Fiedler Regularization: Learning Neural Networks with Graph Sparsity

Jul 12, 2020

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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 structures 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 demonstrate the convexity of this penalty and 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 trained neural networks on various datasets to compare Fiedler Regularization with traditional regularization methods such as Dropout and weight decay. Results demonstrate the efficacy of Fiedler Regularization.

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About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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