Linwei Tao

Linwei Tao, Minjing Dong, Daochang Liu et al.

Confidence calibration - the process to calibrate the output probability distribution of neural networks - is essential for safety-critical applications of such networks. Recent works verify the link between mis-calibration and overfitting. However, early stopping, as a well-known technique to mitigate overfitting, fails to calibrate networks. In this work, we study the limitions of early stopping and comprehensively analyze the overfitting problem of a network considering each individual block. We then propose a novel regularization method, predecessor combination search (PCS), to improve calibration by searching a combination of best-fitting block predecessors, where block predecessors are the corresponding network blocks with weight parameters from earlier training stages. PCS achieves the state-of-the-art calibration performance on multiple datasets and architectures. In addition, PCS improves model robustness under dataset distribution shift.

Linwei Tao, Younan Zhu, Haolan Guo et al.

Deep neural networks are increasingly utilized in various machine learning tasks. However, as these models grow in complexity, they often face calibration issues, despite enhanced prediction accuracy. Many studies have endeavored to improve calibration performance through the use of specific loss functions, data preprocessing and training frameworks. Yet, investigations into calibration properties have been somewhat overlooked. Our study leverages the Neural Architecture Search (NAS) search space, offering an exhaustive model architecture space for thorough calibration properties exploration. We specifically create a model calibration dataset. This dataset evaluates 90 bin-based and 12 additional calibration measurements across 117,702 unique neural networks within the widely employed NATS-Bench search space. Our analysis aims to answer several longstanding questions in the field, using our proposed dataset: (i) Can model calibration be generalized across different datasets? (ii) Can robustness be used as a calibration measurement? (iii) How reliable are calibration metrics? (iv) Does a post-hoc calibration method affect all models uniformly? (v) How does calibration interact with accuracy? (vi) What is the impact of bin size on calibration measurement? (vii) Which architectural designs are beneficial for calibration? Additionally, our study bridges an existing gap by exploring calibration within NAS. By providing this dataset, we enable further research into NAS calibration. As far as we are aware, our research represents the first large-scale investigation into calibration properties and the premier study of calibration issues within NAS. The project page can be found at https://www.taolinwei.com/calibration-study

Yi-Fan Yeh, Linwei Tao, Minjing Dong et al.

Linguistic cues such as "I believe" and "probably" offer an intuitive interface for communicating confidence, yet a generalisable, principled calibration framework for linguistic confidence expressions remains underexplored. In particular, co-occurring linguistic cues, contextual variation, and subjective audience interpretation pose unique challenges. We therefore model linguistic confidence as a distribution over plausible perceived probability values that a statement is correct, capturing interpretation variability that scalar representations discard. Within this distributional framework, we introduce faithfulness as a complementary evaluation dimension and present Faithfulness Divergence (FD), an information-theoretic metric quantifying the surprise induced in audience beliefs upon truth revelation. Building on these foundations, we present Retrieval-Augmented Linguistic Calibration (RALC), a lightweight post-hoc pipeline that propagates calibrated confidence signals back into natural language via retrieval-augmented rewriting. Across three QA benchmarks and five LLM families, RALC improves in-domain faithfulness and calibration up to 66% and 58%, respectively, outperforming black-box and grey-box calibration baselines.

Linwei Tao, Haoyang Luo, Minjing Dong et al.

Confidence calibration assumes a unique ground-truth label per input, yet this assumption fails wherever annotators genuinely disagree. Post-hoc calibrators fitted on majority-voted labels, the standard single-label targets used in practice, can appear well-calibrated under conventional evaluation yet remain substantially miscalibrated against the underlying annotator distribution. We show that this failure is structural: under simplifying assumptions, Temperature Scaling is biased toward temperatures that underestimate annotator uncertainty, with true-label miscalibration increasing monotonically with annotation entropy. To address this, we develop a family of ambiguity-aware post-hoc calibrators that optimise proper scoring rules against the full label distribution and require no model retraining. Our methods span progressively weaker annotation requirements: Dirichlet-Soft leverages the full annotator distribution and achieves the best overall calibration quality across settings; Monte Carlo Temperature Scaling with a single annotation per example (MCTS S=1) matches full-distribution calibration across all benchmarks, demonstrating that pre-aggregated label distributions are unnecessary; and Label-Smooth Temperature Scaling (LS-TS) operates with voted labels alone by constructing data-driven pseudo-soft targets from the model's own confidence. Experiments on four benchmarks with real multi-annotator distributions (CIFAR-10H, ChaosNLI) and clinically-informed synthetic annotations (ISIC~2019, DermaMNIST) show that Dirichlet-Soft reduces true-label ECE by 55-87% relative to Temperature Scaling, while LS-TS reduces ECE by 9-77% without any annotator data.

Haolan Guo, Linwei Tao, Haoyang Luo et al.

Recent advances in deep learning have significantly improved predictive accuracy. However, modern neural networks remain systematically overconfident, posing risks for deployment in safety-critical scenarios. Current post-hoc calibration methods face a fundamental dilemma: global approaches like Temperature Scaling apply uniform adjustments across all samples, introducing high bias despite computational efficiency, while more expressive methods that operate on full logit distributions suffer from high variance due to noisy high-dimensional inputs and insufficient validation data. To address these challenges, we propose Sample Margin-Aware Recalibration of Temperature (SMART), a lightweight, data-efficient recalibration method that precisely scales logits based on the margin between the top two logits -- termed the logit gap. Specifically, the logit gap serves as a denoised, scalar signal directly tied to decision boundary uncertainty, providing a robust indicator that avoids the noise inherent in high-dimensional logit spaces while preserving model prediction invariance. Meanwhile, SMART employs a novel soft-binned Expected Calibration Error (SoftECE) objective that balances model bias and variance through adaptive binning, enabling stable parameter updates even with extremely limited calibration data. Extensive evaluations across diverse datasets and architectures demonstrate that SMART achieves state-of-the-art calibration performance even with substantially fewer parameters compared to existing parametric methods, offering a principled, robust, and highly efficient solution for practical uncertainty quantification in neural network predictions. The source code is available at: https://anonymous.4open.science/r/SMART-8B11.

Linwei Tao, Minjing Dong, Chang Xu

The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident predictions, which leads to poor calibration. Recent efforts have sought to address this issue by focal loss to reduce over-confidence, but this approach can also lead to under-confident predictions. While different variants of focal loss have been explored, it is difficult to find a balance between over-confidence and under-confidence. In our work, we propose a new loss function by focusing on dual logits. Our method not only considers the ground truth logit, but also take into account the highest logit ranked after the ground truth logit. By maximizing the gap between these two logits, our proposed dual focal loss can achieve a better balance between over-confidence and under-confidence. We provide theoretical evidence to support our approach and demonstrate its effectiveness through evaluations on multiple models and datasets, where it achieves state-of-the-art performance. Code is available at https://github.com/Linwei94/DualFocalLoss

Linwei Tao, Yi-Fan Yeh, Minjing Dong et al.

As large language models (LLMs) are increasingly deployed in high-stakes applications, robust uncertainty estimation is essential for ensuring the safe and trustworthy deployment of LLMs. We present the most comprehensive study to date of uncertainty estimation in LLMs, evaluating 80 models spanning open- and closed-source families, dense and Mixture-of-Experts (MoE) architectures, reasoning and non-reasoning modes, quantization variants and parameter scales from 0.6B to 671B. Focusing on three representative black-box single-pass methods, including token probability-based uncertainty (TPU), numerical verbal uncertainty (NVU), and linguistic verbal uncertainty (LVU), we systematically evaluate uncertainty calibration and selective classification using the challenging MMLU-Pro benchmark, which covers both reasoning-intensive and knowledge-based tasks. Our results show that LVU consistently outperforms TPU and NVU, offering stronger calibration and discrimination while being more interpretable. We also find that high accuracy does not imply reliable uncertainty, and that model scale, post-training, reasoning ability and quantization all influence estimation performance. Notably, LLMs exhibit better uncertainty estimates on reasoning tasks than on knowledge-heavy ones, and good calibration does not necessarily translate to effective error ranking. These findings highlight the need for multi-perspective evaluation and position LVU as a practical tool for improving the reliability of LLMs in real-world settings.

Linwei Tao, Minjing Dong, Chang Xu

Deep neural networks (DNNs) have achieved significant success across various tasks, but ensuring reliable uncertainty estimates, known as model calibration, is crucial for their safe and effective deployment. Modern DNNs often suffer from overconfidence, leading to miscalibration. We propose a novel post-hoc calibration method called feature clipping (FC) to address this issue. FC involves clipping feature values to a specified threshold, effectively increasing entropy in high calibration error samples while maintaining the information in low calibration error samples. This process reduces the overconfidence in predictions, improving the overall calibration of the model. Our extensive experiments on datasets such as CIFAR-10, CIFAR-100, and ImageNet, and models including CNNs and transformers, demonstrate that FC consistently enhances calibration performance. Additionally, we provide a theoretical analysis that validates the effectiveness of our method. As the first calibration technique based on feature modification, feature clipping offers a novel approach to improving model calibration, showing significant improvements over both post-hoc and train-time calibration methods and pioneering a new avenue for feature-based model calibration.

Jinxu Lin, Linwei Tao, Minjing Dong et al.

Model calibration is essential for ensuring that the predictions of deep neural networks accurately reflect true probabilities in real-world classification tasks. However, deep networks often produce over-confident or under-confident predictions, leading to miscalibration. Various methods have been proposed to address this issue by designing effective loss functions for calibration, such as focal loss. In this paper, we analyze its effectiveness and provide a unified loss framework of focal loss and its variants, where we mainly attribute their superiority in model calibration to the loss weighting factor that estimates sample-wise uncertainty. Based on our analysis, existing loss functions fail to achieve optimal calibration performance due to two main issues: including misalignment during optimization and insufficient precision in uncertainty estimation. Specifically, focal loss cannot align sample uncertainty with gradient scaling and the single logit cannot indicate the uncertainty. To address these issues, we reformulate the optimization from the perspective of gradients, which focuses on uncertain samples. Meanwhile, we propose using the Brier Score as the loss weight factor, which provides a more accurate uncertainty estimation via all the logits. Extensive experiments on various models and datasets demonstrate that our method achieves state-of-the-art (SOTA) performance.

Linwei Tao, Haolan Guo, Minjing Dong et al.

Calibration is crucial in deep learning applications, especially in fields like healthcare and autonomous driving, where accurate confidence estimates are vital for decision-making. However, deep neural networks often suffer from miscalibration, with reliability diagrams and Expected Calibration Error (ECE) being the only standard perspective for evaluating calibration performance. In this paper, we introduce the concept of consistency as an alternative perspective on model calibration, inspired by uncertainty estimation literature in large language models (LLMs). We highlight its advantages over the traditional reliability-based view. Building on this concept, we propose a post-hoc calibration method called Consistency Calibration (CC), which adjusts confidence based on the model's consistency across perturbed inputs. CC is particularly effective in locally uncertainty estimation, as it requires no additional data samples or label information, instead generating input perturbations directly from the source data. Moreover, we show that performing perturbations at the logit level significantly improves computational efficiency. We validate the effectiveness of CC through extensive comparisons with various post-hoc and training-time calibration methods, demonstrating state-of-the-art performance on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet, as well as on long-tailed datasets like ImageNet-LT.

Xiaoyang Li, Linwei Tao, Haohui Lu et al.

Graph Neural Networks (GNNs) have demonstrated strong predictive performance on relational data; however, their confidence estimates often misalign with actual predictive correctness, posing significant limitations for deployment in safety-critical settings. While existing graph-aware calibration methods seek to mitigate this limitation, they primarily depend on coarse one-hop statistics, such as neighbor-predicted confidence, or latent node embeddings, thereby neglecting the fine-grained structural heterogeneity inherent in graph topology. In this work, we propose Wavelet-Aware Temperature Scaling (WATS), a post-hoc calibration framework that assigns node-specific temperatures based on tunable heat-kernel graph wavelet features. Specifically, WATS harnesses the scalability and topology sensitivity of graph wavelets to refine confidence estimates, all without necessitating model retraining or access to neighboring logits or predictions. Extensive evaluations across seven benchmark datasets with varying graph structures and two GNN backbones demonstrate that WATS achieves the lowest Expected Calibration Error (ECE) among all compared methods, outperforming both classical and graph-specific baselines by up to 42.3\% in ECE and reducing calibration variance by 17.24\% on average compared with graph-specific methods. Moreover, WATS remains computationally efficient, scaling well across graphs of diverse sizes and densities. Code will be released based on publication.

Yunke Wang, Linwei Tao, Bo Du et al.

Adversarial Imitation Learning (AIL) allows the agent to reproduce expert behavior with low-dimensional states and actions. However, challenges arise in handling visual states due to their less distinguishable representation compared to low-dimensional proprioceptive features. While existing methods resort to adopt complex network architectures or separate the process of learning representation and decision-making, they overlook valuable intra-agent information within demonstrations. To address this problem, this paper proposes a simple and effective solution by incorporating calibrated contrastive representative learning into visual AIL framework. Specifically, we present an image encoder in visual AIL, utilizing a combination of unsupervised and supervised contrastive learning to extract valuable features from visual states. Based on the fact that the improved agent often produces demonstrations of varying quality, we propose to calibrate the contrastive loss by treating each agent demonstrations as a mixed sample. The incorporation of contrastive learning can be jointly optimized with the AIL framework, without modifying the architecture or incurring significant computational costs. Experimental results on DMControl Suite demonstrate our proposed method is sample efficient and can outperform other compared methods from different aspects.