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  • 2022
  • Article
  • Advances in Neural Information Processing Systems (NeurIPS)

Efficiently Training Low-Curvature Neural Networks

By: Suraj Srinivas, Kyle Matoba, Himabindu Lakkaraju and Francois Fleuret
  • Format:Print
  • | Pages:14
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Abstract

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. Code to implement our method and replicate our experiments is available at https://github.com/kylematoba/lcnn.

Keywords

AI and Machine Learning

Citation

Srinivas, Suraj, Kyle Matoba, Himabindu Lakkaraju, and Francois Fleuret. "Efficiently Training Low-Curvature Neural Networks." Advances in Neural Information Processing Systems (NeurIPS) (2022).
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About The Author

Himabindu Lakkaraju

Technology and Operations Management
→More Publications

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More from the Authors
  • When Does Uncertainty Matter? Understanding the Impact of Predictive Uncertainty in ML Assisted Decision Making By: Sean McGrath, Parth Mehta, Alexandra Zytek, Isaac Lage and Himabindu Lakkaraju
  • Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse By: Martin Pawelczyk, Teresa Datta, Johannes van-den-Heuvel, Gjergji Kasneci and Himabindu Lakkaraju
  • On the Privacy Risks of Algorithmic Recourse By: Martin Pawelczyk, Himabindu Lakkaraju and Seth Neel
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