LiST: Lipschitz Scaling Training for Robust and Calibrated Neural Networks

arXiv cs.LG Papers

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.

arXiv:2607.07745v1 Announce Type: new 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.
Original Article
View Cached Full Text

Cached at: 07/10/26, 06:14 AM

# 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 \(223 KB\)

Similar Articles

Beyond Surface Statistics: Robust Conformal Prediction for LLMs via Internal Representations

arXiv cs.CL

This paper proposes a conformal prediction framework for LLMs that leverages internal representations rather than output-level statistics, introducing Layer-Wise Information (LI) scores as nonconformity measures to improve validity-efficiency trade-offs under distribution shift. The method demonstrates stronger robustness to calibration-deployment mismatch compared to text-level baselines across QA benchmarks.

Scaling laws for neural language models

OpenAI Blog

Foundational empirical study demonstrating power-law scaling relationships between language model performance and model size, dataset size, and compute budget, with implications for optimal training allocation and sample efficiency.

Scaling Closed-Loop Feature Channel Configuration with LLMs

arXiv cs.LG

This paper scales a closed-loop LLM-based channel configuration search to 250 candidates per cycle, showing positive accuracy trends and improved parameter efficiency on CIFAR-100, and revealing architectural regularities in LLM-generated channel priors.