# Post-Training Neural Network Pruning using Graph Curvature

arXiv: https://arxiv.org/abs/2601.16366 · HTML: https://mlsanity.com/paper/2601.16366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 27 of 27)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [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)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [LLM-Pruner: On the Structural Pruning of Large Language Models](https://mlsanity.com/paper/2305.11627/) (2023)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [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)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [Everybody Prune Now: Structured Pruning of LLMs with only Forward Passes](https://mlsanity.com/paper/2402.05406/) (2024)
- [Where is the Information in a Deep Neural Network?](https://mlsanity.com/paper/1905.12213/) (2019)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [What Matters In The Structured Pruning of Generative Language Models?](https://mlsanity.com/paper/2302.03773/) (2023)
- [Ricci Curvature of the Internet Topology](https://mlsanity.com/paper/1501.04138/) (2015)
- [No Free Prune: Information-Theoretic Barriers to Pruning at Initialization](https://mlsanity.com/paper/2402.01089/) (2024)
- [Neuron-based Multifractal Analysis of Neuron Interaction Dynamics in Large Models](https://mlsanity.com/paper/2402.09099/) (2024)
- [Measuring Road Network Topology Vulnerability by Ricci Curvature](https://mlsanity.com/paper/1811.05743/) (2018)
- [Flow of Information in Feed-Forward Deep Neural Networks](https://mlsanity.com/paper/1603.06220/) (2016)
- [Analyzing Neural Network Robustness Using Graph Curvature](https://mlsanity.com/paper/2410.19607/) (2024)
- [Modeling Information Flow Through Deep Neural Networks](https://mlsanity.com/paper/1712.00003/) (2017)

## Abstract (arXiv)

This paper provides a fresh view of the neural network (NN) pruning problem through the lens of graph theory. To achieve effective pruning, we aim to identify the main NN data flows and the corresponding NN connections that are most and least important for the performance of the full model. Unlike the standard approach to NN data flow analysis, which is based on information theory, we employ the notion of graph curvature, specifically Ollivier-Ricci curvature (ORC). ORC has been successfully used to identify important graph edges in various domains such as road traffic analysis, biological networks, and social networks. In particular, edges with negative ORC are considered bottlenecks and are therefore critical to the graph's overall connectivity, whereas positive-ORC edges are less essential. We use this intuition for NNs to (1) construct a graph induced by the NN structure and introduce the notion of neural curvature (NC) based on ORC; (2) calculate curvatures based on activation patterns for a set of input examples; and (3) demonstrate that NC can be used to rank edges according to their importance for overall NN functionality. We evaluate our method through pruning experiments on a variety of small and medium size models trained on three image datasets: MNIST, CIFAR-10, and CIFAR-100. The results indicate that our method can identify a larger number of unimportant edges compared to existing pruning methods.