Fiedler Regularization: Learning Neural Networks with Graph Sparsity
This addresses regularization for neural networks by leveraging graph sparsity, offering a novel approach that could improve model efficiency and performance, though it appears incremental as it builds on existing regularization concepts.
The paper tackles the problem of neural network regularization by incorporating graph structure, introducing Fiedler regularization based on spectral graph theory, and shows it outperforms traditional methods like dropout and weight decay in experiments.
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.