Scalable Kronecker-Fisher Approximation: Efficient Hessian Analysis for Billion-Parameter Language Models Compression

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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2609.02451 [cs.LG]

(or arXiv:2609.02451v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.02451 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.