# Optimal Pruning for Neural Architectures using Fisher Information Distances

arXiv: https://arxiv.org/abs/2609.16129 · HTML: https://mlsanity.com/paper/2609.16129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Faster gaze prediction with dense networks and Fisher pruning](https://mlsanity.com/paper/1801.05787/) (2018)
- [Bayesian Renormalization](https://mlsanity.com/paper/2305.10491/) (2023)
- [The Inverse of Exact Renormalization Group Flows as Statistical Inference](https://mlsanity.com/paper/2212.11379/) (2022)
- [On the Dynamics of Inference and Learning](https://mlsanity.com/paper/2204.12939/) (2022)
- [Bayesian RG Flow in Neural Network Field Theories](https://mlsanity.com/paper/2405.17538/) (2024)
- [NCoder -- A Quantum Field Theory approach to encoding data](https://mlsanity.com/paper/2402.00944/) (2024)
- [Grokking vs. Learning: Same Features, Different Encodings](https://mlsanity.com/paper/2502.01739/) (2025)

## Abstract (arXiv)

A new scheme for parameter pruning is introduced, derived from the differential-geometric distance in model space. Pruning a parameter sets its value to zero, representing a displacement of the model to the hypersurface on which that parameter vanishes. The minimal distance from the unpruned model to this hypersurface is naturally computed via the geodesic distance in the model space as determined by the Fisher information metric. This distance determines the true change in the model, and its performance, under pruning. By analysing progressively more faithful approximations of this geodesic distance a natural hierarchy of optimality for pruning methods is determined. This starts with the traditional magnitude pruning, then develops into new more sophisticated and effective pruning schemes. The method is demonstrated for both fully-connected networks and vision transformers, on MNIST and CIFAR-10, over the complete 0-100% pruning range and across five random seeds. It outperforms pruning by parameter magnitude and by the local Fisher information alone in every architecture and dataset combination considered, on both accuracy and the Matthews correlation coefficient. Additionally, analysis of different levels of geodesic approximation produces intermediate pruning schemes that are computationally efficient and maintain near-optimal performance. This geometric picture supplies not only a state-of-the-art pruning methodology for AI models, but also a verified and mathematically-motivated justification for pruning schemes.