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.
Modern neural networks can achieve high accuracy while remaining poorly calibrated, producing confidence estimates that do not match empirical correctness. Yet calibration is often treated as a post-hoc attribute. We take a different perspective: we study calibration as a training-time phenomenon on small vision tasks, and ask whether calibrated solutions can be obtained reliably by intervening on the training procedure. We identify a tight coupling between calibration, curvature, and margins during training of deep networks under multiple gradient-based methods. Empirically, Expected Calibration Error (ECE) closely tracks curvature-based sharpness throughout optimization. Mathematically, we show that both ECE and Gauss--Newton curvature are controlled, up to problem-specific constants, by the same margin-dependent exponential tail functional along the trajectory. Guided by this mechanism, we introduce a margin-aware training objective that explicitly targets robust-margin tails and local smoothness, yielding improved out-of-sample calibration across optimizers without sacrificing accuracy.
Deep Neural Network (DNN) classifiers suffer from poor calibration when their softmax outputs (predictive confidence) deviate from the empirical likelihoods. This manifests itself as either overconfident incorrect predictions or under-confident correct predictions. Label smoothing (LS) enhances model calibration by introducing entropy regularization during training through redistributing probability mass from the ground-truth label to the remaining classes. LS, including Margin-based LS (MbLS), have restrictive assumptions: they rely on predefined, uniform smoothing rules and only tackle overconfidence. In reality, samples exhibit diverse characteristics, such as difficulty/ambiguity, that interact with the evolving nature of the model being trained. In training, samples may have various degrees of under- or overconfidence. To overcome this, a mechanism that identifies the specific confidence state of each sample and determines the appropriate degree of smoothing in each training step is needed, tailoring the adjustment to the individual sample. We propose FedLAS: Feature-Modulated Bidirectional Label Smoothing, a plug-and-play algorithm for label smoothing-based losses. In FedLAS, we introduce a Feature Norm-based Confidence Indicator (NCI) to control smoothing and a Bidirectional Calibration Gating (BCG) module to detect both over and under-confidence. Our algorithm can be integrated with LS and MbLS based losses when applied to standard DNNs, enhancing performance. Extensive experiments on standard and fine-grained high-resolution vision benchmarks show that FedLAS consistently improves calibration compared to modern baselines, reducing Expected Calibration Error (ECE) and Adaptive ECE while maintaining Top-1 accuracy. Code: github.com/nadarasarbahavan/FEDLAS
Thiru Thillai Nadarasar Bahavan, Sachith Seneviratne, Saman Halgamuge
Existing calibration methods for Large Language Models (LLMs) often overlook a critical dimension of trustworthiness: a model's {\em behavioral robustness} to irrelevant or misleading information. In this paper, we argue that a model's true confidence should reflect its stability under cognitive pressure. We introduce \textsc{CaliDist}, a novel post-hoc calibration approach that directly measures and penalizes a model's susceptibility to distraction. \textsc{CaliDist} quantifies how an LLM's predictions and uncertainty change when its input prompt is perturbed with semantic \textit{distractors}. This stability (or lack thereof) signal is then used to adaptively scale the model's initial confidence score. Our extensive experiments on seven Natural Language Understanding classification benchmarks using six distinct LLMs show that \textsc{CaliDist} consistently achieves lower Expected Calibration Error (ECE) and Brier Score compared with strong baselines. Remarkably, our method reduces the ECE from 23% to 7% on average--a relative improvement of 70%--demonstrating that behavioral stability is a powerful signal for calibration. We make our code and datasets available at github.com/m-anas-j/CaliDist.