# Fiedler Regularization: Learning Neural Networks with Graph Sparsity

arXiv: https://arxiv.org/abs/2003.00992 · HTML: https://mlsanity.com/paper/2003.00992/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2020.

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

- [Robust Node Classification on Graphs: Jointly from Bayesian Label Transition and Topology-based Label Propagation](https://mlsanity.com/paper/2208.09779/) (2022)
- [Robust Node Representation Learning via Graph Variational Diffusion Networks](https://mlsanity.com/paper/2312.10903/) (2023)
- [Robust Regularized Locality Preserving Indexing for Fiedler Vector Estimation](https://mlsanity.com/paper/2107.12070/) (2021)
- [Generalizable Spectral Embedding with an Application to UMAP](https://mlsanity.com/paper/2501.11305/) (2025)
- [Sparse Graph Learning from Sparse Data via Fiedler Number Maximization](https://mlsanity.com/paper/2604.26132/) (2026)
- [A Novel Sparse Regularizer](https://mlsanity.com/paper/2301.07285/) (2023)
- [Spectral Gap Regularization of Neural Networks](https://mlsanity.com/paper/2304.03096/) (2023)
- [Omega-S: A Functional Resilience Index for LLM Fine-Tuning](https://mlsanity.com/paper/2608.03887/) (2026)

## Abstract (arXiv)

We introduce a novel regularization approach for deep learning that incorporates and respects the underlying graphical structure of the neural network. Existing regularization methods often focus on dropping/penalizing weights in a global manner that ignores the connectivity structure of the neural network. We propose to use the Fiedler value of the neural network's underlying graph as a tool for regularization. We provide theoretical support for this approach via spectral graph theory. We list several useful properties of the Fiedler value that makes it suitable in regularization. We provide an approximate, variational approach for fast computation in practical training of neural networks. We provide bounds on such approximations. We provide an alternative but equivalent formulation of this framework in the form of a structurally weighted L1 penalty, thus linking our approach to sparsity induction. We performed experiments on datasets that compare Fiedler regularization with traditional regularization methods such as dropout and weight decay. Results demonstrate the efficacy of Fiedler regularization.