# Mind the Approximation: Fisher-Weighted SVD Compression for ViTs

arXiv: https://arxiv.org/abs/2609.07155 · HTML: https://mlsanity.com/paper/2609.07155/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 60 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
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- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [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)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Unified Perceptual Parsing for Scene Understanding](https://mlsanity.com/paper/1807.10221/) (2018)
- [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)
- [MambaVision: A Hybrid Mamba-Transformer Vision Backbone](https://mlsanity.com/paper/2407.08083/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Run, Don't Walk: Chasing Higher FLOPS for Faster Neural Networks](https://mlsanity.com/paper/2303.03667/) (2023)
- [Global Vision Transformer Pruning with Hessian-Aware Saliency](https://mlsanity.com/paper/2110.04869/) (2021)
- [SVD-LLM V2: Optimizing Singular Value Truncation for Large Language Model Compression](https://mlsanity.com/paper/2503.12340/) (2025)
- [A New Perspective on Shampoo's Preconditioner](https://mlsanity.com/paper/2406.17748/) (2024)
- [MaskLLM: Learnable Semi-Structured Sparsity for Large Language Models](https://mlsanity.com/paper/2409.17481/) (2024)
- [Kronecker-Factored Approximate Curvature for Modern Neural Network Architectures](https://mlsanity.com/paper/2311.00636/) (2023)
- [Dobi-SVD: Differentiable SVD for LLM Compression and Some New Perspectives](https://mlsanity.com/paper/2502.02723/) (2025)
- [Quantization without Tears](https://mlsanity.com/paper/2411.13918/) (2024)
- [DISP-LLM: Dimension-Independent Structural Pruning for Large Language Models](https://mlsanity.com/paper/2410.11988/) (2024)
- [Isomorphic Pruning for Vision Models](https://mlsanity.com/paper/2407.04616/) (2024)
- [COMCAT: Towards Efficient Compression and Customization of Attention-Based Vision Models](https://mlsanity.com/paper/2305.17235/) (2023)
- [PELA: Learning Parameter-Efficient Models with Low-Rank Approximation](https://mlsanity.com/paper/2310.10700/) (2023)

## Abstract (arXiv)

Model compression is key to mitigate deployment challenges of ever growing machine learning models. In this area of research, singular value decomposition (SVD)-based compression offers a compelling trade-off between computational efficiency and model accuracy. Fisher-weighted SVD in particular provides principled, loss-aware compression. However, we find that improving the fidelity of Fisher approximation used in the compression is poorly predictive of post-compression accuracy for Vision Transformers (ViTs). Motivated by this observation, we propose FACTS, a structured Fisher Approximation tailored to Compressing ViTs with Fisher-weighted SVD, which enforces token-local aggregation while preserving within-token activation-gradient dependence. Additionally, we introduce a fast Constrained Rank Search (CoRS), that optimizes layer-wise rank allocation while adhering to a fixed floating point operation (FLOP) constraint. Extensive experiments across ViTs and hybrid architectures demonstrate that FACTS consistently improves accuracy-efficiency trade-offs without requiring finetuning. Notably, it outperforms the strongest SVD baseline by up to +5.8 percentage points (p.p.) Top-1 on Swin-B, with further gains driven by our search method. Code is available at https://github.com/MoritzTho/FACTS.