the entire Fisher matrix, enabling practical Hessian analysis for
Terminology
Abstract
In this paper, we propose a scalable Kronecker-based approximation that captures cross-layer interactions without storing the entire Fisher matrix, enabling practical Hessian analysis for billion-parameter networks where full computation is infeasible. Our approach reveals consistent vulnerability patterns: value projection layers exhibit the highest sensitivity and strongest cross-layer correlations across multiple model families, while other components exhibit architecture-specific behaviors. Through extensive experiments on quantization, sparsification, inter-layer corruption, and post-corruption fine-tuning, we demonstrate that our approximation strongly correlates with both performance degradation and recovery. Our framework provides a practical, theoretically grounded tool for identifying fragile components in large models, opening new avenues for guided compression and optimization strategies, such as mixed-precision allocation, layer-wise sparsity, and adaptive low-rank decomposition across layers and even individual weight groups.
Sources
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