# Generalized Fisher-Weighted SVD: Scalable Kronecker-Factored Fisher Approximation for Compressing Large Language Models

arXiv: https://arxiv.org/abs/2505.17974 · HTML: https://mlsanity.com/paper/2505.17974/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Dobi-SVD: Differentiable SVD for LLM Compression and Some New Perspectives](https://mlsanity.com/paper/2502.02723/) (2025)
- [Careful Selection of Knowledge to solve Open Book Question Answering](https://mlsanity.com/paper/1907.10738/) (2019)
- [Basis Sharing: Cross-Layer Parameter Sharing for Large Language Model Compression](https://mlsanity.com/paper/2410.03765/) (2024)
- [An Improved Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/2406.06420/) (2024)
- [Trade-Offs of Diagonal Fisher Information Matrix Estimators](https://mlsanity.com/paper/2402.05379/) (2024)
- [Efficient Approximations of the Fisher Matrix in Neural Networks using Kronecker Product Singular Value Decomposition](https://mlsanity.com/paper/2201.10285/) (2022)
- [BitStack: Any-Size Compression of Large Language Models in Variable Memory Environments](https://mlsanity.com/paper/2410.23918/) (2024)
- [BLAST: Block-Level Adaptive Structured Matrices for Efficient Deep Neural Network Inference](https://mlsanity.com/paper/2410.21262/) (2024)

## Built on by (most cited first, 8 of 8)

- [SAES-SVD: Self-Adaptive Suppression of Accumulated and Local Errors for SVD-based LLM Compression](https://mlsanity.com/paper/2602.03051/) (2026)
- [Low-Rank Prehab: Preparing Neural Networks for SVD Compression](https://mlsanity.com/paper/2512.01980/) (2025)
- [FlashSVD v1.5: Making Low-Rank Transformers Inference Actually Fast](https://mlsanity.com/paper/2605.08314/) (2026)
- [IO-SVD: Input-Output Whitened SVD for Adaptive-Rank LLM Compression](https://mlsanity.com/paper/2605.15626/) (2026)
- [Activation- and Influence-Aware Ranks (AIR): Function-Preserving SVD Compression for LLMs](https://mlsanity.com/paper/2606.19993/) (2026)
- [TaRA: Training-Aware Low-Rank Adaptation Initialization](https://mlsanity.com/paper/2609.02639/) (2026)
- [Mind the Approximation: Fisher-Weighted SVD Compression for ViTs](https://mlsanity.com/paper/2609.07155/) (2026)
- [The Functional Structure of Post-Compression Recovery in Low-Rank LLMs](https://mlsanity.com/paper/2610.05504/) (2026)

## Abstract (arXiv)

The Fisher information is a fundamental concept for characterizing the sensitivity of parameters in neural networks. However, leveraging the full observed Fisher information is too expensive for large models, so most methods rely on simple diagonal approximations. While efficient, this approach ignores parameter correlations, often resulting in reduced performance on downstream tasks. In this work, we mitigate these limitations and propose Generalized Fisher-Weighted SVD (GFWSVD), a post-training LLM compression technique that accounts for both diagonal and off-diagonal elements of the Fisher information matrix, providing a more accurate reflection of parameter importance. To make the method tractable, we introduce a scalable adaptation of the Kronecker-factored approximation algorithm for the observed Fisher information. We demonstrate the effectiveness of our method on LLM compression, showing improvements over existing compression baselines. For example, at a 20 compression rate on the MMLU benchmark, our method outperforms FWSVD, which is based on a diagonal approximation of the Fisher information, by 5 percent, SVD-LLM by 3 percent, and ASVD by 6 percent compression rate.