LiST: Lipschitz Scaling Training for Robust and Calibrated Neural Networks
Summary
Introduces LiST, a training paradigm that uses Lipschitz constraints to achieve robust and calibrated neural networks, selecting optimal operating points on the accuracy-robustness Pareto front. Demonstrates competitive performance on CIFAR and Tiny-ImageNet.
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# LiST: Lipschitz Scaling Training for Robust and Calibrated Neural Networks Source: [https://arxiv.org/abs/2607.07745](https://arxiv.org/abs/2607.07745) [View PDF](https://arxiv.org/pdf/2607.07745) > Abstract:While accuracy, robustness, and calibration are all essential for reliable neural networks, they are often studied separately; developing models that satisfy all three simultaneously remains a central challenge\. Lipschitz\-constrained models guarantee robustness by design, yet the manual selection of the Lipschitz constraint L governs the resulting accuracy\-robustness trade\-off, and their calibration properties remain largely underexplored\. In this work, we highlight a theoretical and empirical link between the enforced Lipschitz constraint and Temperature Scaling, a state\-of\-the\-art calibration method\. Specifically, we find that for a given training scheme, there exists a non\-trivial value L\* that yields an out\-of\-the\-box calibrated network, and that calibration acts as a principled criterion to select a well\-defined operating point on the accuracy\-robustness Pareto front\. Leveraging these insights, we introduce Lipschitz Scaling Training \(LiST\), a novel training paradigm that iteratively adjusts the global Lipschitz constant to reach this operating point\. Through a margin parameter in the training loss, LiST further enables the construction of a fully calibrated Pareto front, allowing users to navigate the accuracy\-robustness trade\-off while remaining calibrated throughout\. At convergence, LiST also enables the reintegration of calibration data into training, improving sample efficiency without sacrificing calibration\. We validate LiST on CIFAR\-10/100 and Tiny\-ImageNet, demonstrating competitive accuracy and robustness against constrained and unconstrained baselines, while remaining calibrated out of the box\. Code is available at GitHub\. ## Submission history From: Arthur Chiron \[[view email](https://arxiv.org/show-email/7645c942/2607.07745)\] \[via CCSD proxy\] **\[v1\]**Wed, 8 Jul 2026 08:34:01 UTC \(223 KB\)
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