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Efficient Training of Low-Curvature Neural Networks
Suraj Srinivas · Kyle Matoba · Himabindu Lakkaraju · François Fleuret

Tue Nov 29 02:00 PM -- 04:00 PM (PST) @ Hall J #527

Standard deep neural networks often have excess non-linearity, making them susceptible to issues such as low adversarial robustness and gradient instability. Common methods to address these downstream issues, such as adversarial training, are expensive and often sacrifice predictive accuracy. In this work, we address the core issue of excess non-linearity via curvature, and demonstrate low-curvature neural networks (LCNNs) that obtain drastically lower curvature than standard models while exhibiting similar predictive performance. This leads to improved robustness and stable gradients, at a fraction of the cost of standard adversarial training. To achieve this, we decompose overall model curvature in terms of curvatures and slopes of its constituent layers. To enable efficient curvature minimization of constituent layers, we introduce two novel architectural components: first, a non-linearity called centered-softplus that is a stable variant of the softplus non-linearity, and second, a Lipschitz-constrained batch normalization layer.Our experiments show that LCNNs have lower curvature, more stable gradients and increased off-the-shelf adversarial robustness when compared to standard neural networks, all without affecting predictive performance. Our approach is easy to use and can be readily incorporated into existing neural network architectures.

Author Information

Suraj Srinivas (School of Engineering and Applied Sciences, Harvard University)
Kyle Matoba (EPFL)
Himabindu Lakkaraju (Harvard)
François Fleuret (University of Geneva)

François Fleuret got a PhD in Mathematics from INRIA and the University of Paris VI in 2000, and an Habilitation degree in Mathematics from the University of Paris XIII in 2006. He is Full Professor in the department of Computer Science at the University of Geneva, and Adjunct Professor in the School of Engineering of the École Polytechnique Fédérale de Lausanne. He has published more than 80 papers in peer-reviewed international conferences and journals. He is Associate Editor of the IEEE Transactions on Pattern Analysis and Machine Intelligence, serves as Area Chair for NeurIPS, AAAI, and ICCV, and in the program committee of many top-tier international conferences in machine learning and computer vision. He was or is expert for multiple funding agencies. He is the inventor of several patents in the field of machine learning, and co-founder of Neural Concept SA, a company specializing in the development and commercialization of deep learning solutions for engineering design. His main research interest is machine learning, with a particular focus on computational aspects and sample efficiency.

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