Daily Papers

Mixture-of-Experts (MoE) models have emerged as a cornerstone of large-scale deep learning by efficiently distributing computation and enhancing performance. However, their unique architecture-characterized by sparse expert activation and dynamic routing mechanisms-introduces inherent complexities that challenge conventional quantization techniques. Existing post-training quantization (PTQ) methods struggle to address activation outliers, router consistency and sparse expert calibration, leading to significant performance degradation. To bridge this gap, we propose EAQuant, a novel PTQ framework tailored for MoE architectures. Our method systematically tackles these challenges through three key innovations: (1) expert-aware smoothing aggregation to suppress activation outliers and stabilize quantization, (2) router logits distribution alignment to preserve expert selection consistency post-quantization, and (3) expert-level calibration data balance to optimize sparsely activated experts. Extensive experiments across W4A4 and extreme W3A4 quantization configurations demonstrate that EAQuant significantly outperforms existing methods, achieving average score improvements of 1.15 - 2.28% across three diverse MoE architectures, with particularly pronounced gains in reasoning tasks and robust performance retention under aggressive quantization. By integrating these innovations, EAQuant establishes a new state-of-the-art for high-precision, efficient MoE model compression. Our code is available at https://github.com/darren-fzq/EAQuant.

Large language model (LLM)-based agents have shown promise in tackling complex tasks by interacting dynamically with the environment. Existing work primarily focuses on behavior cloning from expert demonstrations or preference learning through exploratory trajectory sampling. However, these methods often struggle to address long-horizon tasks, where suboptimal actions accumulate step by step, causing agents to deviate from correct task trajectories. To address this, we highlight the importance of timely calibration and the need to automatically construct calibration trajectories for training agents. We propose Step-Level Trajectory Calibration (STeCa), a novel framework for LLM agent learning. Specifically, STeCa identifies suboptimal actions through a step-level reward comparison during exploration. It constructs calibrated trajectories using LLM-driven reflection, enabling agents to learn from improved decision-making processes. We finally leverage these calibrated trajectories with successful trajectories for reinforced training. Extensive experiments demonstrate that STeCa significantly outperforms existing methods. Further analysis highlights that timely calibration enables agents to complete tasks with greater robustness. Our code and data are available at https://github.com/WangHanLinHenry/STeCa.

A well-calibrated model should express confidence that matches its actual accuracy -- when it claims 80\% confidence, it should be correct 80\% of the time. While large language models (LLMs) have achieved remarkable performance across diverse tasks, their epistemic calibration remains poorly understood. We introduce KalshiBench, a benchmark of 300 prediction market questions from Kalshi, a CFTC-regulated exchange, with verifiable real-world outcomes occurring after model training cutoffs. Unlike traditional benchmarks measuring accuracy on static knowledge, KalshiBench evaluates whether models can appropriately quantify uncertainty about genuinely unknown future events. We evaluate five frontier models -- Claude Opus 4.5, GPT-5.2, DeepSeek-V3.2, Qwen3-235B, and Kimi-K2 -- and find systematic overconfidence across all models. Even the best-calibrated model (Claude Opus 4.5, ECE=0.120) shows substantial calibration errors, while reasoning-enhanced models like GPT-5.2-XHigh exhibit worse calibration (ECE=0.395) despite comparable accuracy. Critically, only one model achieves a positive Brier Skill Score, indicating most models perform worse than simply predicting base rates. Our findings suggest that scaling and enhanced reasoning do not automatically confer calibration benefits, highlighting epistemic calibration as a distinct capability requiring targeted development.

Confidence calibration -- the problem of predicting probability estimates representative of the true correctness likelihood -- is important for classification models in many applications. We discover that modern neural networks, unlike those from a decade ago, are poorly calibrated. Through extensive experiments, we observe that depth, width, weight decay, and Batch Normalization are important factors influencing calibration. We evaluate the performance of various post-processing calibration methods on state-of-the-art architectures with image and document classification datasets. Our analysis and experiments not only offer insights into neural network learning, but also provide a simple and straightforward recipe for practical settings: on most datasets, temperature scaling -- a single-parameter variant of Platt Scaling -- is surprisingly effective at calibrating predictions.

Mixture-of-Experts (MoE) has demonstrated promising potential in scaling LLMs. However, it is hindered by two critical challenges: (1) substantial GPU memory consumption to load all experts; (2) low activated parameters cannot be equivalently translated into inference acceleration effects. In this work, we propose EAC-MoE, an Expert-Selection Aware Compressor for MoE-LLMs, which deeply aligns with the characteristics of MoE from the perspectives of quantization and pruning, and introduces two modules to address these two challenges respectively: (1) The expert selection bias caused by low-bit quantization is a major factor contributing to the performance degradation in MoE-LLMs. Based on this, we propose Quantization with Expert-Selection Calibration (QESC), which mitigates the expert selection bias by calibrating the routers within the MoE; (2) There are always certain experts that are not crucial for the corresponding tasks, yet causing inference latency. Therefore, we propose Pruning based on Expert-Selection Frequency (PESF), which significantly improves inference speed by pruning less frequently used experts for current task. Extensive experiments demonstrate that our approach significantly reduces memory usage and improves inference speed with minimal performance degradation.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model calibration, the rigorous statistical evaluation of model calibration remains less explored. In this work, we develop confidence intervals the ell_2 Expected Calibration Error (ECE). We consider top-1-to-k calibration, which includes both the popular notion of confidence calibration as well as full calibration. For a debiased estimator of the ECE, we show asymptotic normality, but with different convergence rates and asymptotic variances for calibrated and miscalibrated models. We develop methods to construct asymptotically valid confidence intervals for the ECE, accounting for this behavior as well as non-negativity. Our theoretical findings are supported through extensive experiments, showing that our methods produce valid confidence intervals with shorter lengths compared to those obtained by resampling-based methods.

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.

As LLM-based judges become integral to industry applications, obtaining well-calibrated uncertainty estimates efficiently has become critical for production deployment. However, existing techniques, such as verbalized confidence and multi-generation methods, are often either poorly calibrated or computationally expensive. We introduce linear probes trained with a Brier score-based loss to provide calibrated uncertainty estimates from reasoning judges' hidden states, requiring no additional model training. We evaluate our approach on both objective tasks (reasoning, mathematics, factuality, coding) and subjective human preference judgments. Our results demonstrate that probes achieve superior calibration compared to existing methods with approx10x computational savings, generalize robustly to unseen evaluation domains, and deliver higher accuracy on high-confidence predictions. However, probes produce conservative estimates that underperform on easier datasets but may benefit safety-critical deployments prioritizing low false-positive rates. Overall, our work demonstrates that interpretability-based uncertainty estimation provides a practical and scalable plug-and-play solution for LLM judges in production.

Large language models (LLMs) have demonstrated remarkable capabilities out of box for a wide range of applications, yet accuracy still remains a major growth area, especially in mission-critical domains such as biomedicine. An effective method to calibrate the confidence level on LLM responses is essential to automatically detect errors and facilitate human-in-the-loop verification. An important source of calibration signals stems from expert-stipulated programmatic supervision, which is often available at low cost but has its own limitations such as noise and coverage. In this paper, we introduce a Pareto optimal self-supervision framework that can leverage available programmatic supervision to systematically calibrate LLM responses by producing a risk score for every response, without any additional manual efforts. This is accomplished by learning a harmonizer model to align LLM output with other available supervision sources, which would assign higher risk scores to more uncertain LLM responses and facilitate error correction. Experiments on standard relation extraction tasks in biomedical and general domains demonstrate the promise of this approach, with our proposed risk scores highly correlated with the real error rate of LLMs. For the most uncertain test instances, dynamic prompting based on our proposed risk scores results in significant accuracy improvement for off-the-shelf LLMs, boosting GPT-3 results past state-of-the-art (SOTA) weak supervision and GPT-4 results past SOTA supervised results on challenging evaluation datasets.

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications and in particular safety-critical ones. In this work we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for calibration of a regression uncertainty [Kuleshov et al. 2018] has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Quantifying the uncertainty of predictions made by large language models (LLMs) in binary text classification tasks remains a challenge. Calibration, in the context of LLMs, refers to the alignment between the model's predicted probabilities and the actual correctness of its predictions. A well-calibrated model should produce probabilities that accurately reflect the likelihood of its predictions being correct. We propose a novel approach that utilizes the inductive Venn--Abers predictor (IVAP) to calibrate the probabilities associated with the output tokens corresponding to the binary labels. Our experiments on the BoolQ dataset using the Llama 2 model demonstrate that IVAP consistently outperforms the commonly used temperature scaling method for various label token choices, achieving well-calibrated probabilities while maintaining high predictive quality. Our findings contribute to the understanding of calibration techniques for LLMs and provide a practical solution for obtaining reliable uncertainty estimates in binary question answering tasks, enhancing the interpretability and trustworthiness of LLM predictions.

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.

A probabilistic classifier with reliable predictive uncertainties i) fits successfully to the target domain data, ii) provides calibrated class probabilities in difficult regions of the target domain (e.g.\ class overlap), and iii) accurately identifies queries coming out of the target domain and rejects them. We introduce an original combination of Evidential Deep Learning, Neural Processes, and Neural Turing Machines capable of providing all three essential properties mentioned above for total uncertainty quantification. We observe our method on five classification tasks to be the only one that can excel all three aspects of total calibration with a single standalone predictor. Our unified solution delivers an implementation-friendly and compute efficient recipe for safety clearance and provides intellectual economy to an investigation of algorithmic roots of epistemic awareness in deep neural nets.

The fusion of LiDARs and cameras has been increasingly adopted in autonomous driving for perception tasks. The performance of such fusion-based algorithms largely depends on the accuracy of sensor calibration, which is challenging due to the difficulty of identifying common features across different data modalities. Previously, many calibration methods involved specific targets and/or manual intervention, which has proven to be cumbersome and costly. Learning-based online calibration methods have been proposed, but their performance is barely satisfactory in most cases. These methods usually suffer from issues such as sparse feature maps, unreliable cross-modality association, inaccurate calibration parameter regression, etc. In this paper, to address these issues, we propose CalibFormer, an end-to-end network for automatic LiDAR-camera calibration. We aggregate multiple layers of camera and LiDAR image features to achieve high-resolution representations. A multi-head correlation module is utilized to identify correlations between features more accurately. Lastly, we employ transformer architectures to estimate accurate calibration parameters from the correlation information. Our method achieved a mean translation error of 0.8751 cm and a mean rotation error of 0.0562 ^{circ} on the KITTI dataset, surpassing existing state-of-the-art methods and demonstrating strong robustness, accuracy, and generalization capabilities.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Tool-using agents that act in the world need to be both useful and safe. Well-calibrated model confidences can be used to weigh the risk versus reward of potential actions, but prior work shows that many models are poorly calibrated. Inspired by interpretability literature exploring the internals of models, we propose a novel class of model-internal confidence estimators (MICE) to better assess confidence when calling tools. MICE first decodes from each intermediate layer of the language model using logitLens and then computes similarity scores between each layer's generation and the final output. These features are fed into a learned probabilistic classifier to assess confidence in the decoded output. On the simulated trial and error (STE) tool-calling dataset using Llama3 models, we find that MICE beats or matches the baselines on smoothed expected calibration error. Using MICE confidences to determine whether to call a tool significantly improves over strong baselines on a new metric, expected tool-calling utility. Further experiments show that MICE is sample-efficient, can generalize zero-shot to unseen APIs, and results in higher tool-calling utility in scenarios with varying risk levels. Our code is open source, available at https://github.com/microsoft/mice_for_cats.

Uncertainty estimation is a significant issue for current large language models (LLMs) that are generally poorly calibrated and over-confident, especially with reinforcement learning from human feedback (RLHF). Unlike humans, whose decisions and confidences not only stem from intrinsic beliefs but can also be adjusted through daily observations, existing calibration methods for LLMs focus on estimating or eliciting individual confidence without taking full advantage of the "Collective Wisdom": the interaction among multiple LLMs that can collectively improve both accuracy and calibration. In this work, we propose Collaborative Calibration, a post-hoc training-free calibration strategy that leverages the collaborative and expressive capabilities of multiple tool-augmented LLM agents in a simulated group deliberation process. We demonstrate the effectiveness of Collaborative Calibration on generative QA tasks across various domains, showing its potential in harnessing the rationalization of collectively calibrated confidence assessments and improving the reliability of model predictions.

When answering questions, LLMs can convey not only an answer, but a level of confidence about the answer being correct. This includes explicit confidence markers (e.g. giving a numeric score) as well as implicit markers, like an authoritative tone or elaborating with additional knowledge. For LLMs to be trustworthy knowledge sources, the confidence they convey should match their actual expertise; however, most current models tend towards overconfidence. To calibrate both implicit and explicit confidence markers, we introduce a pragmatic, listener-aware finetuning method (LACIE) that models the listener, considering not only whether an answer is right, but whether it will be accepted by a listener. We cast calibration as preference optimization, creating data via a two-agent game, where a speaker model's outputs are judged by a simulated listener. We then finetune three LLMs (Mistral-7B, Llama3-8B, Llama3-70B) with LACIE, and show that the resulting models are better calibrated w.r.t. a simulated listener. Crucially, these trends transfer to human listeners, helping them correctly predict model correctness: we conduct a human evaluation where annotators accept or reject an LLM's answers, finding that training with LACIE results in 47% fewer incorrect answers being accepted while maintaining the same level of acceptance for correct answers. Furthermore, LACIE generalizes to another dataset, resulting in a large increase in truthfulness on TruthfulQA when trained on TriviaQA. Our analysis indicates that LACIE leads to a better confidence separation between correct and incorrect examples. Qualitatively, we find that a LACIE-trained model hedges more and implicitly signals certainty when it is correct by using an authoritative tone or including details. Finally, LACIE finetuning leads to an emergent increase in model abstention (e.g. saying "I don't know") for answers that are likely wrong.

Deep clustering has exhibited remarkable performance; however, the overconfidence problem, i.e., the estimated confidence for a sample belonging to a particular cluster greatly exceeds its actual prediction accuracy, has been overlooked in prior research. To tackle this critical issue, we pioneer the development of a calibrated deep clustering framework. Specifically, we propose a novel dual-head deep clustering pipeline that can effectively calibrate the estimated confidence and the actual accuracy. The calibration head adjusts the overconfident predictions of the clustering head using regularization methods, generating prediction confidence and pseudo-labels that match the model learning status. This calibration process also guides the clustering head in dynamically selecting reliable high-confidence samples for training. Additionally, we introduce an effective network initialization strategy that enhances both training speed and network robustness. Extensive experiments demonstrate the proposed calibrated deep clustering framework not only surpasses state-of-the-art deep clustering methods by approximately 10 times in terms of expected calibration error but also significantly outperforms them in terms of clustering accuracy.

Machine learning models are widely used, but can also often be wrong. Users would benefit from a reliable indication of whether a given output from a given model should be trusted, so a rational decision can be made whether to use the output or not. For example, outputs can be associated with a confidence measure; if this confidence measure is strongly associated with likelihood of correctness, then the model is said to be well-calibrated. A well-calibrated confidence measure can serve as a basis for rational, graduated decision-making on how much review and care is needed when using generated code. Calibration has so far been studied in mostly non-generative (e.g. classification) settings, especially in software engineering. However, generated code can quite often be wrong: Given generated code, developers must decide whether to use directly, use after varying intensity of careful review, or discard model-generated code. Thus, calibration is vital in generative settings. We make several contributions. We develop a framework for evaluating the calibration of code-generating models. We consider several tasks, correctness criteria, datasets, and approaches, and find that, by and large, generative code models we test are not well-calibrated out of the box. We then show how calibration can be improved using standard methods, such as Platt scaling. Since Platt scaling relies on the prior availability of correctness data, we evaluate the applicability and generalizability of Platt scaling in software engineering, discuss settings where it has good potential for practical use, and settings where it does not. Our contributions will lead to better-calibrated decision-making in the current use of code generated by language models, and offers a framework for future research to further improve calibration methods for generative models in software engineering.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

Following the standard supervised fine-tuning (SFT) paradigm, in-context learning (ICL) has become an efficient approach propelled by the recent advancements in large language models (LLMs), yielding promising performance across various tasks in few-shot data setups. However, both paradigms are prone to suffer from the critical problem of overconfidence (i.e., miscalibration), especially in such limited data setups. In this work, we deliver an in-depth analysis of the behavior across different choices of learning methods from the perspective of both performance and calibration, as well as their interplay. Through extensive controlled experiments, we find that simultaneous gains for both task performance and calibration are difficult to achieve, and the problem of miscalibration exists across all learning methods in low-resource scenarios. To address this challenging trade-off between performance and calibration, we then investigate the potential of self-ensembling techniques applied at different modeling stages (e.g., variations of in-context examples or variations in prompts or different ensembling strategies). We justify the feasibility of self-ensembling on SFT in addition to ICL, to make the predictions more calibrated and have comparable or even better performance. Our work sheds light on which learning paradigm to choose and how to enhance both task performance and calibration of LLMs.

Previous literature has proved that Pretrained Language Models (PLMs) can store factual knowledge. However, we find that facts stored in the PLMs are not always correct. It motivates us to explore a fundamental question: How do we calibrate factual knowledge in PLMs without re-training from scratch? In this work, we propose a simple and lightweight method CaliNet to achieve this goal. To be specific, we first detect whether PLMs can learn the right facts via a contrastive score between right and fake facts. If not, we then use a lightweight method to add and adapt new parameters to specific factual texts. Experiments on the knowledge probing task show the calibration effectiveness and efficiency. In addition, through closed-book question answering, we find that the calibrated PLM possesses knowledge generalization ability after fine-tuning. Beyond the calibration performance, we further investigate and visualize the knowledge calibration mechanism.

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.

Accurate sensor calibration is crucial for autonomous systems, yet its uncertainty quantification remains underexplored. We present the first approach to integrate uncertainty awareness into online extrinsic calibration, combining Monte Carlo Dropout with Conformal Prediction to generate prediction intervals with a guaranteed level of coverage. Our method proposes a framework to enhance existing calibration models with uncertainty quantification, compatible with various network architectures. Validated on KITTI (RGB Camera-LiDAR) and DSEC (Event Camera-LiDAR) datasets, we demonstrate effectiveness across different visual sensor types, measuring performance with adapted metrics to evaluate the efficiency and reliability of the intervals. By providing calibration parameters with quantifiable confidence measures, we offer insights into the reliability of calibration estimates, which can greatly improve the robustness of sensor fusion in dynamic environments and usefully serve the Computer Vision community.

Calibrating deep learning models to yield uncertainty-aware predictions is crucial as deep neural networks get increasingly deployed in safety-critical applications. While existing post-hoc calibration methods achieve impressive results on in-domain test datasets, they are limited by their inability to yield reliable uncertainty estimates in domain-shift and out-of-domain (OOD) scenarios. We aim to bridge this gap by proposing DAC, an accuracy-preserving as well as Density-Aware Calibration method based on k-nearest-neighbors (KNN). In contrast to existing post-hoc methods, we utilize hidden layers of classifiers as a source for uncertainty-related information and study their importance. We show that DAC is a generic method that can readily be combined with state-of-the-art post-hoc methods. DAC boosts the robustness of calibration performance in domain-shift and OOD, while maintaining excellent in-domain predictive uncertainty estimates. We demonstrate that DAC leads to consistently better calibration across a large number of model architectures, datasets, and metrics. Additionally, we show that DAC improves calibration substantially on recent large-scale neural networks pre-trained on vast amounts of data.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

Multimodal machine learning has achieved remarkable progress in a wide range of scenarios. However, the reliability of multimodal learning remains largely unexplored. In this paper, through extensive empirical studies, we identify current multimodal classification methods suffer from unreliable predictive confidence that tend to rely on partial modalities when estimating confidence. Specifically, we find that the confidence estimated by current models could even increase when some modalities are corrupted. To address the issue, we introduce an intuitive principle for multimodal learning, i.e., the confidence should not increase when one modality is removed. Accordingly, we propose a novel regularization technique, i.e., Calibrating Multimodal Learning (CML) regularization, to calibrate the predictive confidence of previous methods. This technique could be flexibly equipped by existing models and improve the performance in terms of confidence calibration, classification accuracy, and model robustness.

Conformal Prediction (CP) controls the prediction uncertainty of classification systems by producing a small prediction set, ensuring a predetermined probability that the true class lies within this set. This is commonly done by defining a score, based on the model predictions, and setting a threshold on this score using a validation set. In this study, we address the problem of CP calibration when we only have access to a calibration set with noisy labels. We show how we can estimate the noise-free conformal threshold based on the noisy labeled data. We derive a finite sample coverage guarantee for uniform noise that remains effective even in tasks with a large number of classes. We dub our approach Noise-Aware Conformal Prediction (NACP). We illustrate the performance of the proposed results on several standard image classification datasets with a large number of classes.

Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we propose a novel calibration method that can be used to combat hallucinations. We add a special [IDK] ("I don't know") token to the model's vocabulary and introduce an objective function that shifts probability mass to the [IDK] token for incorrect predictions. This approach allows the model to express uncertainty in its output explicitly. We evaluate our proposed method across multiple model architectures and factual downstream tasks. We find that models trained with our method are able to express uncertainty in places where they would previously make mistakes while suffering only a small loss of encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide a detailed analysis of the precision-recall tradeoff of our method.

Although Neural Radiance Fields (NeRFs) have markedly improved novel view synthesis, accurate uncertainty quantification in their image predictions remains an open problem. The prevailing methods for estimating uncertainty, including the state-of-the-art Density-aware NeRF Ensembles (DANE) [29], quantify uncertainty without calibration. This frequently leads to over- or under-confidence in image predictions, which can undermine their real-world applications. In this paper, we propose a method which, for the first time, achieves calibrated uncertainties for NeRFs. To accomplish this, we overcome a significant challenge in adapting existing calibration techniques to NeRFs: a need to hold out ground truth images from the target scene, reducing the number of images left to train the NeRF. This issue is particularly problematic in sparse-view settings, where we can operate with as few as three images. To address this, we introduce the concept of a meta-calibrator that performs uncertainty calibration for NeRFs with a single forward pass without the need for holding out any images from the target scene. Our meta-calibrator is a neural network that takes as input the NeRF images and uncalibrated uncertainty maps and outputs a scene-specific calibration curve that corrects the NeRF's uncalibrated uncertainties. We show that the meta-calibrator can generalize on unseen scenes and achieves well-calibrated and state-of-the-art uncertainty for NeRFs, significantly beating DANE and other approaches. This opens opportunities to improve applications that rely on accurate NeRF uncertainty estimates such as next-best view planning and potentially more trustworthy image reconstruction for medical diagnosis. The code is available at https://niki-amini-naieni.github.io/instantcalibration.github.io/.

Network calibration aims to accurately estimate the level of confidences, which is particularly important for employing deep neural networks in real-world systems. Recent approaches leverage mixup to calibrate the network's predictions during training. However, they do not consider the problem that mixtures of labels in mixup may not accurately represent the actual distribution of augmented samples. In this paper, we present RankMixup, a novel mixup-based framework alleviating the problem of the mixture of labels for network calibration. To this end, we propose to use an ordinal ranking relationship between raw and mixup-augmented samples as an alternative supervisory signal to the label mixtures for network calibration. We hypothesize that the network should estimate a higher level of confidence for the raw samples than the augmented ones (Fig.1). To implement this idea, we introduce a mixup-based ranking loss (MRL) that encourages lower confidences for augmented samples compared to raw ones, maintaining the ranking relationship. We also propose to leverage the ranking relationship among multiple mixup-augmented samples to further improve the calibration capability. Augmented samples with larger mixing coefficients are expected to have higher confidences and vice versa (Fig.1). That is, the order of confidences should be aligned with that of mixing coefficients. To this end, we introduce a novel loss, M-NDCG, in order to reduce the number of misaligned pairs of the coefficients and confidences. Extensive experimental results on standard benchmarks for network calibration demonstrate the effectiveness of RankMixup.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

We consider the problem of ranking n experts based on their performances on d tasks. We make a monotonicity assumption stating that for each pair of experts, one outperforms the other on all tasks. We consider the sequential setting where in each round, the learner has access to noisy evaluations of actively chosen pair of expert-task, given the information available up to the actual round. Given a confidence parameter delta in (0, 1), we provide strategies allowing to recover the correct ranking of experts and develop a bound on the total number of queries made by our algorithm that hold with probability at least 1 -- delta. We show that our strategy is adaptive to the complexity of the problem (our bounds are instance dependent), and develop matching lower bounds up to a poly-logarithmic factor. Finally, we adapt our strategy to the relaxed problem of best expert identification and provide numerical simulation consistent with our theoretical results.

Multimodal large language models (MLLMs) hold considerable promise for applications in healthcare. However, their deployment in safety-critical settings is hindered by two key limitations: (i) sensitivity to prompt design, and (ii) a tendency to generate incorrect responses with high confidence. As clinicians may rely on a model's stated confidence to gauge the reliability of its predictions, it is especially important that when a model expresses high confidence, it is also highly accurate. We introduce Prompt4Trust, the first reinforcement learning (RL) framework for prompt augmentation targeting confidence calibration in MLLMs. A lightweight LLM is trained to produce context-aware auxiliary prompts that guide a downstream task MLLM to generate responses in which the expressed confidence more accurately reflects predictive accuracy. Unlike conventional calibration techniques, Prompt4Trust specifically prioritizes aspects of calibration most critical for safe and trustworthy clinical decision-making. Beyond improvements driven by this clinically motivated calibration objective, our proposed method also improves task accuracy, achieving state-of-the-art medical visual question answering (VQA) performance on the PMC-VQA benchmark, which is composed of multiple-choice questions spanning diverse medical imaging modalities. Moreover, our framework trained with a small downstream task MLLM showed promising zero-shot generalization to larger MLLMs in our experiments, suggesting the potential for scalable calibration without the associated computational costs. This work demonstrates the potential of automated yet human-aligned prompt engineering for improving the the trustworthiness of MLLMs in safety critical settings. Our codebase can be found at https://github.com/xingbpshen/prompt4trust.

Large Language Models deployed as question answering tools require robust calibration to avoid overconfidence. We systematically evaluate how reasoning capabilities and budget affect confidence assessment accuracy, using the ClimateX dataset (Lacombe et al., 2023) and expanding it to human and planetary health. Our key finding challenges the "test-time scaling" paradigm: while recent reasoning LLMs achieve 48.7% accuracy in assessing expert confidence, increasing reasoning budgets consistently impairs rather than improves calibration. Extended reasoning leads to systematic overconfidence that worsens with longer thinking budgets, producing diminishing and negative returns beyond modest computational investments. Conversely, search-augmented generation dramatically outperforms pure reasoning, achieving 89.3% accuracy by retrieving relevant evidence. Our results suggest that information access, rather than reasoning depth or inference budget, may be the critical bottleneck for improved confidence calibration of knowledge-intensive tasks.

Recent advancements in large language models (LLMs) on language modeling and emergent capabilities make them a promising reference-free evaluator of natural language generation quality, and a competent alternative to human evaluation. However, hindered by the closed-source or high computational demand to host and tune, there is a lack of practice to further calibrate an off-the-shelf LLM-based evaluator towards better human alignment. In this work, we propose AutoCalibrate, a multi-stage, gradient-free approach to automatically calibrate and align an LLM-based evaluator toward human preference. Instead of explicitly modeling human preferences, we first implicitly encompass them within a set of human labels. Then, an initial set of scoring criteria is drafted by the language model itself, leveraging in-context learning on different few-shot examples. To further calibrate this set of criteria, we select the best performers and re-draft them with self-refinement. Our experiments on multiple text quality evaluation datasets illustrate a significant improvement in correlation with expert evaluation through calibration. Our comprehensive qualitative analysis conveys insightful intuitions and observations on the essence of effective scoring criteria.

A trustworthy real-world prediction system should produce well-calibrated confidence scores; that is, its confidence in an answer should be indicative of the likelihood that the answer is correct, enabling deferral to an expert in cases of low-confidence predictions. Recent studies have shown that unsupervised pre-training produces large language models (LMs) whose conditional probabilities are remarkably well-calibrated. However, the most widely-used LMs are fine-tuned with reinforcement learning from human feedback (RLHF-LMs), and some studies have suggested that RLHF-LMs produce conditional probabilities that are very poorly calibrated. In light of this perceived weakness, we conduct a broad evaluation of methods for extracting confidence scores from RLHF-LMs. For RLHF-LMs such as ChatGPT, GPT-4, and Claude, we find that verbalized confidences emitted as output tokens are typically better-calibrated than the model's conditional probabilities on the TriviaQA, SciQ, and TruthfulQA benchmarks, often reducing the expected calibration error by a relative 50%.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Knowledge distillation (KD) has gained a lot of attention in the field of model compression for edge devices thanks to its effectiveness in compressing large powerful networks into smaller lower-capacity models. Online distillation, in which both the teacher and the student are learning collaboratively, has also gained much interest due to its ability to improve on the performance of the networks involved. The Kullback-Leibler (KL) divergence ensures the proper knowledge transfer between the teacher and student. However, most online KD techniques present some bottlenecks under the network capacity gap. By cooperatively and simultaneously training, the models the KL distance becomes incapable of properly minimizing the teacher's and student's distributions. Alongside accuracy, critical edge device applications are in need of well-calibrated compact networks. Confidence calibration provides a sensible way of getting trustworthy predictions. We propose BD-KD: Balancing of Divergences for online Knowledge Distillation. We show that adaptively balancing between the reverse and forward divergences shifts the focus of the training strategy to the compact student network without limiting the teacher network's learning process. We demonstrate that, by performing this balancing design at the level of the student distillation loss, we improve upon both performance accuracy and calibration of the compact student network. We conducted extensive experiments using a variety of network architectures and show improvements on multiple datasets including CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet. We illustrate the effectiveness of our approach through comprehensive comparisons and ablations with current state-of-the-art online and offline KD techniques.

Despite their impressive predictive performance in various computer vision tasks, deep neural networks (DNNs) tend to make overly confident predictions, which hinders their widespread use in safety-critical applications. While there have been recent attempts to calibrate DNNs, most of these efforts have primarily been focused on classification tasks, thus neglecting DNN-based object detectors. Although several recent works addressed calibration for object detection and proposed differentiable penalties, none of them are consistent estimators of established concepts in calibration. In this work, we tackle the challenge of defining and estimating calibration error specifically for this task. In particular, we adapt the definition of classification calibration error to handle the nuances associated with object detection, and predictions in structured output spaces more generally. Furthermore, we propose a consistent and differentiable estimator of the detection calibration error, utilizing kernel density estimation. Our experiments demonstrate the effectiveness of our estimator against competing train-time and post-hoc calibration methods, while maintaining similar detection performance.

Neural network calibration is an essential task in deep learning to ensure consistency between the confidence of model prediction and the true correctness likelihood. In this paper, we propose a new post-processing calibration method called Neural Clamping, which employs a simple joint input-output transformation on a pre-trained classifier via a learnable universal input perturbation and an output temperature scaling parameter. Moreover, we provide theoretical explanations on why Neural Clamping is provably better than temperature scaling. Evaluated on CIFAR-100 and ImageNet image recognition datasets and a variety of deep neural network models, our empirical results show that Neural Clamping significantly outperforms state-of-the-art post-processing calibration methods.

Calibration measures and reliability diagrams are two fundamental tools for measuring and interpreting the calibration of probabilistic predictors. Calibration measures quantify the degree of miscalibration, and reliability diagrams visualize the structure of this miscalibration. However, the most common constructions of reliability diagrams and calibration measures -- binning and ECE -- both suffer from well-known flaws (e.g. discontinuity). We show that a simple modification fixes both constructions: first smooth the observations using an RBF kernel, then compute the Expected Calibration Error (ECE) of this smoothed function. We prove that with a careful choice of bandwidth, this method yields a calibration measure that is well-behaved in the sense of (B{\l}asiok, Gopalan, Hu, and Nakkiran 2023a) -- a consistent calibration measure. We call this measure the SmoothECE. Moreover, the reliability diagram obtained from this smoothed function visually encodes the SmoothECE, just as binned reliability diagrams encode the BinnedECE. We also provide a Python package with simple, hyperparameter-free methods for measuring and plotting calibration: `pip install relplot\`.

Empowering large language models to accurately express confidence in their answers is essential for trustworthy decision-making. Previous confidence elicitation methods, which primarily rely on white-box access to internal model information or model fine-tuning, have become less suitable for LLMs, especially closed-source commercial APIs. This leads to a growing need to explore the untapped area of black-box approaches for LLM uncertainty estimation. To better break down the problem, we define a systematic framework with three components: prompting strategies for eliciting verbalized confidence, sampling methods for generating multiple responses, and aggregation techniques for computing consistency. We then benchmark these methods on two key tasks-confidence calibration and failure prediction-across five types of datasets (e.g., commonsense and arithmetic reasoning) and five widely-used LLMs including GPT-4 and LLaMA 2 Chat. Our analysis uncovers several key insights: 1) LLMs, when verbalizing their confidence, tend to be overconfident, potentially imitating human patterns of expressing confidence. 2) As model capability scales up, both calibration and failure prediction performance improve. 3) Employing our proposed strategies, such as human-inspired prompts, consistency among multiple responses, and better aggregation strategies can help mitigate this overconfidence from various perspectives. 4) Comparisons with white-box methods indicate that while white-box methods perform better, the gap is narrow, e.g., 0.522 to 0.605 in AUROC. Despite these advancements, none of these techniques consistently outperform others, and all investigated methods struggle in challenging tasks, such as those requiring professional knowledge, indicating significant scope for improvement. We believe this study can serve as a strong baseline and provide insights for eliciting confidence in black-box LLMs.

While confidence estimation is a promising direction for mitigating hallucinations in Large Language Models (LLMs), current research dominantly focuses on single-turn settings. The dynamics of model confidence in multi-turn conversations, where context accumulates and ambiguity is progressively resolved, remain largely unexplored. Reliable confidence estimation in multi-turn settings is critical for many downstream applications, such as autonomous agents and human-in-the-loop systems. This work presents the first systematic study of confidence estimation in multi-turn interactions, establishing a formal evaluation framework grounded in two key desiderata: per-turn calibration and monotonicity of confidence as more information becomes available. To facilitate this, we introduce novel metrics, including a length-normalized Expected Calibration Error (InfoECE), and a new "Hinter-Guesser" paradigm for generating controlled evaluation datasets. Our experiments reveal that widely-used confidence techniques struggle with calibration and monotonicity in multi-turn dialogues. We propose P(Sufficient), a logit-based probe that achieves comparatively better performance, although the task remains far from solved. Our work provides a foundational methodology for developing more reliable and trustworthy conversational agents.

Accurate confidence calibration in Large Language Models (LLMs) is critical for safe use in high-stakes domains, where clear verbalized confidence enhances user trust. Traditional methods that mimic reference confidence expressions often fail to capture the reasoning needed for accurate confidence assessment. We propose natural language critiques as a solution, ideally suited for confidence calibration, as precise gold confidence labels are hard to obtain and often require multiple generations. This paper studies how natural language critiques can enhance verbalized confidence, addressing: (1) What to critique: uncertainty (question-focused) or confidence (answer-specific)? Analysis shows confidence suits multiple-choice tasks, while uncertainty excels in open-ended scenarios. (2) How to critique: self-critique or critique calibration training? We propose Self-Critique, enabling LLMs to critique and optimize their confidence beyond mere accuracy, and CritiCal, a novel Critique Calibration training method that leverages natural language critiques to improve confidence calibration, moving beyond direct numerical optimization. Experiments show that CritiCal significantly outperforms Self-Critique and other competitive baselines, even surpassing its teacher model, GPT-4o, in complex reasoning tasks. CritiCal also shows robust generalization in out-of-distribution settings, advancing LLM's reliability.

Large language models (LLMs) are increasingly used in decision-making contexts, but when they present answers without signaling low confidence, users may unknowingly act on erroneous outputs. Prior work shows that LLMs maintain internal uncertainty signals, yet their expressed confidence is often miscalibrated and poorly discriminates between correct and incorrect answers. We investigate whether supervised fine-tuning can improve models' ability to communicate uncertainty and whether such improvements generalize across tasks and domains. We fine-tune LLMs on datasets spanning general knowledge, mathematics, and open-ended trivia, and evaluate two metacognitive tasks: (1) single-question confidence estimation, where the model assigns a numeric certainty to its answer, and (2) pairwise confidence comparison, where the model selects which of two answers it is more likely to answer correctly. We assess generalization to unseen domains, including medical and legal reasoning. Results show that fine-tuning improves calibration (alignment between stated confidence and accuracy) and discrimination (higher confidence for correct vs. incorrect responses) within and across domains. However, gains are task-specific: training on single-question calibration does not transfer to pairwise comparison, and vice versa. Multitask fine-tuning yields broader gains, lowering calibration error and strengthening discrimination in out-of-domain evaluations. This suggests that uncertainty communication in LLMs is trainable but requires multitask training to generalize effectively.

Allocating more computation during inference time (test-time scaling) improves language model performance, especially for reasoning tasks. However, popular methods like Best-of-N sampling often show diminishing returns as N increases. To address this inefficiency, we introduce a general test-time calibration framework that adaptively modifies the model toward high-reward reasoning paths, with theoretical guarantees of improving the lower bound of expected reward under finite sampling, all without large language model (LLM) retraining. Within this framework, we propose CarBoN (Calibrated Best-of-N), a two-phase method that first explores the solution space and then learns a calibration of the logits via an input-specific temperature T and additive shift vector delta, guiding generation toward more reliable reasoning. Experiments on MATH-500 and AIME-2024 show that CarBoN improves efficiency, with up to 4times fewer rollouts to reach the same accuracy, while often achieving higher accuracy under fixed budgets. We also analyze the complementary roles of T and delta in balancing output diversity and correctness, and demonstrate that the framework also generalizes to step-level sampling strategies such as beam search. For more information, please refer to our project page at huggingface.co/spaces/TrustSafeAI/Test-Time-Calibration.

We present AnyCalib, a method for calibrating the intrinsic parameters of a camera from a single in-the-wild image, that is agnostic to the camera model. Current methods are predominantly tailored to specific camera models and/or require extrinsic cues, such as the direction of gravity, to be visible in the image. In contrast, we argue that the perspective and distortion cues inherent in images are sufficient for model-agnostic camera calibration. To demonstrate this, we frame the calibration process as the regression of the rays corresponding to each pixel. We show, for the first time, that this intermediate representation allows for a closed-form recovery of the intrinsics for a wide range of camera models, including but not limited to: pinhole, Brown-Conrady and Kannala-Brandt. Our approach also applies to edited -- cropped and stretched -- images. Experimentally, we demonstrate that AnyCalib consistently outperforms alternative methods, including 3D foundation models, despite being trained on orders of magnitude less data. Code is available at https://github.com/javrtg/AnyCalib.

In this paper, we uncover a systematic bias in the evaluation paradigm of adopting large language models~(LLMs), e.g., GPT-4, as a referee to score and compare the quality of responses generated by candidate models. We find that the quality ranking of candidate responses can be easily hacked by simply altering their order of appearance in the context. This manipulation allows us to skew the evaluation result, making one model appear considerably superior to the other, e.g., Vicuna-13B could beat ChatGPT on 66 over 80 tested queries with ChatGPT as an evaluator. To address this issue, we propose a calibration framework with three simple yet effective strategies: 1) Multiple Evidence Calibration, which requires the evaluator model to generate multiple evaluation evidence before assigning ratings; 2) Balanced Position Calibration, which aggregates results across various orders to determine the final score; 3) Human-in-the-Loop Calibration, which introduces a balanced position diversity entropy to measure the difficulty of each example and seeks human assistance when needed. We also manually annotate the "win/tie/lose" outcomes of responses from ChatGPT and Vicuna-13B in the Vicuna Benchmark's question prompt, and extensive experiments demonstrate that our approach successfully mitigates evaluation bias, resulting in closer alignment with human judgments. We release our code and human annotation at https://github.com/i-Eval/FairEval to facilitate future research.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

Uncertainty quantification (UQ) is vital for trustworthy deep learning, yet existing methods are either computationally intensive, such as Bayesian or ensemble methods, or provide only partial, task-specific estimates, such as single-forward-pass techniques. In this paper, we propose a post-hoc single-forward-pass framework that jointly captures aleatoric and epistemic uncertainty without modifying or retraining pretrained models. Our method applies Split-Point Analysis (SPA) to decompose predictive residuals into upper and lower subsets, computing Mean Absolute Residuals (MARs) on each side. We prove that, under ideal conditions, the total MAR equals the harmonic mean of subset MARs; deviations define a novel Self-consistency Discrepancy Score (SDS) for fine-grained epistemic estimation across regression and classification. For regression, side-specific quantile regression yields prediction intervals with improved empirical coverage, which are further calibrated via SDS. For classification, when calibration data are available, we apply SPA-based calibration identities to adjust the softmax outputs and then compute predictive entropy on these calibrated probabilities. Extensive experiments on diverse regression and classification benchmarks demonstrate that our framework matches or exceeds several state-of-the-art UQ methods while incurring minimal overhead. Our source code is available at https://github.com/zzz0527/SPC-UQ.

Large Language models (LLMs) can generate complicated source code from natural language prompts. However, LLMs can generate output that deviates from what the user wants, requiring supervision and editing. To support this process, we offer techniques to localize where generations might be misaligned from user intent. We first create a dataset of "Minimal Intent Aligning Patches" of repaired LLM generated programs. Each program uses test cases to verify correctness. After creating a dataset of programs, we measure how well various techniques can assign a well-calibrated probability to indicate which parts of code will be edited in a minimal patch (i.e., give a probability that corresponds with empirical odds it is edited). We compare white-box probing (where we propose a technique for efficient arbitrary-span querying), against black-box reflective and self-consistency based approaches. We find probes with a small supervisor model can achieve low calibration error and Brier Skill Score of approx 0.2 estimating edited lines on code generated by models many orders of magnitude larger. We discuss the generalizability of the techniques, and the connections to AI oversight and control, finding a probe trained only on code shows some signs of generalizing to natural language errors if new probability scaling is allowed.

Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes error, and epistemic uncertainty via the size of the set. In this paper, we extend the notion of calibration, which is commonly used to evaluate the validity of the aleatoric uncertainty representation of a single probabilistic classifier, to assess the validity of an epistemic uncertainty representation obtained by sets of probabilistic classifiers. Broadly speaking, we call a set of probabilistic classifiers calibrated if one can find a calibrated convex combination of these classifiers. To evaluate this notion of calibration, we propose a novel nonparametric calibration test that generalizes an existing test for single probabilistic classifiers to the case of sets of probabilistic classifiers. Making use of this test, we empirically show that ensembles of deep neural networks are often not well calibrated.

Reliable usage of object detectors require them to be calibrated -- a crucial problem that requires careful attention. Recent approaches towards this involve (1) designing new loss functions to obtain calibrated detectors by training them from scratch, and (2) post-hoc Temperature Scaling (TS) that learns to scale the likelihood of a trained detector to output calibrated predictions. These approaches are then evaluated based on a combination of Detection Expected Calibration Error (D-ECE) and Average Precision. In this work, via extensive analysis and insights, we highlight that these recent evaluation frameworks, evaluation metrics, and the use of TS have notable drawbacks leading to incorrect conclusions. As a step towards fixing these issues, we propose a principled evaluation framework to jointly measure calibration and accuracy of object detectors. We also tailor efficient and easy-to-use post-hoc calibration approaches such as Platt Scaling and Isotonic Regression specifically for object detection task. Contrary to the common notion, our experiments show that once designed and evaluated properly, post-hoc calibrators, which are extremely cheap to build and use, are much more powerful and effective than the recent train-time calibration methods. To illustrate, D-DETR with our post-hoc Isotonic Regression calibrator outperforms the recent train-time state-of-the-art calibration method Cal-DETR by more than 7 D-ECE on the COCO dataset. Additionally, we propose improved versions of the recently proposed Localization-aware ECE and show the efficacy of our method on these metrics as well. Code is available at: https://github.com/fiveai/detection_calibration.

For safety-related applications, it is crucial to produce trustworthy deep neural networks whose prediction is associated with confidence that can represent the likelihood of correctness for subsequent decision-making. Existing dense binary classification models are prone to being over-confident. To improve model calibration, we propose Adaptive Stochastic Label Perturbation (ASLP) which learns a unique label perturbation level for each training image. ASLP employs our proposed Self-Calibrating Binary Cross Entropy (SC-BCE) loss, which unifies label perturbation processes including stochastic approaches (like DisturbLabel), and label smoothing, to correct calibration while maintaining classification rates. ASLP follows Maximum Entropy Inference of classic statistical mechanics to maximise prediction entropy with respect to missing information. It performs this while: (1) preserving classification accuracy on known data as a conservative solution, or (2) specifically improves model calibration degree by minimising the gap between the prediction accuracy and expected confidence of the target training label. Extensive results demonstrate that ASLP can significantly improve calibration degrees of dense binary classification models on both in-distribution and out-of-distribution data. The code is available on https://github.com/Carlisle-Liu/ASLP.

We consider the issue of calibration in large language models (LLM). Recent studies have found that common interventions such as instruction tuning often result in poorly calibrated LLMs. Although calibration is well-explored in traditional applications, calibrating LLMs is uniquely challenging. These challenges stem as much from the severe computational requirements of LLMs as from their versatility, which allows them to be applied to diverse tasks. Addressing these challenges, we propose THERMOMETER, a calibration approach tailored to LLMs. THERMOMETER learns an auxiliary model, given data from multiple tasks, for calibrating a LLM. It is computationally efficient, preserves the accuracy of the LLM, and produces better-calibrated responses for new tasks. Extensive empirical evaluations across various benchmarks demonstrate the effectiveness of the proposed method.

Despite the impressive generalization capabilities of deep neural networks, they have been repeatedly shown to be overconfident when they are wrong. Fixing this issue is known as model calibration, and has consequently received much attention in the form of modified training schemes and post-training calibration procedures such as temperature scaling. While temperature scaling is frequently used because of its simplicity, it is often outperformed by modified training schemes. In this work, we identify a specific bottleneck for the performance of temperature scaling. We show that for empirical risk minimizers for a general set of distributions in which the supports of classes have overlaps, the performance of temperature scaling degrades with the amount of overlap between classes, and asymptotically becomes no better than random when there are a large number of classes. On the other hand, we prove that optimizing a modified form of the empirical risk induced by the Mixup data augmentation technique can in fact lead to reasonably good calibration performance, showing that training-time calibration may be necessary in some situations. We also verify that our theoretical results reflect practice by showing that Mixup significantly outperforms empirical risk minimization (with respect to multiple calibration metrics) on image classification benchmarks with class overlaps introduced in the form of label noise.

When language models (LMs) are trained via reinforcement learning (RL) to generate natural language "reasoning chains", their performance improves on a variety of difficult question answering tasks. Today, almost all successful applications of RL for reasoning use binary reward functions that evaluate the correctness of LM outputs. Because such reward functions do not penalize guessing or low-confidence outputs, they often have the unintended side-effect of degrading calibration and increasing the rate at which LMs generate incorrect responses (or "hallucinate") in other problem domains. This paper describes RLCR (Reinforcement Learning with Calibration Rewards), an approach to training reasoning models that jointly improves accuracy and calibrated confidence estimation. During RLCR, LMs generate both predictions and numerical confidence estimates after reasoning. They are trained to optimize a reward function that augments a binary correctness score with a Brier score -- a scoring rule for confidence estimates that incentivizes calibrated prediction. We first prove that this reward function (or any analogous reward function that uses a bounded, proper scoring rule) yields models whose predictions are both accurate and well-calibrated. We next show that across diverse datasets, RLCR substantially improves calibration with no loss in accuracy, on both in-domain and out-of-domain evaluations -- outperforming both ordinary RL training and classifiers trained to assign post-hoc confidence scores. While ordinary RL hurts calibration, RLCR improves it. Finally, we demonstrate that verbalized confidence can be leveraged at test time to improve accuracy and calibration via confidence-weighted scaling methods. Our results show that explicitly optimizing for calibration can produce more generally reliable reasoning models.

In legal decisions, split votes (SV) occur when judges cannot reach a unanimous decision, posing a difficulty for lawyers who must navigate diverse legal arguments and opinions. In high-stakes domains, understanding the alignment of perceived difficulty between humans and AI systems is crucial to build trust. However, existing NLP calibration methods focus on a classifier's awareness of predictive performance, measured against the human majority class, overlooking inherent human label variation (HLV). This paper explores split votes as naturally observable human disagreement and value pluralism. We collect judges' vote distributions from the European Court of Human Rights (ECHR), and present SV-ECHR, a case outcome classification (COC) dataset with SV information. We build a taxonomy of disagreement with SV-specific subcategories. We further assess the alignment of perceived difficulty between models and humans, as well as confidence- and human-calibration of COC models. We observe limited alignment with the judge vote distribution. To our knowledge, this is the first systematic exploration of calibration to human judgements in legal NLP. Our study underscores the necessity for further research on measuring and enhancing model calibration considering HLV in legal decision tasks.

We address the neural network robustness problem by adding Similarity (i.e., correctly predicted depth-matches into training)-awareness and Distance-to-training-distribution-awareness to the existing output Magnitude (i.e., decision-boundary)-awareness of the softmax function. The resulting SDM activation function provides strong signals of the relative epistemic (reducible) predictive uncertainty. We use this novel behavior to further address the complementary HCI problem of mapping the output to human-interpretable summary statistics over relevant partitions of a held-out calibration set. Estimates of prediction-conditional uncertainty are obtained via a parsimonious learned transform over the class-conditional empirical CDFs of the output of a final-layer SDM activation function. For decision-making and as an intrinsic model check, estimates of class-conditional accuracy are obtained by further partitioning the high-probability regions of this calibrated output into class-conditional, region-specific CDFs. The uncertainty estimates from SDM calibration are remarkably robust to test-time distribution shifts and out-of-distribution inputs; incorporate awareness of the effective sample size; provide estimates of uncertainty from the learning and data splitting processes; and are well-suited for selective classification and conditional branching for additional test-time compute based on the predictive uncertainty, as for selective LLM generation, routing, and composition over multiple models and retrieval. Finally, we construct SDM networks, LLMs with uncertainty-aware verification and interpretability-by-exemplar as intrinsic properties. We provide open-source software implementing these results.

Datasets scraped from the internet have been critical to the successes of large-scale machine learning. Yet, this very success puts the utility of future internet-derived datasets at potential risk, as model outputs begin to replace human annotations as a source of supervision. In this work, we first formalize a system where interactions with one model are recorded as history and scraped as training data in the future. We then analyze its stability over time by tracking changes to a test-time bias statistic (e.g. gender bias of model predictions). We find that the degree of bias amplification is closely linked to whether the model's outputs behave like samples from the training distribution, a behavior which we characterize and define as consistent calibration. Experiments in three conditional prediction scenarios - image classification, visual role-labeling, and language generation - demonstrate that models that exhibit a sampling-like behavior are more calibrated and thus more stable. Based on this insight, we propose an intervention to help calibrate and stabilize unstable feedback systems. Code is available at https://github.com/rtaori/data_feedback.

Ensuring reliable confidence scores from deep neural networks is of paramount significance in critical decision-making systems, particularly in real-world domains such as healthcare. Recent literature on calibrating deep segmentation networks has resulted in substantial progress. Nevertheless, these approaches are strongly inspired by the advancements in classification tasks, and thus their uncertainty is usually modeled by leveraging the information of individual pixels, disregarding the local structure of the object of interest. Indeed, only the recent Spatially Varying Label Smoothing (SVLS) approach considers pixel spatial relationships across classes, by softening the pixel label assignments with a discrete spatial Gaussian kernel. In this work, we first present a constrained optimization perspective of SVLS and demonstrate that it enforces an implicit constraint on soft class proportions of surrounding pixels. Furthermore, our analysis shows that SVLS lacks a mechanism to balance the contribution of the constraint with the primary objective, potentially hindering the optimization process. Based on these observations, we propose NACL (Neighbor Aware CaLibration), a principled and simple solution based on equality constraints on the logit values, which enables to control explicitly both the enforced constraint and the weight of the penalty, offering more flexibility. Comprehensive experiments on a wide variety of well-known segmentation benchmarks demonstrate the superior calibration performance of the proposed approach, without affecting its discriminative power. Furthermore, ablation studies empirically show the model agnostic nature of our approach, which can be used to train a wide span of deep segmentation networks.

Honesty alignment-the ability of large language models (LLMs) to recognize their knowledge boundaries and express calibrated confidence-is essential for trustworthy deployment. Existing methods either rely on training-free confidence estimation (e.g., token probabilities, self-consistency) or training-based calibration with correctness annotations. While effective, achieving universal honesty alignment with training-based calibration requires costly, large-scale labeling. To support annotation-efficient training, we introduce Elicitation-Then-Calibration (EliCal), a two-stage framework that first elicits internal confidence using inexpensive self-consistency supervision, then calibrates this confidence with a small set of correctness annotations. To support a large-scale study, we release HonestyBench, a benchmark covering ten free-form QA datasets with 560k training and 70k evaluation instances annotated with correctness and self-consistency signals. Experiments show that EliCal achieves near-optimal alignment with only 1k correctness annotations (0.18% of full supervision) and better alignment performance on unseen MMLU tasks than the calibration-only baseline, offering a scalable solution toward universal honesty alignment in LLMs.

LLM-as-judge evaluation has become the de facto standard for scaling model assessment, but the practice is statistically unsound: uncalibrated scores can invert preferences, naive confidence intervals on uncalibrated scores achieve near-0% coverage, and importance-weighted estimators collapse under limited overlap despite high effective sample size (ESS). We introduce Causal Judge Evaluation (CJE), a framework that fixes all three failures. On n=4,961 Chatbot Arena prompts (after filtering from 5k), CJE achieves 99% pairwise ranking accuracy at full sample size (94% averaged across configurations), matching oracle quality, at 14x lower cost (for ranking 5 policies) by calibrating a 16x cheaper judge on just 5% oracle labels (~250 labels). CJE combines three components: (i) AutoCal-R, reward calibration via mean-preserving isotonic regression; (ii) SIMCal-W, weight stabilization via stacking of S-monotone candidates; and (iii) Oracle-Uncertainty Aware (OUA) inference that propagates calibration uncertainty into confidence intervals. We formalize the Coverage-Limited Efficiency (CLE) diagnostic, which explains why IPS-style estimators fail even when ESS exceeds 90%: the logger rarely visits regions where target policies concentrate. Key findings: SNIPS inverts rankings even with reward calibration (38% pairwise, negative Kendall's tau) due to weight instability; calibrated IPS remains near-random (47%) despite weight stabilization, consistent with CLE; OUA improves coverage from near-0% to ~86% (Direct) and ~96% (stacked-DR), where naive intervals severely under-cover.

Although appearance-based point-of-gaze (PoG) estimation has improved, the estimators still struggle to generalize across individuals due to personal differences. Therefore, person-specific calibration is required for accurate PoG estimation. However, calibrated PoG estimators are often sensitive to head pose variations. To address this, we investigate the key factors influencing calibrated estimators and explore pose-robust calibration strategies. Specifically, we first construct a benchmark, MobilePoG, which includes facial images from 32 individuals focusing on designated points under either fixed or continuously changing head poses. Using this benchmark, we systematically analyze how the diversity of calibration points and head poses influences estimation accuracy. Our experiments show that introducing a wider range of head poses during calibration improves the estimator's ability to handle pose variation. Building on this insight, we propose a dynamic calibration strategy in which users fixate on calibration points while moving their phones. This strategy naturally introduces head pose variation during a user-friendly and efficient calibration process, ultimately producing a better calibrated PoG estimator that is less sensitive to head pose variations than those using conventional calibration strategies. Codes and datasets are available at our project page.

In this paper, we present the practical problems and the lessons learned at short-video services from Kuaishou. In industry, a widely-used multi-task framework is the Mixture-of-Experts (MoE) paradigm, which always introduces some shared and specific experts for each task and then uses gate networks to measure related experts' contributions. Although the MoE achieves remarkable improvements, we still observe three anomalies that seriously affect model performances in our iteration: (1) Expert Collapse: We found that experts' output distributions are significantly different, and some experts have over 90% zero activations with ReLU, making it hard for gate networks to assign fair weights to balance experts. (2) Expert Degradation: Ideally, the shared-expert aims to provide predictive information for all tasks simultaneously. Nevertheless, we find that some shared-experts are occupied by only one task, which indicates that shared-experts lost their ability but degenerated into some specific-experts. (3) Expert Underfitting: In our services, we have dozens of behavior tasks that need to be predicted, but we find that some data-sparse prediction tasks tend to ignore their specific-experts and assign large weights to shared-experts. The reason might be that the shared-experts can perceive more gradient updates and knowledge from dense tasks, while specific-experts easily fall into underfitting due to their sparse behaviors. Motivated by those observations, we propose HoME to achieve a simple, efficient and balanced MoE system for multi-task learning.

Tool learning empowers large language models (LLMs) as agents to use external tools to extend their capability. Existing methods employ one single LLM-based agent to iteratively select and execute tools, thereafter incorporating the result into the next action prediction. However, they still suffer from potential performance degradation when addressing complex tasks due to: (1) the limitation of the inherent capability of a single LLM to perform diverse actions, and (2) the struggle to adaptively correct mistakes when the task fails. To mitigate these problems, we propose the ConAgents, a Cooperative and interactive Agents framework, which modularizes the workflow of tool learning into Grounding, Execution, and Observing agents. We also introduce an iterative calibration (IterCali) method, enabling the agents to adapt themselves based on the feedback from the tool environment. Experiments conducted on three datasets demonstrate the superiority of our ConAgents (e.g., 6 point improvement over the SOTA baseline). We further provide fine-granularity analysis for the efficiency and consistency of our framework.

Extrinsic calibration is essential for multi-sensor fusion, existing methods rely on structured targets or fully-excited data, limiting real-world applicability. Online calibration further suffers from weak excitation, leading to unreliable estimates. To address these limitations, we propose a reinforcement learning (RL)-based extrinsic calibration framework that formulates extrinsic calibration as a decision-making problem, directly optimizes SE(3) extrinsics to enhance odometry accuracy. Our approach leverages a probabilistic Bingham distribution to model 3D rotations, ensuring stable optimization while inherently retaining quaternion symmetry. A trajectory alignment reward mechanism enables robust calibration without structured targets by quantitatively evaluating estimated tightly-coupled trajectory against a reference trajectory. Additionally, an automated data selection module filters uninformative samples, significantly improving efficiency and scalability for large-scale datasets. Extensive experiments on UAVs, UGVs, and handheld platforms demonstrate that our method outperforms traditional optimization-based approaches, achieving high-precision calibration even under weak excitation conditions. Our framework simplifies deployment on diverse robotic platforms by eliminating the need for high-quality initial extrinsics and enabling calibration from routine operating data. The code is available at https://github.com/APRIL-ZJU/learn-to-calibrate.

Numerous crucial tasks in real-world decision-making rely on machine learning algorithms with calibrated uncertainty estimates. However, modern methods often yield overconfident and uncalibrated predictions. Various approaches involve training an ensemble of separate models to quantify the uncertainty related to the model itself, known as epistemic uncertainty. In an explicit implementation, the ensemble approach has high computational cost and high memory requirements. This particular challenge is evident in state-of-the-art neural networks such as transformers, where even a single network is already demanding in terms of compute and memory. Consequently, efforts are made to emulate the ensemble model without actually instantiating separate ensemble members, referred to as implicit ensembling. We introduce LoRA-Ensemble, a parameter-efficient deep ensemble method for self-attention networks, which is based on Low-Rank Adaptation (LoRA). Initially developed for efficient LLM fine-tuning, we extend LoRA to an implicit ensembling approach. By employing a single pre-trained self-attention network with weights shared across all members, we train member-specific low-rank matrices for the attention projections. Our method exhibits superior calibration compared to explicit ensembles and achieves similar or better accuracy across various prediction tasks and datasets.

A critical component in the trustworthiness of LLMs is reliable uncertainty communication, yet LLMs often use assertive language when conveying false claims, leading to over-reliance and eroded trust. We present the first systematic study of faithful confidence calibration of LLMs, benchmarking models' ability to use linguistic expressions of uncertainty that faithfully reflect their intrinsic uncertainty, across a comprehensive array of models, datasets, and prompting strategies. Our results demonstrate that LLMs largely fail at this task, and that existing interventions are insufficient: standard prompt approaches provide only marginal gains, and existing, factuality-based calibration techniques can even harm faithful calibration. To address this critical gap, we introduce MetaFaith, a novel prompt-based calibration approach inspired by human metacognition. We show that MetaFaith robustly improves faithful calibration across diverse models and task domains, enabling up to 61% improvement in faithfulness and achieving an 83% win rate over original generations as judged by humans.

Generalizability and few-shot learning are key challenges in Neural Radiance Fields (NeRF), often due to the lack of a holistic understanding in pixel-level rendering. We introduce CaesarNeRF, an end-to-end approach that leverages scene-level CAlibratEd SemAntic Representation along with pixel-level representations to advance few-shot, generalizable neural rendering, facilitating a holistic understanding without compromising high-quality details. CaesarNeRF explicitly models pose differences of reference views to combine scene-level semantic representations, providing a calibrated holistic understanding. This calibration process aligns various viewpoints with precise location and is further enhanced by sequential refinement to capture varying details. Extensive experiments on public datasets, including LLFF, Shiny, mip-NeRF 360, and MVImgNet, show that CaesarNeRF delivers state-of-the-art performance across varying numbers of reference views, proving effective even with a single reference image. The project page of this work can be found at https://haidongz-usc.github.io/project/caesarnerf.

Large language models (LLMs) have become increasingly prevalent in our daily lives, leading to an expectation for LLMs to be trustworthy -- - both accurate and well-calibrated (the prediction confidence should align with its ground truth correctness likelihood). Nowadays, fine-tuning has become the most popular method for adapting a model to practical usage by significantly increasing accuracy on downstream tasks. Despite the great accuracy it achieves, we found fine-tuning is still far away from satisfactory trustworthiness due to "tuning-induced mis-calibration". In this paper, we delve deeply into why and how mis-calibration exists in fine-tuned models, and how distillation can alleviate the issue. Then we further propose a brand new method named Efficient Trustworthy Distillation (FIRST), which utilizes a small portion of teacher's knowledge to obtain a reliable language model in a cost-efficient way. Specifically, we identify the "concentrated knowledge" phenomenon during distillation, which can significantly reduce the computational burden. Then we apply a "trustworthy maximization" process to optimize the utilization of this small portion of concentrated knowledge before transferring it to the student. Experimental results demonstrate the effectiveness of our method, where better accuracy (+2.3%) and less mis-calibration (-10%) are achieved on average across both in-domain and out-of-domain scenarios, indicating better trustworthiness.

Recently, there has been a trend of evaluating the Large Language Model (LLM) quality in the flavor of LLM-as-a-Judge, namely leveraging another LLM to evaluate the current output quality. However, existing judges are proven to be biased, namely they would favor answers which present better superficial quality (such as verbosity, fluency) while ignoring the instruction following ability. In this work, we propose systematic research about the bias of LLM-as-a-Judge. Specifically, for closed-source judge models, we apply calibration to mitigate the significance of superficial quality, both on probability level and prompt level. For open-source judge models, we propose to mitigate the bias by contrastive training, with curated negative samples that deviate from instruction but present better superficial quality. We apply our methods on the bias evaluation benchmark, and experiment results show our methods mitigate the bias by a large margin while maintaining a satisfactory evaluation accuracy.

Model merging, which combines multiple domain-specialized experts into a single model, offers a practical path to endow Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) with broad capabilities without the cost of joint training or serving many models. However, training-free methods rely on hand-tuned coefficients, whereas training-based methods primarily align parameters rather than downstream task behavior and typically treat all layers uniformly, ignoring inter-layer heterogeneity. We introduce Expert Merging, a training-light method that learns a small set of layer-wise coefficients using only unlabeled calibration data. The coefficients are optimized to explicitly align the merged model's hidden states and logits with those of the corresponding experts, with a coefficient regularizer for stability and task-weighted losses for controllable trade-offs. To capture inter-layer variation, Expert Merging++ augments this design with importance-guided chunking: a normalized layer-importance metric, derived from learned coefficients, task-vector magnitudes, and parameter counts, allocates more chunk-wise coefficients to high-importance layers while keeping low-importance layers lightweight. The result is a label-free, parameter-efficient, and scalable approach to multi-expert model merging across LLMs and MLLMs. Across MLLM backbones (InternVL and Qwen2-VL) and the LLM backbone (Mistral), our method surpasses strong training-free and training-based merging baselines, with Expert Merging++ delivering further gains and, in some cases, even exceeding supervised Mixture Training. The source code is available at https://github.com/Littleor/ExpertMerging.

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

Given the importance of getting calibrated predictions and reliable uncertainty estimations, various post-hoc calibration methods have been developed for neural networks on standard multi-class classification tasks. However, these methods are not well suited for calibrating graph neural networks (GNNs), which presents unique challenges such as accounting for the graph structure and the graph-induced correlations between the nodes. In this work, we conduct a systematic study on the calibration qualities of GNN node predictions. In particular, we identify five factors which influence the calibration of GNNs: general under-confident tendency, diversity of nodewise predictive distributions, distance to training nodes, relative confidence level, and neighborhood similarity. Furthermore, based on the insights from this study, we design a novel calibration method named Graph Attention Temperature Scaling (GATS), which is tailored for calibrating graph neural networks. GATS incorporates designs that address all the identified influential factors and produces nodewise temperature scaling using an attention-based architecture. GATS is accuracy-preserving, data-efficient, and expressive at the same time. Our experiments empirically verify the effectiveness of GATS, demonstrating that it can consistently achieve state-of-the-art calibration results on various graph datasets for different GNN backbones.

Prompting and in-context learning (ICL) have become efficient learning paradigms for large language models (LLMs). However, LLMs suffer from prompt brittleness and various bias factors in the prompt, including but not limited to the formatting, the choice verbalizers, and the ICL examples. To address this problem that results in unexpected performance degradation, calibration methods have been developed to mitigate the effects of these biases while recovering LLM performance. In this work, we first conduct a systematic analysis of the existing calibration methods, where we both provide a unified view and reveal the failure cases. Inspired by these analyses, we propose Batch Calibration (BC), a simple yet intuitive method that controls the contextual bias from the batched input, unifies various prior approaches, and effectively addresses the aforementioned issues. BC is zero-shot, inference-only, and incurs negligible additional costs. In the few-shot setup, we further extend BC to allow it to learn the contextual bias from labeled data. We validate the effectiveness of BC with PaLM 2-(S, M, L) and CLIP models and demonstrate state-of-the-art performance over previous calibration baselines across more than 10 natural language understanding and image classification tasks.

Camera calibration involves estimating camera parameters to infer geometric features from captured sequences, which is crucial for computer vision and robotics. However, conventional calibration is laborious and requires dedicated collection. Recent efforts show that learning-based solutions have the potential to be used in place of the repeatability works of manual calibrations. Among these solutions, various learning strategies, networks, geometric priors, and datasets have been investigated. In this paper, we provide a comprehensive survey of learning-based camera calibration techniques, by analyzing their strengths and limitations. Our main calibration categories include the standard pinhole camera model, distortion camera model, cross-view model, and cross-sensor model, following the research trend and extended applications. As there is no unified benchmark in this community, we collect a holistic calibration dataset that can serve as a public platform to evaluate the generalization of existing methods. It comprises both synthetic and real-world data, with images and videos captured by different cameras in diverse scenes. Toward the end of this paper, we discuss the challenges and provide further research directions. To our knowledge, this is the first survey for the learning-based camera calibration (spanned 10 years). The summarized methods, datasets, and benchmarks are available and will be regularly updated at https://github.com/KangLiao929/Awesome-Deep-Camera-Calibration.

Fine-tuned large language models (LLMs) often exhibit overconfidence, particularly when trained on small datasets, resulting in poor calibration and inaccurate uncertainty estimates. Evidential Deep Learning (EDL), an uncertainty-aware approach, enables uncertainty estimation in a single forward pass, making it a promising method for calibrating fine-tuned LLMs. However, despite its computational efficiency, EDL is prone to overfitting, as its training objective can result in overly concentrated probability distributions. To mitigate this, we propose regularizing EDL by incorporating an information bottleneck (IB). Our approach IB-EDL suppresses spurious information in the evidence generated by the model and encourages truly predictive information to influence both the predictions and uncertainty estimates. Extensive experiments across various fine-tuned LLMs and tasks demonstrate that IB-EDL outperforms both existing EDL and non-EDL approaches. By improving the trustworthiness of LLMs, IB-EDL facilitates their broader adoption in domains requiring high levels of confidence calibration. Code is available at https://github.com/sandylaker/ib-edl.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Process reward models (PRMs) play a central role in guiding inference-time scaling algorithms for large language models (LLMs). However, we observe that even state-of-the-art PRMs can be poorly calibrated and often overestimate success probabilities. To address this, we present a calibration approach, performed via quantile regression, that adjusts PRM outputs to better align with true success probabilities. Leveraging these calibrated success estimates and their associated confidence bounds, we introduce an instance-adaptive scaling (IAS) framework that dynamically adjusts the inference budget based on the estimated likelihood that a partial reasoning trajectory will yield a correct final answer. Unlike conventional methods that allocate a fixed number of reasoning trajectories per query, this approach successfully adapts to each instance and reasoning step when using our calibrated PRMs. Experiments on mathematical reasoning benchmarks show that (i) our PRM calibration method successfully achieves small calibration error, outperforming the baseline methods, (ii) calibration is crucial for enabling effective adaptive scaling, and (iii) the proposed IAS strategy reduces inference costs while maintaining final answer accuracy, utilizing less compute on more confident problems as desired.

As large language models (LLMs) are increasingly deployed in user-facing applications, building trust and maintaining safety by accurately quantifying a model's confidence in its prediction becomes even more important. However, finding effective ways to calibrate LLMs - especially when the only interface to the models is their generated text - remains a challenge. We propose APRICOT (auxiliary prediction of confidence targets): A method to set confidence targets and train an additional model that predicts an LLM's confidence based on its textual input and output alone. This approach has several advantages: It is conceptually simple, does not require access to the target model beyond its output, does not interfere with the language generation, and has a multitude of potential usages, for instance by verbalizing the predicted confidence or adjusting the given answer based on the confidence. We show how our approach performs competitively in terms of calibration error for white-box and black-box LLMs on closed-book question-answering to detect incorrect LLM answers.

Post-Training Quantization (PTQ) enhances the efficiency of Large Language Models (LLMs) by enabling faster operation and compatibility with more accessible hardware through reduced memory usage, at the cost of small performance drops. We explore the role of calibration sets in PTQ, specifically their effect on hidden activations in various notable open-source LLMs. Calibration sets are crucial for evaluating activation magnitudes and identifying outliers, which can distort the quantization range and negatively impact performance. Our analysis reveals a marked contrast in quantization effectiveness across models. The older OPT model, upon which much of the quantization literature is based, shows significant performance deterioration and high susceptibility to outliers with varying calibration sets. In contrast, newer models like Llama-2 7B, Llama-3 8B, Command-R 35B, and Mistral 7B demonstrate strong robustness, with Mistral 7B showing near-immunity to outliers and stable activations. These findings suggest a shift in PTQ strategies might be needed. As advancements in pre-training methods reduce the relevance of outliers, there is an emerging need to reassess the fundamentals of current quantization literature. The emphasis should pivot towards optimizing inference speed, rather than primarily focusing on outlier preservation, to align with the evolving characteristics of state-of-the-art LLMs.

Mixture-of-Experts (MoE) large language models (LLMs), which leverage dynamic routing and sparse activation to enhance efficiency and scalability, have achieved higher performance while reducing computational costs. However, these models face significant memory overheads, limiting their practical deployment and broader adoption. Post-training quantization (PTQ), a widely used method for compressing LLMs, encounters severe accuracy degradation and diminished generalization performance when applied to MoE models. This paper investigates the impact of MoE's sparse and dynamic characteristics on quantization and identifies two primary challenges: (1) Inter-expert imbalance, referring to the uneven distribution of samples across experts, which leads to insufficient and biased calibration for less frequently utilized experts; (2) Intra-expert imbalance, arising from MoE's unique aggregation mechanism, which leads to varying degrees of correlation between different samples and their assigned experts. To address these challenges, we propose MoEQuant, a novel quantization framework tailored for MoE LLMs. MoE-Quant includes two novel techniques: 1) Expert-Balanced Self-Sampling (EBSS) is an efficient sampling method that efficiently constructs a calibration set with balanced expert distributions by leveraging the cumulative probabilities of tokens and expert balance metrics as guiding factors. 2) Affinity-Guided Quantization (AGQ), which incorporates affinities between experts and samples into the quantization process, thereby accurately assessing the impact of individual samples on different experts within the MoE layer. Experiments demonstrate that MoEQuant achieves substantial performance gains (more than 10 points accuracy gain in the HumanEval for DeepSeekMoE-16B under 4-bit quantization) and boosts efficiency.

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform calibration automatically. More precisely, we consider the setup y = A(d) x + epsilon where only partial information about the sensing matrix A(d) is known and where A(d) linearly depends on d. The goal is to estimate the calibration parameter d (resolve the uncertainty in the sensing process) and the signal/object of interests x simultaneously. For three different models of practical relevance, we show how such a bilinear inverse problem, including blind deconvolution as an important example, can be solved via a simple linear least squares approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus potentially allowing for real-time deployment. We also present a variation of the least squares approach, which leads to a~spectral method, where the solution to the bilinear inverse problem can be found by computing the singular vector associated with the smallest singular value of a certain matrix derived from the bilinear system. Explicit theoretical guarantees and stability theory are derived for both techniques; and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

We address the problem of network calibration adjusting miscalibrated confidences of deep neural networks. Many approaches to network calibration adopt a regularization-based method that exploits a regularization term to smooth the miscalibrated confidences. Although these approaches have shown the effectiveness on calibrating the networks, there is still a lack of understanding on the underlying principles of regularization in terms of network calibration. We present in this paper an in-depth analysis of existing regularization-based methods, providing a better understanding on how they affect to network calibration. Specifically, we have observed that 1) the regularization-based methods can be interpreted as variants of label smoothing, and 2) they do not always behave desirably. Based on the analysis, we introduce a novel loss function, dubbed ACLS, that unifies the merits of existing regularization methods, while avoiding the limitations. We show extensive experimental results for image classification and semantic segmentation on standard benchmarks, including CIFAR10, Tiny-ImageNet, ImageNet, and PASCAL VOC, demonstrating the effectiveness of our loss function.

Existing language model evaluations primarily measure general capabilities, yet reliable use of these models across a range of domains demands factual accuracy and recognition of knowledge gaps. We introduce AA-Omniscience, a benchmark designed to measure both factual recall and knowledge calibration across 6,000 questions. Questions are derived from authoritative academic and industry sources, and cover 42 economically relevant topics within six different domains. The evaluation measures a model's Omniscience Index, a bounded metric (-100 to 100) measuring factual recall that jointly penalizes hallucinations and rewards abstention when uncertain, with 0 equating to a model that answers questions correctly as much as it does incorrectly. Among evaluated models, Claude 4.1 Opus attains the highest score (4.8), making it one of only three models to score above zero. These results reveal persistent factuality and calibration weaknesses across frontier models. Performance also varies by domain, with the models from three different research labs leading across the six domains. This performance variability suggests models should be chosen according to the demands of the use case rather than general performance for tasks where knowledge is important.

Large multimodal Mixture-of-Experts (MoEs) effectively scale the model size to boost performance while maintaining fixed active parameters. However, previous works primarily utilized full-precision experts during sparse up-cycling. Despite they show superior performance on end tasks, the large amount of experts introduces higher memory footprint, which poses significant challenges for the deployment on edge devices. In this work, we propose MoTE, a scalable and memory-efficient approach to train Mixture-of-Ternary-Experts models from dense checkpoint. Instead of training fewer high-precision experts, we propose to train more low-precision experts during up-cycling. Specifically, we use the pre-trained FFN as a shared expert and train ternary routed experts with parameters in {-1, 0, 1}. Extensive experiments show that our approach has promising scaling trend along model size. MoTE achieves comparable performance to full-precision baseline MoE-LLaVA while offering lower memory footprint. Furthermore, our approach is compatible with post-training quantization methods and the advantage further amplifies when memory-constraint goes lower. Given the same amount of expert memory footprint of 3.4GB and combined with post-training quantization, MoTE outperforms MoE-LLaVA by a gain of 4.3% average accuracy on end tasks, demonstrating its effectiveness and potential for memory-constrained devices.

Autonomous Graphical User Interface (GUI) agents rely on accurate GUI grounding, which maps language instructions to on-screen coordinates, to execute user commands. However, current models, whether trained via supervised fine-tuning (SFT) or reinforcement fine-tuning (RFT), lack self-awareness of their capability boundaries, leading to overconfidence and unreliable predictions. We first systematically evaluate probabilistic and verbalized confidence in general and GUI-specific models, revealing a misalignment between confidence and actual accuracy, which is particularly critical in dynamic GUI automation tasks, where single errors can cause task failure. To address this, we propose HyperClick, a novel framework that enhances reliable GUI grounding through uncertainty calibration. HyperClick introduces a dual reward mechanism, combining a binary reward for correct actions with a truncated Gaussian-based spatial confidence modeling, calibrated using the Brier score. This approach jointly optimizes grounding accuracy and confidence reliability, fostering introspective self-criticism. Extensive experiments on seven challenge benchmarks show that HyperClick achieves state-of-the-art performance while providing well-calibrated confidence. By enabling explicit confidence calibration and introspective self-criticism, HyperClick reduces overconfidence and supports more reliable GUI automation.

Modern Artificial Intelligence (AI) increasingly relies on multi-agent architectures that blend visual and language understanding. Yet, a pressing challenge remains: How can we trust these agents especially in zero-shot settings with no fine-tuning? We introduce a novel modular Agentic AI visual classification framework that integrates generalist multimodal agents with a non-visual reasoning orchestrator and a Retrieval-Augmented Generation (RAG) module. Applied to apple leaf disease diagnosis, we benchmark three configurations: (I) zero-shot with confidence-based orchestration, (II) fine-tuned agents with improved performance, and (III) trust-calibrated orchestration enhanced by CLIP-based image retrieval and re-evaluation loops. Using confidence calibration metrics (ECE, OCR, CCC), the orchestrator modulates trust across agents. Our results demonstrate a 77.94\% accuracy improvement in the zero-shot setting using trust-aware orchestration and RAG, achieving 85.63\% overall. GPT-4o showed better calibration, while Qwen-2.5-VL displayed overconfidence. Furthermore, image-RAG grounded predictions with visually similar cases, enabling correction of agent overconfidence via iterative re-evaluation. The proposed system separates perception (vision agents) from meta-reasoning (orchestrator), enabling scalable and interpretable multi-agent AI. This blueprint is extensible to diagnostics, biology, and other trust-critical domains. All models, prompts, results, and system components including the complete software source code are openly released to support reproducibility, transparency, and community benchmarking at Github: https://github.com/Applied-AI-Research-Lab/Orchestrator-Agent-Trust

Existing calibration methods occasionally fail for large field-of-view cameras due to the non-linearity of the underlying problem and the lack of good initial values for all parameters of the used camera model. This might occur because a simpler projection model is assumed in an initial step, or a poor initial guess for the internal parameters is pre-defined. A lot of the difficulties of general camera calibration lie in the use of a forward projection model. We side-step these challenges by first proposing a solver to calibrate the parameters in terms of a back-projection model and then regress the parameters for a target forward model. These steps are incorporated in a robust estimation framework to cope with outlying detections. Extensive experiments demonstrate that our approach is very reliable and returns the most accurate calibration parameters as measured on the downstream task of absolute pose estimation on test sets. The code is released at https://github.com/ylochman/babelcalib.

Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations' dynamic ranges. Furthermore, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1\% accuracy degradation --- with 4-bit weights and activations in all layers, but the smallest two. We open-sourced our code.

We present a principled approach to provide LLM-based evaluation with a rigorous guarantee of human agreement. We first propose that a reliable evaluation method should not uncritically rely on model preferences for pairwise evaluation, but rather assess the confidence of judge models and selectively decide when to trust its judgement. We then show that under this selective evaluation framework, human agreement can be provably guaranteed -- such that the model evaluation aligns with that of humans to a user-specified agreement level. As part of our framework, we also introduce Simulated Annotators, a novel confidence estimation method that significantly improves judge calibration and thus enables high coverage of evaluated instances. Finally, we propose Cascaded Selective Evaluation, where we use cheaper models as initial judges and escalate to stronger models only when necessary -- again, while still providing a provable guarantee of human agreement. Experimental results show that Cascaded Selective Evaluation guarantees strong alignment with humans, far beyond what LLM judges could achieve without selective evaluation. For example, on a subset of Chatbot Arena where GPT-4 almost never achieves 80% human agreement, our method, even while employing substantially cost-effective models such as Mistral-7B, guarantees over 80% human agreement with almost 80% test coverage.

Large language models (LLMs) offer powerful capabilities but incur substantial computational costs, driving the need for efficient compression techniques. This study evaluates the impact of popular compression methods - Magnitude Pruning, SparseGPT, and Wanda - on the LLaMA-2-7B model, focusing on the trade-offs between model size reduction, downstream task performance, and the role of calibration data. Our findings reveal that while SparseGPT and Wanda preserve perplexity even at 50% sparsity, they suffer significant degradation on downstream tasks, highlighting the inadequacy of perplexity as the sole evaluation metric. To address this, we introduce Jensen-Shannon (JS) Divergence as a more comprehensive metric that captures nuanced changes in model behavior post-compression. We further demonstrate that task-specific calibration data significantly enhances the downstream performance of compressed models compared to general calibration data. This research underscores the necessity for diverse evaluation metrics and careful calibration data selection to fully understand the complexities of LLM compression and its implications for practical applications.

Assessing human skill levels in complex activities is a challenging problem with applications in sports, rehabilitation, and training. In this work, we present SkillFormer, a parameter-efficient architecture for unified multi-view proficiency estimation from egocentric and exocentric videos. Building on the TimeSformer backbone, SkillFormer introduces a CrossViewFusion module that fuses view-specific features using multi-head cross-attention, learnable gating, and adaptive self-calibration. We leverage Low-Rank Adaptation to fine-tune only a small subset of parameters, significantly reducing training costs. In fact, when evaluated on the EgoExo4D dataset, SkillFormer achieves state-of-the-art accuracy in multi-view settings while demonstrating remarkable computational efficiency, using 4.5x fewer parameters and requiring 3.75x fewer training epochs than prior baselines. It excels in multiple structured tasks, confirming the value of multi-view integration for fine-grained skill assessment.

When deployed in the real world, AI agents will inevitably face challenges that exceed their individual capabilities. Leveraging assistance from experts, whether humans or highly capable AI systems, can significantly improve both safety and performance in such situations. Since expert assistance is costly, a central challenge is determining when to consult an expert. In this paper, we explore a novel variant of this problem, termed YRC-0, in which an agent must learn to collaborate with an expert in new environments in an unsupervised manner--that is, without interacting with the expert during training. This setting motivates the development of low-cost, robust approaches for training expert-leveraging agents. To support research in this area, we introduce YRC-Bench, an open-source benchmark that instantiates YRC-0 across diverse environments. YRC-Bench provides a standardized Gym-like API, simulated experts, an evaluation pipeline, and implementations of popular baselines. Toward tackling YRC-0, we propose a validation strategy and evaluate a range of learning methods, offering insights that can inform future research. Codebase: github.com/modanesh/YRC-Bench

The hallucination of non-existent facts by LLMs is an important problem given its widespread adoption across various applications. Previous research addresses this problem by analyzing the internal parameterized knowledge boundaries to estimate confidence. However, these studies focus on the single-problem setting and have not explored the more challenging multi-problem setting, which requires accurately answering multiple questions simultaneously. We introduce a novel method for the multi-problem setting, Multiple Answers and Confidence Stepwise Tuning (MAC-Tuning), that separates the learning of answer prediction and confidence estimation during fine-tuning on instruction data. Extensive experiments demonstrate that our method outperforms baselines by up to 25\% in average precision.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

As Large Language Models (LLMs) become increasingly computationally complex, developing efficient deployment strategies, such as quantization, becomes crucial. State-of-the-art Post-training Quantization (PTQ) techniques often rely on calibration processes to maintain the accuracy of these models. However, while these calibration techniques can enhance performance in certain domains, they may not be as effective in others. This paper aims to draw attention to robust statistical approaches that can mitigate such issues. We propose a weight-adaptive PTQ method that can be considered a precursor to calibration-based PTQ methods, guiding the quantization process to preserve the distribution of weights by minimizing the Kullback-Leibler divergence between the quantized weights and the originally trained weights. This minimization ensures that the quantized model retains the Shannon information content of the original model to a great extent, guaranteeing robust and efficient deployment across many tasks. As such, our proposed approach can perform on par with most common calibration-based PTQ methods, establishing a new pre-calibration step for further adjusting the quantized weights with calibration. We show that our pre-calibration results achieve the same accuracy as some existing calibration-based PTQ methods on various LLMs.

In recent years, multimodal large language models (MLLMs) have made significant progress but continue to face inherent challenges in multimodal reasoning, which requires multi-level (e.g., perception, reasoning) and multi-granular (e.g., multi-step reasoning chain) advanced inferencing. Prior work on estimating model confidence tends to focus on the overall response for training and calibration, but fails to assess confidence in each reasoning step, leading to undesirable hallucination snowballing. In this work, we present MMBoundary, a novel framework that advances the knowledge boundary awareness of MLLMs through reasoning step confidence calibration. To achieve this, we propose to incorporate complementary textual and cross-modal self-rewarding signals to estimate confidence at each step of the MLLM reasoning process. In addition to supervised fine-tuning MLLM on this set of self-rewarded confidence estimation signal for initial confidence expression warm-up, we introduce a reinforcement learning stage with multiple reward functions for further aligning model knowledge and calibrating confidence at each reasoning step, enhancing reasoning chain self-correction. Empirical results show that MMBoundary significantly outperforms existing methods across diverse domain datasets and metrics, achieving an average of 7.5% reduction in multimodal confidence calibration errors and up to 8.3% improvement in task performance.

We present a comprehensive evaluation of proprietary and open-weights large language models using the first astronomy-specific benchmarking dataset. This dataset comprises 4,425 multiple-choice questions curated from the Annual Review of Astronomy and Astrophysics, covering a broad range of astrophysical topics. Our analysis examines model performance across various astronomical subfields and assesses response calibration, crucial for potential deployment in research environments. Claude-3.5-Sonnet outperforms competitors by up to 4.6 percentage points, achieving 85.0% accuracy. For proprietary models, we observed a universal reduction in cost every 3-to-12 months to achieve similar score in this particular astronomy benchmark. Open-source models have rapidly improved, with LLaMA-3-70b (80.6%) and Qwen-2-72b (77.7%) now competing with some of the best proprietary models. We identify performance variations across topics, with non-English-focused models generally struggling more in exoplanet-related fields, stellar astrophysics, and instrumentation related questions. These challenges likely stem from less abundant training data, limited historical context, and rapid recent developments in these areas. This pattern is observed across both open-weights and proprietary models, with regional dependencies evident, highlighting the impact of training data diversity on model performance in specialized scientific domains. Top-performing models demonstrate well-calibrated confidence, with correlations above 0.9 between confidence and correctness, though they tend to be slightly underconfident. The development for fast, low-cost inference of open-weights models presents new opportunities for affordable deployment in astronomy. The rapid progress observed suggests that LLM-driven research in astronomy may become feasible in the near future.

Deep learning (DL) has become the dominant approach for medical image segmentation, yet ensuring the reliability and clinical applicability of these models requires addressing key challenges such as annotation variability, calibration, and uncertainty estimation. This is why we created the Calibration and Uncertainty for multiRater Volume Assessment in multiorgan Segmentation (CURVAS), which highlights the critical role of multiple annotators in establishing a more comprehensive ground truth, emphasizing that segmentation is inherently subjective and that leveraging inter-annotator variability is essential for robust model evaluation. Seven teams participated in the challenge, submitting a variety of DL models evaluated using metrics such as Dice Similarity Coefficient (DSC), Expected Calibration Error (ECE), and Continuous Ranked Probability Score (CRPS). By incorporating consensus and dissensus ground truth, we assess how DL models handle uncertainty and whether their confidence estimates align with true segmentation performance. Our findings reinforce the importance of well-calibrated models, as better calibration is strongly correlated with the quality of the results. Furthermore, we demonstrate that segmentation models trained on diverse datasets and enriched with pre-trained knowledge exhibit greater robustness, particularly in cases deviating from standard anatomical structures. Notably, the best-performing models achieved high DSC and well-calibrated uncertainty estimates. This work underscores the need for multi-annotator ground truth, thorough calibration assessments, and uncertainty-aware evaluations to develop trustworthy and clinically reliable DL-based medical image segmentation models.

The Mixture of Experts (MoE) paradigm provides a powerful way to decompose inscrutable dense layers into smaller, modular computations often more amenable to human interpretation, debugging, and editability. A major problem however lies in the computational cost of scaling the number of experts to achieve sufficiently fine-grained specialization. In this paper, we propose the Multilinear Mixutre of Experts (MMoE) layer to address this, focusing on vision models. MMoE layers perform an implicit computation on prohibitively large weight tensors entirely in factorized form. Consequently, MMoEs both (1) avoid the issues incurred through the discrete expert routing in the popular 'sparse' MoE models, yet (2) do not incur the restrictively high inference-time costs of 'soft' MoE alternatives. We present both qualitative and quantitative evidence (through visualization and counterfactual interventions respectively) that scaling MMoE layers when fine-tuning foundation models for vision tasks leads to more specialized experts at the class-level whilst remaining competitive with the performance of parameter-matched linear layer counterparts. Finally, we show that learned expert specialism further facilitates manual correction of demographic bias in CelebA attribute classification. Our MMoE model code is available at https://github.com/james-oldfield/MMoE.

Large Language Models (LLMs) have demonstrated great capabilities in solving a wide range of tasks in a resource-efficient manner through prompting, which does not require task-specific training, but suffers from performance fluctuation when there are multiple prompt candidates. Previous works have introduced gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but fail to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common NLP tasks. We find that all existing methods can be unified into some variant of the method that maximizes the mutual information between the input and the corresponding model output (denoted as MI). Using the finding, we develop several variants of MI and increases the effectiveness of the best prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to existing methods and helps increase the prompt selection effectiveness of the best method by 99.44%. The code and datasets used in our work will be released at https://github.com/soheeyang/unified-prompt-selection.

Context faithfulness is essential for reliable reasoning in context-dependent scenarios. However, large language models often struggle to ground their outputs in the provided context, resulting in irrelevant responses. Inspired by the emergent expert specialization observed in mixture-of-experts architectures, this work investigates whether certain experts exhibit specialization in context utilization, offering a potential pathway toward targeted optimization for improved context faithfulness. To explore this, we propose Router Lens, a method that accurately identifies context-faithful experts. Our analysis reveals that these experts progressively amplify attention to relevant contextual information, thereby enhancing context grounding. Building on this insight, we introduce Context-faithful Expert Fine-Tuning (CEFT), a lightweight optimization approach that selectively fine-tunes context-faithful experts. Experiments across a wide range of benchmarks and models demonstrate that CEFT matches or surpasses the performance of full fine-tuning while being significantly more efficient.

Large language models (LLMs) are able to solve various tasks with only a few demonstrations utilizing their in-context learning (ICL) abilities. However, LLMs often rely on their pre-trained semantic priors of demonstrations rather than on the input-label relationships to proceed with ICL prediction. In this work, we term this phenomenon as the 'Demonstration Shortcut'. While previous works have primarily focused on improving ICL prediction results for predefined tasks, we aim to rectify the Demonstration Shortcut, thereby enabling the LLM to effectively learn new input-label relationships from demonstrations. To achieve this, we introduce In-Context Calibration, a demonstration-aware calibration method. We evaluate the effectiveness of the proposed method in two settings: (1) the Original ICL Task using the standard label space and (2) the Task Learning setting, where the label space is replaced with semantically unrelated tokens. In both settings, In-Context Calibration demonstrates substantial improvements, with results generalized across three LLM families (OPT, GPT, and Llama2) under various configurations.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific ``skills,'' but there has been limited study of where these newly-learnt skills reside inside the massive model. This paper introduces the term skill localization for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters (sim0.01% of model parameters) responsible for (>95%) of the model's performance, in the sense that grafting the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further re-training is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution (40-90% error reduction) as well as the quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms of continual learning.

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach leverages human judgment to distinguish inputs which are algorithmically indistinguishable, or "look the same" to predictive algorithms. We argue that this framing clarifies the problem of human-AI collaboration in prediction tasks, as experts often form judgments by drawing on information which is not encoded in an algorithm's training data. Algorithmic indistinguishability yields a natural test for assessing whether experts incorporate this kind of "side information", and further provides a simple but principled method for selectively incorporating human feedback into algorithmic predictions. We show that this method provably improves the performance of any feasible algorithmic predictor and precisely quantify this improvement. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can improve algorithmic predictions on specific instances (which can be identified ex-ante). In an X-ray classification task, we find that this subset constitutes nearly 30% of the patient population. Our approach provides a natural way of uncovering this heterogeneity and thus enabling effective human-AI collaboration.

Large language models (LLMs) are increasingly used as evaluators in lieu of humans. While scalable, their judgments are noisy due to imperfect specificity and sensitivity of LLMs, leading to biased accuracy estimates. Although bias-correction methods exist, they are underutilized in LLM research and typically assume exact knowledge of the model's specificity and sensitivity. Furthermore, in general we only have estimates of these values and it is not well known how to properly construct confidence intervals using only estimates. This work presents a simple plug-in framework that corrects such bias and constructs confidence intervals reflecting uncertainty from both test and calibration dataset, enabling practical and statistically sound LLM-based evaluation. Additionally, to reduce uncertainty in the accuracy estimate, we introduce an adaptive algorithm that efficiently allocates calibration sample sizes.

Fluorescence LiDAR (FLiDAR), a Light Detection and Ranging (LiDAR) technology employed for distance and depth estimation across medical, automotive, and other fields, encounters significant computational challenges in scattering media. The complex nature of the acquired FLiDAR signal, particularly in such environments, makes isolating photon time-of-flight (related to target depth) and intrinsic fluorescence lifetime exceptionally difficult, thus limiting the effectiveness of current analytical and computational methodologies. To overcome this limitation, we present a Physics-Guided Mixture-of-Experts (MoE) framework tailored for specialized modeling of diverse temporal components. In contrast to the conventional MoE approaches our expert models are informed by underlying physics, such as the radiative transport equation governing photon propagation in scattering media. Central to our approach is EvidenceMoE, which integrates Evidence-Based Dirichlet Critics (EDCs). These critic models assess the reliability of each expert's output by providing per-expert quality scores and corrective feedback. A Decider Network then leverages this information to fuse expert predictions into a robust final estimate adaptively. We validate our method using realistically simulated Fluorescence LiDAR (FLiDAR) data for non-invasive cancer cell depth detection generated from photon transport models in tissue. Our framework demonstrates strong performance, achieving a normalized root mean squared error (NRMSE) of 0.030 for depth estimation and 0.074 for fluorescence lifetime.

Recent advancements indicate that scaling up Multimodal Large Language Models (MLLMs) effectively enhances performance on downstream multimodal tasks. The prevailing MLLM paradigm, e.g., LLaVA, transforms visual features into text-like tokens using a static vision-language mapper, thereby enabling static LLMs to develop the capability to comprehend visual information through visual instruction tuning. Although promising, the static tuning strategy~The static tuning refers to the trained model with static parameters. that shares the same parameters may constrain performance across different downstream multimodal tasks. In light of this, we introduce HyperLLaVA, which involves adaptive tuning of the projector and LLM parameters, in conjunction with a dynamic visual expert and language expert, respectively. These experts are derived from HyperNetworks, which generates adaptive parameter shifts through visual and language guidance, enabling dynamic projector and LLM modeling in two-stage training. Our experiments demonstrate that our solution significantly surpasses LLaVA on existing MLLM benchmarks, including MME, MMBench, SEED-Bench, and LLaVA-Bench. ~Our project is available on the link https://github.com/DCDmllm/HyperLLaVA.

The partial label challenge in Multi-Label Class-Incremental Learning (MLCIL) arises when only the new classes are labeled during training, while past and future labels remain unavailable. This issue leads to a proliferation of false-positive errors due to erroneously high confidence multi-label predictions, exacerbating catastrophic forgetting within the disjoint label space. In this paper, we aim to refine multi-label confidence calibration in MLCIL and propose a Confidence Self-Calibration (CSC) approach. Firstly, for label relationship calibration, we introduce a class-incremental graph convolutional network that bridges the isolated label spaces by constructing learnable, dynamically extended label relationship graph. Then, for confidence calibration, we present a max-entropy regularization for each multi-label increment, facilitating confidence self-calibration through the penalization of over-confident output distributions. Our approach attains new state-of-the-art results in MLCIL tasks on both MS-COCO and PASCAL VOC datasets, with the calibration of label confidences confirmed through our methodology.

We introduce a novel architecture, UniCal, for Camera-to-LiDAR (C2L) extrinsic calibration which leverages self-attention mechanisms through a Transformer-based backbone network to infer the 6-degree of freedom (DoF) relative transformation between the sensors. Unlike previous methods, UniCal performs an early fusion of the input camera and LiDAR data by aggregating camera image channels and LiDAR mappings into a multi-channel unified representation before extracting their features jointly with a single-branch architecture. This single-branch architecture makes UniCal lightweight, which is desirable in applications with restrained resources such as autonomous driving. Through experiments, we show that UniCal achieves state-of-the-art results compared to existing methods. We also show that through transfer learning, weights learned on the calibration task can be applied to a calibration validation task without re-training the backbone.

We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts during each iteration, rather than being statically assigned. As a result, CoE introduces a flexible routing mechanism that increases the diversity of expert combinations and enriches the model's representational capacity. CoE demonstrates improved performance under fixed compute: on math reasoning tasks, it reduces validation loss from 1.20 to 1.12 compared to a standard MoE. Beyond performance, CoE offers a new scaling axis: depth through expert iteration, which complements conventional width/depth scaling. For example, using 2x iterations matches the performance of 3x expert selections (in width), while reducing memory usage by 17.6-42% relative to other scaling strategies. Our analysis reveals that CoE's benefits stem from its iterative residual structure and enhanced expert specialization empowered by iterative routing, which together unlock more expressive representations. Code is available at https://github.com/ZihanWang314/coe.

Mixture-of-Experts (MoE) enables efficient scaling of large language models by activating only a subset of experts per input token. However, deploying MoE-based models incurs significant memory overhead due to the need to retain all experts in memory. While structured pruning is promising to reduce memory costs, existing methods often show suboptimal performance and unstable degradation in three dimensions: model architectures, calibration data sources, and calibration sample sizes. This paper proposes Mixture-of-Novices-and-Experts (MoNE), a novel expert pruning method that replaces redundant experts with lightweight novices to achieve effective and robust model compression. MoNE evaluates expert redundancy based on two metrics: access frequency and output variance. Experts exhibiting low usage and stable outputs are pruned and replaced with lightweight novices-unbiased estimations of their original outputs-minimizing performance degradation. Extensive experiments demonstrate that MoNE consistently outperforms baseline methods with minimal accuracy degradation across the three dimensions, confirming its effectiveness and robustness. Notably, it improves the average zero shot accuracy across nine downstream tasks by up to 2.71 under 25\% pruning ratio and 3.61 under 50\% pruning. The code is available at https://github.com/zxgx/mode-pd.

We study the tradeoff between computational effort and classification accuracy in a cascade of deep neural networks. During inference, the user sets the acceptable accuracy degradation which then automatically determines confidence thresholds for the intermediate classifiers. As soon as the confidence threshold is met, inference terminates immediately without having to compute the output of the complete network. Confidence levels are derived directly from the softmax outputs of intermediate classifiers, as we do not train special decision functions. We show that using a softmax output as a confidence measure in a cascade of deep neural networks leads to a reduction of 15%-50% in the number of MAC operations while degrading the classification accuracy by roughly 1%. Our method can be easily incorporated into pre-trained non-cascaded architectures, as we exemplify on ResNet. Our main contribution is a method that dynamically adjusts the tradeoff between accuracy and computation without retraining the model.

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift, this behavior remains understudied for GNNs. Hence, we begin with a case study on CI calibration under controlled structural and feature distribution shifts and demonstrate that increased expressivity or model size do not always lead to improved CI performance. Consequently, we instead advocate for the use of epistemic uncertainty quantification (UQ) methods to modulate CIs. To this end, we propose G-DeltaUQ, a new single model UQ method that extends the recently proposed stochastic centering framework to support structured data and partial stochasticity. Evaluated across covariate, concept, and graph size shifts, G-DeltaUQ not only outperforms several popular UQ methods in obtaining calibrated CIs, but also outperforms alternatives when CIs are used for generalization gap prediction or OOD detection. Overall, our work not only introduces a new, flexible GNN UQ method, but also provides novel insights into GNN CIs on safety-critical tasks.

Mixture-of-Experts (MoE) architectures in large language models (LLMs) deliver exceptional performance and reduced inference costs compared to dense LLMs. However, their large parameter counts result in prohibitive memory requirements, limiting practical deployment. While existing pruning methods primarily focus on expert-level pruning, this coarse granularity often leads to substantial accuracy degradation. In this work, we introduce HEAPr, a novel pruning algorithm that decomposes experts into smaller, indivisible atomic experts, enabling more precise and flexible atomic expert pruning. To measure the importance of each atomic expert, we leverage second-order information based on principles similar to Optimal Brain Surgeon (OBS) theory. To address the computational and storage challenges posed by second-order information, HEAPr exploits the inherent properties of atomic experts to transform the second-order information from expert parameters into that of atomic expert parameters, and further simplifies it to the second-order information of atomic expert outputs. This approach reduces the space complexity from O(d^4), where d is the model's dimensionality, to O(d^2). HEAPr requires only two forward passes and one backward pass on a small calibration set to compute the importance of atomic experts. Extensive experiments on MoE models, including DeepSeek MoE and Qwen MoE family, demonstrate that HEAPr outperforms existing expert-level pruning methods across a wide range of compression ratios and benchmarks. Specifically, HEAPr achieves nearly lossless compression at compression ratios of 20% ~ 25% in most models, while also reducing FLOPs nearly by 20%. The code can be found at https://github.com/LLIKKE/HEAPr{https://github.com/LLIKKE/HEAPr}.