# RicciNets: Curvature-guided Pruning of High-performance Neural Networks Using Ricci Flow

arXiv: https://arxiv.org/abs/2007.04216 · HTML: https://mlsanity.com/paper/2007.04216/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 4 of 4)

- [Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space](https://mlsanity.com/paper/2501.12116/) (2025)
- [Thoughts on the Consistency between Ricci Flow and Neural Network Behavior](https://mlsanity.com/paper/2111.08410/) (2021)
- [Curvature-enhanced Graph Convolutional Network for Biomolecular Interaction Prediction](https://mlsanity.com/paper/2306.13699/) (2023)
- [Application of discrete Ricci curvature in pruning randomly wired neural networks: A case study with chest x-ray classification of COVID-19](https://mlsanity.com/paper/2509.05322/) (2025)

## Abstract (arXiv)

A novel method to identify salient computational paths within randomly wired neural networks before training is proposed. The computational graph is pruned based on a node mass probability function defined by local graph measures and weighted by hyperparameters produced by a reinforcement learning-based controller neural network. We use the definition of Ricci curvature to remove edges of low importance before mapping the computational graph to a neural network. We show a reduction of almost 35% in the number of floating-point operations (FLOPs) per pass, with no degradation in performance. Further, our method can successfully regularize randomly wired neural networks based on purely structural properties, and also find that the favourable characteristics identified in one network generalise to other networks. The method produces networks with better performance under similar compression to those pruned by lowest-magnitude weights. To our best knowledge, this is the first work on pruning randomly wired neural networks, as well as the first to utilize the topological measure of Ricci curvature in the pruning mechanism.