Daily Papers

Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the joint log-likelihood of the reasoning and final answer. The joint log-likelihood of the reasoning and final answer naturally decomposes into reasoning confidence and answer confidence. PiCSAR achieves substantial gains across diverse benchmarks (+10.18 on MATH500, +9.81 on AIME2025), outperforming baselines with at least 2x fewer samples in 16 out of 20 comparisons. Our analysis reveals that correct reasoning chains exhibit significantly higher reasoning and answer confidence, justifying the effectiveness of PiCSAR.

Benefiting from prompt tuning, recent years have witnessed the promising performance of pre-trained vision-language models, e.g., CLIP, on versatile downstream tasks. In this paper, we focus on a particular setting of learning adaptive prompts on the fly for each test sample from an unseen new domain, which is known as test-time prompt tuning (TPT). Existing TPT methods typically rely on data augmentation and confidence selection. However, conventional data augmentation techniques, e.g., random resized crops, suffers from the lack of data diversity, while entropy-based confidence selection alone is not sufficient to guarantee prediction fidelity. To address these issues, we propose a novel TPT method, named DiffTPT, which leverages pre-trained diffusion models to generate diverse and informative new data. Specifically, we incorporate augmented data by both conventional method and pre-trained stable diffusion to exploit their respective merits, improving the models ability to adapt to unknown new test data. Moreover, to ensure the prediction fidelity of generated data, we introduce a cosine similarity-based filtration technique to select the generated data with higher similarity to the single test sample. Our experiments on test datasets with distribution shifts and unseen categories demonstrate that DiffTPT improves the zero-shot accuracy by an average of 5.13\% compared to the state-of-the-art TPT method. Our code and models will be publicly released.

Pre-trained vision-language models (e.g., CLIP) have shown promising zero-shot generalization in many downstream tasks with properly designed text prompts. Instead of relying on hand-engineered prompts, recent works learn prompts using the training data from downstream tasks. While effective, training on domain-specific data reduces a model's generalization capability to unseen new domains. In this work, we propose test-time prompt tuning (TPT), a method that can learn adaptive prompts on the fly with a single test sample. For image classification, TPT optimizes the prompt by minimizing the entropy with confidence selection so that the model has consistent predictions across different augmented views of each test sample. In evaluating generalization to natural distribution shifts, TPT improves the zero-shot top-1 accuracy of CLIP by 3.6% on average, surpassing previous prompt tuning approaches that require additional task-specific training data. In evaluating cross-dataset generalization with unseen categories, TPT performs on par with the state-of-the-art approaches that use additional training data. Project page: https://azshue.github.io/TPT.

Large language model pretraining is compute-intensive, yet many tokens contribute marginally to learning, resulting in inefficiency. We introduce Efficient Selective Language Modeling (ESLM), a risk-aware algorithm that improves training efficiency and distributional robustness by performing online token-level batch selection. ESLM leverages per-token statistics (e.g., entropy or loss) and applies value-at-risk thresholding to retain only the most informative tokens per batch. This data-centric mechanism reshapes the training loss, prioritizing high-risk tokens and eliminating redundant gradient computation. We frame ESLM as a bilevel game: the model competes with a masking adversary that selects worst-case token subsets under a constrained thresholding rule. In the loss-based setting, ESLM recovers conditional value-at-risk loss minimization, providing a principled connection to distributionally robust optimization. We extend our approach to Ada-ESLM, which adaptively tunes the selection confidence during training. Experiments on GPT-2 pretraining show that ESLM significantly reduces training FLOPs while maintaining or improving both perplexity and downstream performance compared to baselines. Our approach also scales across model sizes, pretraining corpora, and integrates naturally with knowledge distillation.

Several recent studies have shown that the use of extra in-distribution data can lead to a high level of adversarial robustness. However, there is no guarantee that it will always be possible to obtain sufficient extra data for a selected dataset. In this paper, we propose a biased multi-domain adversarial training (BiaMAT) method that induces training data amplification on a primary dataset using publicly available auxiliary datasets, without requiring the class distribution match between the primary and auxiliary datasets. The proposed method can achieve increased adversarial robustness on a primary dataset by leveraging auxiliary datasets via multi-domain learning. Specifically, data amplification on both robust and non-robust features can be accomplished through the application of BiaMAT as demonstrated through a theoretical and empirical analysis. Moreover, we demonstrate that while existing methods are vulnerable to negative transfer due to the distributional discrepancy between auxiliary and primary data, the proposed method enables neural networks to flexibly leverage diverse image datasets for adversarial training by successfully handling the domain discrepancy through the application of a confidence-based selection strategy. The pre-trained models and code are available at: https://github.com/Saehyung-Lee/BiaMAT.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

While semi-supervised learning (SSL) has yielded promising results, the more realistic SSL scenario remains to be explored, in which the unlabeled data exhibits extremely high recognition difficulty, e.g., fine-grained visual classification in the context of SSL (SS-FGVC). The increased recognition difficulty on fine-grained unlabeled data spells disaster for pseudo-labeling accuracy, resulting in poor performance of the SSL model. To tackle this challenge, we propose Soft Label Selection with Confidence-Aware Clustering based on Class Transition Tracking (SoC) by reconstructing the pseudo-label selection process by jointly optimizing Expansion Objective and Shrinkage Objective, which is based on a soft label manner. Respectively, the former objective encourages soft labels to absorb more candidate classes to ensure the attendance of ground-truth class, while the latter encourages soft labels to reject more noisy classes, which is theoretically proved to be equivalent to entropy minimization. In comparisons with various state-of-the-art methods, our approach demonstrates its superior performance in SS-FGVC. Checkpoints and source code are available at https://github.com/NJUyued/SoC4SS-FGVC.

Neural Radiance Fields (NeRFs) are emerging as a ubiquitous scene representation that allows for novel view synthesis. Increasingly, NeRFs will be shareable with other people. Before sharing a NeRF, though, it might be desirable to remove personal information or unsightly objects. Such removal is not easily achieved with the current NeRF editing frameworks. We propose a framework to remove objects from a NeRF representation created from an RGB-D sequence. Our NeRF inpainting method leverages recent work in 2D image inpainting and is guided by a user-provided mask. Our algorithm is underpinned by a confidence based view selection procedure. It chooses which of the individual 2D inpainted images to use in the creation of the NeRF, so that the resulting inpainted NeRF is 3D consistent. We show that our method for NeRF editing is effective for synthesizing plausible inpaintings in a multi-view coherent manner. We validate our approach using a new and still-challenging dataset for the task of NeRF inpainting.

While significant advances exist in pseudo-label generation for semi-supervised semantic segmentation, pseudo-label selection remains understudied. Existing methods typically use fixed confidence thresholds to retain high-confidence predictions as pseudo-labels. However, these methods cannot cope with network overconfidence tendency, where correct and incorrect predictions overlap significantly in high-confidence regions, making separation challenging and amplifying model cognitive bias. Meanwhile, the direct discarding of low-confidence predictions disrupts spatial-semantic continuity, causing critical context loss. We propose Confidence Separable Learning (CSL) to address these limitations. CSL formulates pseudo-label selection as a convex optimization problem within the confidence distribution feature space, establishing sample-specific decision boundaries to distinguish reliable from unreliable predictions. Additionally, CSL introduces random masking of reliable pixels to guide the network in learning contextual relationships from low-reliability regions, thereby mitigating the adverse effects of discarding uncertain predictions. Extensive experimental results on the Pascal, Cityscapes, and COCO benchmarks show that CSL performs favorably against state-of-the-art methods. Code and model weights are available at https://github.com/PanLiuCSU/CSL.

Recent advancements in video large multimodal models (LMMs) have significantly improved their video understanding and reasoning capabilities. However, their performance drops on out-of-distribution (OOD) tasks that are underrepresented in training data. Traditional methods like fine-tuning on OOD datasets are impractical due to high computational costs. While In-context learning (ICL) with demonstration examples has shown promising generalization performance in language tasks and image-language tasks without fine-tuning, applying ICL to video-language tasks faces challenges due to the limited context length in Video LMMs, as videos require longer token lengths. To address these issues, we propose VideoICL, a novel video in-context learning framework for OOD tasks that introduces a similarity-based relevant example selection strategy and a confidence-based iterative inference approach. This allows to select the most relevant examples and rank them based on similarity, to be used for inference. If the generated response has low confidence, our framework selects new examples and performs inference again, iteratively refining the results until a high-confidence response is obtained. This approach improves OOD video understanding performance by extending effective context length without incurring high costs. The experimental results on multiple benchmarks demonstrate significant performance gains, especially in domain-specific scenarios, laying the groundwork for broader video comprehension applications. Code will be released at https://github.com/KangsanKim07/VideoICL

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

Domain adaptive panoptic segmentation promises to resolve the long tail of corner cases in natural scene understanding. Previous state of the art addresses this problem with cross-task consistency, careful system-level optimization and heuristic improvement of teacher predictions. In contrast, we propose to build upon remarkable capability of mask transformers to estimate their own prediction uncertainty. Our method avoids noise amplification by leveraging fine-grained confidence of panoptic teacher predictions. In particular, we modulate the loss with mask-wide confidence and discourage back-propagation in pixels with uncertain teacher or confident student. Experimental evaluation on standard benchmarks reveals a substantial contribution of the proposed selection techniques. We report 47.4 PQ on Synthia to Cityscapes, which corresponds to an improvement of 6.2 percentage points over the state of the art. The source code is available at https://github.com/helen1c/MC-PanDA.

Large language models (LLMs) are increasingly trained with reinforcement learning from verifiable rewards (RLVR), yet real-world deployment demands models that can self-improve without labels or external judges. Existing label-free methods, confidence minimization, self-consistency, or majority-vote objectives, stabilize learning but steadily shrink exploration, causing an entropy collapse: generations become shorter, less diverse, and brittle. Unlike prior approaches such as Test-Time Reinforcement Learning (TTRL), which primarily adapt models to the immediate unlabeled dataset at hand, our goal is broader: to enable general improvements without sacrificing the model's inherent exploration capacity and generalization ability, i.e., evolving. We formalize this issue and propose EVolution-Oriented and Label-free Reinforcement Learning (EVOL-RL), a simple rule that couples stability with variation under a label-free setting. EVOL-RL keeps the majority-voted answer as a stable anchor (selection) while adding a novelty-aware reward that favors responses whose reasoning differs from what has already been produced (variation), measured in semantic space. Implemented with GRPO, EVOL-RL also uses asymmetric clipping to preserve strong signals and an entropy regularizer to sustain search. This majority-for-selection + novelty-for-variation design prevents collapse, maintains longer and more informative chains of thought, and improves both pass@1 and pass@n. EVOL-RL consistently outperforms the majority-only TTRL baseline; e.g., training on label-free AIME24 lifts Qwen3-4B-Base AIME25 pass@1 from TTRL's 4.6% to 16.4%, and pass@16 from 18.5% to 37.9%. EVOL-RL not only prevents diversity collapse but also unlocks stronger generalization across domains (e.g., GPQA). Furthermore, we demonstrate that EVOL-RL also boosts performance in the RLVR setting, highlighting its broad applicability.

Masked speech modeling (MSM) methods such as wav2vec2 or w2v-BERT learn representations over speech frames which are randomly masked within an utterance. While these methods improve performance of Automatic Speech Recognition (ASR) systems, they have one major limitation. They treat all unsupervised speech samples with equal weight, which hinders learning as not all samples have relevant information to learn meaningful representations. In this work, we address this limitation. We propose ask2mask (ATM), a novel approach to focus on specific samples during MSM pre-training. ATM employs an external ASR model or scorer to weight unsupervised input samples in two different ways: 1) A fine-grained data selection is performed by masking over the highly confident input frames as chosen by the scorer. This allows the model to learn meaningful representations. 2) ATM is further extended to focus at utterance-level by weighting the final MSM loss with the utterance-level confidence score. We conduct fine-tuning experiments on two well-benchmarked corpora: LibriSpeech (matching the pre-training data) and Commonvoice, TED-LIUM, AMI and CHiME-6 (not matching the pre-training data). The results substantiate the efficacy of ATM on significantly improving the recognition performance under mismatched conditions (up to 11.6\% relative over published results and upto 4.46\% relative over our internal baseline) while still yielding modest improvements under matched conditions.

Large Reasoning Models (LRMs) perform strongly in complex reasoning tasks via Chain-of-Thought (CoT) prompting, but often suffer from verbose outputs caused by redundant content, increasing computational overhead, and degrading user experience. Existing compression methods either operate post-hoc pruning, risking disruption to reasoning coherence, or rely on sampling-based selection, which fails to intervene effectively during generation. In this work, we introduce a confidence-guided perspective to explain the emergence of redundant reflection in LRMs, identifying two key patterns: Confidence Deficit, where the model reconsiders correct steps due to low internal confidence, and Termination Delay, where reasoning continues even after reaching a confident answer. Based on this analysis, we propose ConCISE (Confidence-guided Compression In Step-by-step Efficient Reasoning), a framework that simplifies reasoning chains by reinforcing the model's confidence during inference, thus preventing the generation of redundant reflection steps. It integrates Confidence Injection to stabilize intermediate steps and Early Stopping to terminate reasoning when confidence is sufficient. Extensive experiments demonstrate that fine-tuning LRMs on ConCISE-generated data yields significantly shorter outputs, reducing length by up to approximately 50% under SimPO, while maintaining high task accuracy. ConCISE consistently outperforms existing baselines across multiple reasoning benchmarks.

Existing frameworks for evaluating and comparing generative models consider an offline setting, where the evaluator has access to large batches of data produced by the models. However, in practical scenarios, the goal is often to identify and select the best model using the fewest possible generated samples to minimize the costs of querying data from the sub-optimal models. In this work, we propose an online evaluation and selection framework to find the generative model that maximizes a standard assessment score among a group of available models. We view the task as a multi-armed bandit (MAB) and propose upper confidence bound (UCB) bandit algorithms to identify the model producing data with the best evaluation score that quantifies the quality and diversity of generated data. Specifically, we develop the MAB-based selection of generative models considering the Fr\'echet Distance (FD) and Inception Score (IS) metrics, resulting in the FD-UCB and IS-UCB algorithms. We prove regret bounds for these algorithms and present numerical results on standard image datasets. Our empirical results suggest the efficacy of MAB approaches for the sample-efficient evaluation and selection of deep generative models. The project code is available at https://github.com/yannxiaoyanhu/dgm-online-eval.

Best-of-N selection is a key technique for improving the reasoning performance of Large Language Models (LLMs) through increased test-time computation. Current state-of-the-art methods often employ computationally intensive reward models for response evaluation and selection. Reward-free alternatives, like self-consistency and universal self-consistency, are limited in their ability to handle open-ended generation tasks or scale effectively. To address these limitations, we propose self-certainty, a novel and efficient metric that leverages the inherent probability distribution of LLM outputs to estimate response quality without requiring external reward models. We hypothesize that higher distributional self-certainty, aggregated across multiple samples, correlates with improved response accuracy, as it reflects greater confidence in the generated output. Through extensive experiments on various reasoning tasks, we demonstrate that self-certainty (1) scales effectively with increasing sample size N, akin to reward models but without the computational overhead; (2) complements chain-of-thought, improving reasoning performance beyond greedy decoding; and (3) generalizes to open-ended tasks where traditional self-consistency methods fall short. Our findings establish self-certainty as a practical and efficient way for improving LLM reasoning capabilities. The code is available at https://github.com/backprop07/Self-Certainty

The choice of initial noise significantly affects the quality and prompt alignment of video diffusion models, where different noise seeds for the same prompt can lead to drastically different generations. While recent methods rely on externally designed priors such as frequency filters or inter-frame smoothing, they often overlook internal model signals that indicate which noise seeds are inherently preferable. To address this, we propose ANSE (Active Noise Selection for Generation), a model-aware framework that selects high-quality noise seeds by quantifying attention-based uncertainty. At its core is BANSA (Bayesian Active Noise Selection via Attention), an acquisition function that measures entropy disagreement across multiple stochastic attention samples to estimate model confidence and consistency. For efficient inference-time deployment, we introduce a Bernoulli-masked approximation of BANSA that enables score estimation using a single diffusion step and a subset of attention layers. Experiments on CogVideoX-2B and 5B demonstrate that ANSE improves video quality and temporal coherence with only an 8% and 13% increase in inference time, respectively, providing a principled and generalizable approach to noise selection in video diffusion. See our project page: https://anse-project.github.io/anse-project/

While multi-modal large language models (MLLMs) have made significant progress in complex reasoning tasks via reinforcement learning, it is commonly believed that extensive training data is necessary for improving multi-modal reasoning ability, inevitably leading to data redundancy and substantial computational costs. However, can smaller high-value datasets match or outperform full corpora for multi-modal reasoning in MLLMs? In this work, we challenge this assumption through a key observation: meaningful multi-modal reasoning is triggered by only a sparse subset of training samples, termed cognitive samples, whereas the majority contribute marginally. Building on this insight, we propose a novel data selection paradigm termed Reasoning Activation Potential (RAP), which identifies cognitive samples by estimating each sample's potential to stimulate genuine multi-modal reasoning by two complementary estimators: 1) Causal Discrepancy Estimator (CDE) based on the potential outcome model principle, eliminates samples that overly rely on language priors by comparing outputs between multi-modal and text-only inputs; 2) Attention Confidence Estimator (ACE), which exploits token-level self-attention to discard samples dominated by irrelevant but over-emphasized tokens in intermediate reasoning stages. Moreover, we introduce a Difficulty-aware Replacement Module (DRM) to substitute trivial instances with cognitively challenging ones, thereby ensuring complexity for robust multi-modal reasoning. Experiments on six datasets show that our RAP method consistently achieves superior performance using only 9.3% of the training data, while reducing computational costs by over 43%. Our code is available at https://github.com/Leo-ssl/RAP.

Image attribution algorithms aim to identify important regions that are highly relevant to model decisions. Although existing attribution solutions can effectively assign importance to target elements, they still face the following challenges: 1) existing attribution methods generate inaccurate small regions thus misleading the direction of correct attribution, and 2) the model cannot produce good attribution results for samples with wrong predictions. To address the above challenges, this paper re-models the above image attribution problem as a submodular subset selection problem, aiming to enhance model interpretability using fewer regions. To address the lack of attention to local regions, we construct a novel submodular function to discover more accurate small interpretation regions. To enhance the attribution effect for all samples, we also impose four different constraints on the selection of sub-regions, i.e., confidence, effectiveness, consistency, and collaboration scores, to assess the importance of various subsets. Moreover, our theoretical analysis substantiates that the proposed function is in fact submodular. Extensive experiments show that the proposed method outperforms SOTA methods on two face datasets (Celeb-A and VGG-Face2) and one fine-grained dataset (CUB-200-2011). For correctly predicted samples, the proposed method improves the Deletion and Insertion scores with an average of 4.9% and 2.5% gain relative to HSIC-Attribution. For incorrectly predicted samples, our method achieves gains of 81.0% and 18.4% compared to the HSIC-Attribution algorithm in the average highest confidence and Insertion score respectively. The code is released at https://github.com/RuoyuChen10/SMDL-Attribution.

To develop a trustworthy AI system, which aim to identify the input regions that most influence the models decisions. The primary task of existing attribution methods lies in efficiently and accurately identifying the relationships among input-prediction interactions. Particularly when the input data is discrete, such as images, analyzing the relationship between inputs and outputs poses a significant challenge due to the combinatorial explosion. In this paper, we propose a novel and efficient black-box attribution mechanism, LiMA (Less input is More faithful for Attribution), which reformulates the attribution of important regions as an optimization problem for submodular subset selection. First, to accurately assess interactions, we design a submodular function that quantifies subset importance and effectively captures their impact on decision outcomes. Then, efficiently ranking input sub-regions by their importance for attribution, we improve optimization efficiency through a novel bidirectional greedy search algorithm. LiMA identifies both the most and least important samples while ensuring an optimal attribution boundary that minimizes errors. Extensive experiments on eight foundation models demonstrate that our method provides faithful interpretations with fewer regions and exhibits strong generalization, shows an average improvement of 36.3% in Insertion and 39.6% in Deletion. Our method also outperforms the naive greedy search in attribution efficiency, being 1.6 times faster. Furthermore, when explaining the reasons behind model prediction errors, the average highest confidence achieved by our method is, on average, 86.1% higher than that of state-of-the-art attribution algorithms. The code is available at https://github.com/RuoyuChen10/LIMA.

The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

Audio and visual signals typically occur simultaneously, and humans possess an innate ability to correlate and synchronize information from these two modalities. Recently, a challenging problem known as Audio-Visual Segmentation (AVS) has emerged, intending to produce segmentation maps for sounding objects within a scene. However, the methods proposed so far have not sufficiently integrated audio and visual information, and the computational costs have been extremely high. Additionally, the outputs of different stages have not been fully utilized. To facilitate this research, we introduce a novel Progressive Confident Masking Attention Network (PMCANet). It leverages attention mechanisms to uncover the intrinsic correlations between audio signals and visual frames. Furthermore, we design an efficient and effective cross-attention module to enhance semantic perception by selecting query tokens. This selection is determined through confidence-driven units based on the network's multi-stage predictive outputs. Experiments demonstrate that our network outperforms other AVS methods while requiring less computational resources. The code is available at: https://github.com/PrettyPlate/PCMANet.

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

In this paper, the causal bandit problem is investigated, in which the objective is to select an optimal sequence of interventions on nodes in a causal graph. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. By exploiting the causal relationships between the nodes whose signals contribute to the reward, interventions are optimized. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed, which strongly reduces sample complexity relative to the prior art by learning sub-graphs. Under the assumption of Gaussian exogenous inputs and minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound based intervention selection to optimize the reward. To cope with non-stationary bandits, a sub-graph change detection mechanism is proposed, with high sample efficiency. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in both stationary and non-stationary settings. Compared to existing approaches, the proposed scheme takes 67% fewer samples to learn the causal structure and achieves an average reward gain of 85%.

The LLM-as-a-Judge paradigm shows promise for evaluating generative content but lacks reliability in reasoning-intensive scenarios, such as programming. Inspired by recent advances in reasoning models and shifts in scaling laws, we pioneer bringing test-time computation into LLM-as-a-Judge, proposing MCTS-Judge, a resource-efficient, System-2 thinking framework for code correctness evaluation. MCTS-Judge leverages Monte Carlo Tree Search (MCTS) to decompose problems into simpler, multi-perspective evaluations. Through a node-selection strategy that combines self-assessment based on historical actions in the current trajectory and the Upper Confidence Bound for Trees based on prior rollouts, MCTS-Judge balances global optimization and refinement of the current trajectory. We further designed a high-precision, unit-test-level reward mechanism to encourage the Large Language Model (LLM) to perform line-by-line analysis. Extensive experiments on three benchmarks and five LLMs demonstrate the effectiveness of MCTS-Judge, which improves the base model's accuracy from 41% to 80%, surpassing the o1-series models with 3x fewer tokens. Further evaluations validate the superiority of its reasoning trajectory in logic, analytics, thoroughness, and overall quality, while revealing the test-time scaling law of the LLM-as-a-Judge paradigm.

Object detection via inaccurate bounding boxes supervision has boosted a broad interest due to the expensive high-quality annotation data or the occasional inevitability of low annotation quality (\eg tiny objects). The previous works usually utilize multiple instance learning (MIL), which highly depends on category information, to select and refine a low-quality box. Those methods suffer from object drift, group prediction and part domination problems without exploring spatial information. In this paper, we heuristically propose a Spatial Self-Distillation based Object Detector (SSD-Det) to mine spatial information to refine the inaccurate box in a self-distillation fashion. SSD-Det utilizes a Spatial Position Self-Distillation (SPSD) module to exploit spatial information and an interactive structure to combine spatial information and category information, thus constructing a high-quality proposal bag. To further improve the selection procedure, a Spatial Identity Self-Distillation (SISD) module is introduced in SSD-Det to obtain spatial confidence to help select the best proposals. Experiments on MS-COCO and VOC datasets with noisy box annotation verify our method's effectiveness and achieve state-of-the-art performance. The code is available at https://github.com/ucas-vg/PointTinyBenchmark/tree/SSD-Det.

We explore the potential of large-scale noisily labeled data to enhance feature learning by pretraining semantic segmentation models within a multi-modal framework for geospatial applications. We propose a novel Cross-modal Sample Selection (CromSS) method, a weakly supervised pretraining strategy designed to improve feature representations through cross-modal consistency and noise mitigation techniques. Unlike conventional pretraining approaches, CromSS exploits massive amounts of noisy and easy-to-come-by labels for improved feature learning beneficial to semantic segmentation tasks. We investigate middle and late fusion strategies to optimize the multi-modal pretraining architecture design. We also introduce a cross-modal sample selection module to mitigate the adverse effects of label noise, which employs a cross-modal entangling strategy to refine the estimated confidence masks within each modality to guide the sampling process. Additionally, we introduce a spatial-temporal label smoothing technique to counteract overconfidence for enhanced robustness against noisy labels. To validate our approach, we assembled the multi-modal dataset, NoLDO-S12, which consists of a large-scale noisy label subset from Google's Dynamic World (DW) dataset for pretraining and two downstream subsets with high-quality labels from Google DW and OpenStreetMap (OSM) for transfer learning. Experimental results on two downstream tasks and the publicly available DFC2020 dataset demonstrate that when effectively utilized, the low-cost noisy labels can significantly enhance feature learning for segmentation tasks. All data, code, and pretrained weights will be made publicly available.

This paper introduces the MCT Self-Refine (MCTSr) algorithm, an innovative integration of Large Language Models (LLMs) with Monte Carlo Tree Search (MCTS), designed to enhance performance in complex mathematical reasoning tasks. Addressing the challenges of accuracy and reliability in LLMs, particularly in strategic and mathematical reasoning, MCTSr leverages systematic exploration and heuristic self-refine mechanisms to improve decision-making frameworks within LLMs. The algorithm constructs a Monte Carlo search tree through iterative processes of Selection, self-refine, self-evaluation, and Backpropagation, utilizing an improved Upper Confidence Bound (UCB) formula to optimize the exploration-exploitation balance. Extensive experiments demonstrate MCTSr's efficacy in solving Olympiad-level mathematical problems, significantly improving success rates across multiple datasets, including GSM8K, GSM Hard, MATH, and Olympiad-level benchmarks, including Math Odyssey, AIME, and OlympiadBench. The study advances the application of LLMs in complex reasoning tasks and sets a foundation for future AI integration, enhancing decision-making accuracy and reliability in LLM-driven applications.

Self-training has proven to be an effective approach for cross-domain tasks, and in this study, we explore its application to cross-domain constituency parsing. Traditional self-training methods rely on limited and potentially low-quality raw corpora. To overcome this limitation, we propose enhancing self-training with the large language model (LLM) to generate domain-specific raw corpora iteratively. For the constituency parsing, we introduce grammar rules that guide the LLM in generating raw corpora and establish criteria for selecting pseudo instances. Our experimental results demonstrate that self-training for constituency parsing, equipped with an LLM, outperforms traditional methods regardless of the LLM's performance. Moreover, the combination of grammar rules and confidence criteria for pseudo-data selection yields the highest performance in the cross-domain constituency parsing.

Recent advances in masked diffusion models (MDMs) have established them as powerful non-autoregressive alternatives for sequence generation. Nevertheless, our preliminary experiments reveal that the generation quality of MDMs is still highly sensitive to the choice of decoding strategy. In particular, widely adopted uncertainty-based samplers suffer from two key limitations: a lack of global trajectory control and a pronounced bias toward trivial tokens in the early stages of decoding. These shortcomings restrict the full potential of MDMs. In this work, we introduce Position-Aware Confidence-Calibrated Sampling (PC-Sampler), a novel decoding strategy that unifies global trajectory planning with content-aware informativeness maximization. PC-Sampler incorporates a position-aware weighting mechanism to regulate the decoding path and a calibrated confidence score to suppress the premature selection of trivial tokens. Extensive experiments on three advanced MDMs across seven challenging benchmarks-including logical reasoning and planning tasks-demonstrate that PC-Sampler consistently outperforms existing MDM decoding strategies by more than 10% on average, significantly narrowing the performance gap with state-of-the-art autoregressive models. All codes are available at https://github.com/NEUIR/PC-Sampler.

Training large neural networks on large-scale datasets requires substantial computational resources, particularly for dense prediction tasks such as object detection. Although dataset distillation (DD) has been proposed to alleviate these demands by synthesizing compact datasets from larger ones, most existing work focuses solely on image classification, leaving the more complex detection setting largely unexplored. In this paper, we introduce OD3, a novel optimization-free data distillation framework specifically designed for object detection. Our approach involves two stages: first, a candidate selection process in which object instances are iteratively placed in synthesized images based on their suitable locations, and second, a candidate screening process using a pre-trained observer model to remove low-confidence objects. We perform our data synthesis framework on MS COCO and PASCAL VOC, two popular detection datasets, with compression ratios ranging from 0.25% to 5%. Compared to the prior solely existing dataset distillation method on detection and conventional core set selection methods, OD3 delivers superior accuracy, establishes new state-of-the-art results, surpassing prior best method by more than 14% on COCO mAP50 at a compression ratio of 1.0%. Code and condensed datasets are available at: https://github.com/VILA-Lab/OD3.

State-of-the-art supervised stereo matching methods have achieved remarkable performance on various benchmarks. However, their generalization to real-world scenarios remains challenging due to the scarcity of annotated real-world stereo data. In this paper, we propose ZeroStereo, a novel stereo image generation pipeline for zero-shot stereo matching. Our approach synthesizes high-quality right images from arbitrary single images by leveraging pseudo disparities generated by a monocular depth estimation model. Unlike previous methods that address occluded regions by filling missing areas with neighboring pixels or random backgrounds, we fine-tune a diffusion inpainting model to recover missing details while preserving semantic structure. Additionally, we propose Training-Free Confidence Generation, which mitigates the impact of unreliable pseudo labels without additional training, and Adaptive Disparity Selection, which ensures a diverse and realistic disparity distribution while preventing excessive occlusion and foreground distortion. Experiments demonstrate that models trained with our pipeline achieve state-of-the-art zero-shot generalization across multiple datasets with only a dataset volume comparable to Scene Flow. Code: https://github.com/Windsrain/ZeroStereo.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

Table reasoning with the large language models (LLMs) is a fundamental path toward building intelligent systems that can understand and analyze over structured data. While recent progress has shown promising results, they still suffer from two key limitations: (i) the reasoning processes lack the depth and iterative refinement characteristic of human cognition; and (ii) the reasoning processes exhibit instability, which compromises their reliability in downstream applications. In this work, we present STaR (slow-thinking for table reasoning), a new framework achieving cognitive table reasoning, in which LLMs are equipped with slow-thinking capabilities by explicitly modeling step-by-step thinking and uncertainty-aware inference. During training, STaR employs two-stage difficulty-aware reinforcement learning (DRL), progressively learning from simple to complex queries under a composite reward. During inference, STaR performs trajectory-level uncertainty quantification by integrating token-level confidence and answer consistency, enabling selection of more credible reasoning paths. Extensive experiments on benchmarks demonstrate that STaR achieves superior performance and enhanced reasoning stability. Moreover, strong generalization over out-of-domain datasets further demonstrates STaR's potential as a reliable and cognitively inspired solution for table reasoning with LLMs.

Mathematical reasoning has proven to be a critical yet challenging task for large language models (LLMs), as they often struggle with complex multi-step problems. To address these limitations, we introduce the Monte Carlo Nash Equilibrium Self-Refine Tree (MC-NEST) algorithm, an enhancement of the Monte Carlo Tree Self-Refine (MCTSr) approach. By integrating Nash Equilibrium strategies with LLM-based self-refinement and self-evaluation processes, MC-NEST aims to improve decision-making for complex mathematical reasoning tasks. This method ensures balanced exploration and exploitation of potential solutions, leveraging Upper Confidence Bound (UCT) scores and various selection policies. Through iterative critique and refinement, MC-NEST enhances the reasoning capabilities of LLMs, particularly for problems requiring strategic decision-making. Comparative analysis reveals that GPT-4o, equipped with MC-NEST using an Importance Sampling Policy, achieved superior accuracy in domains such as Number Theory and Geometry. These results suggest that both LLMs GPT-4o and Phi-3-mini can benefit from MC-NEST, with iterative self-refinement proving especially effective in expanding the reasoning capacity and problem-solving performance of LLMs. We evaluate the effectiveness of MC-NEST on challenging Olympiad-level benchmarks, demonstrating its potential to significantly boost complex mathematical reasoning performance in LLMs.

We introduce a new family of particle evolution samplers suitable for constrained domains and non-Euclidean geometries. Stein Variational Mirror Descent and Mirrored Stein Variational Gradient Descent minimize the Kullback-Leibler (KL) divergence to constrained target distributions by evolving particles in a dual space defined by a mirror map. Stein Variational Natural Gradient exploits non-Euclidean geometry to more efficiently minimize the KL divergence to unconstrained targets. We derive these samplers from a new class of mirrored Stein operators and adaptive kernels developed in this work. We demonstrate that these new samplers yield accurate approximations to distributions on the simplex, deliver valid confidence intervals in post-selection inference, and converge more rapidly than prior methods in large-scale unconstrained posterior inference. Finally, we establish the convergence of our new procedures under verifiable conditions on the target distribution.

In recent years, there have been remarkable advancements in node classification achieved by Graph Neural Networks (GNNs). However, they necessitate abundant high-quality labels to ensure promising performance. In contrast, Large Language Models (LLMs) exhibit impressive zero-shot proficiency on text-attributed graphs. Yet, they face challenges in efficiently processing structural data and suffer from high inference costs. In light of these observations, this work introduces a label-free node classification on graphs with LLMs pipeline, LLM-GNN. It amalgamates the strengths of both GNNs and LLMs while mitigating their limitations. Specifically, LLMs are leveraged to annotate a small portion of nodes and then GNNs are trained on LLMs' annotations to make predictions for the remaining large portion of nodes. The implementation of LLM-GNN faces a unique challenge: how can we actively select nodes for LLMs to annotate and consequently enhance the GNN training? How can we leverage LLMs to obtain annotations of high quality, representativeness, and diversity, thereby enhancing GNN performance with less cost? To tackle this challenge, we develop an annotation quality heuristic and leverage the confidence scores derived from LLMs to advanced node selection. Comprehensive experimental results validate the effectiveness of LLM-GNN. In particular, LLM-GNN can achieve an accuracy of 74.9% on a vast-scale dataset \products with a cost less than 1 dollar.

Large language models (LLMs) are powerful zero- and few-shot learners. However, when predicting over a set of candidate options, LLMs suffer from label biases, and existing calibration methods overlook biases arising from multi-token class labels. We tackle an issue we call label length bias, where labels of different lengths are treated inconsistently, even after standard length normalization. To mitigate it, we propose normalized contextual calibration (NCC), an effective method that normalizes and calibrates predictions at the full-label level. NCC achieves statistically significant improvements over prior approaches across multiple datasets and models, with gains of up to 10% F1. Moreover, NCC extends bias mitigation to broader tasks such as multiple-choice question answering. Our analysis shows that, when combined with in-context learning, NCC is less sensitive to few-shot example selection, requires fewer examples for competitive performance, and produces more reliable confidence estimates. These findings highlight the importance of mitigating full-label biases to improve the performance and robustness of LLM-based methods, particularly in real-world applications where class labels naturally consist of multiple tokens.

Training large language models (LLMs) with a large and diverse instruction dataset aligns the models to comprehend and follow human instructions. Recent works have shown that using a small set of high-quality instructions can outperform using large yet more noisy ones. Because instructions are unlabeled and their responses are natural text, traditional active learning schemes with the model's confidence cannot be directly applied to the selection of unlabeled instructions. In this work, we propose a novel method for instruction selection, called SelectLLM, that leverages LLMs for the selection of high-quality instructions. Our high-level idea is to use LLMs to estimate the usefulness and impactfulness of each instruction without the corresponding labels (i.e., responses), via prompting. SelectLLM involves two steps: dividing the unlabelled instructions using a clustering algorithm (e.g., CoreSet) to multiple clusters, and then prompting LLMs to choose high-quality instructions within each cluster. SelectLLM showed comparable or slightly better performance on the popular instruction benchmarks, compared to the recent state-of-the-art selection methods. All code and data are publicly available (https://github.com/minnesotanlp/select-llm).

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

In this paper, we introduce a novel dynamic expert selection framework for Mixture of Experts (MoE) models, aiming to enhance computational efficiency and model performance by adjusting the number of activated experts based on input difficulty. Unlike traditional MoE approaches that rely on fixed Top-K routing, which activates a predetermined number of experts regardless of the input's complexity, our method dynamically selects experts based on the confidence level in expert selection for each input. This allows for a more efficient utilization of computational resources, activating more experts for complex tasks requiring advanced reasoning and fewer for simpler tasks. Through extensive evaluations, our dynamic routing method demonstrates substantial improvements over conventional Top-2 routing across various benchmarks, achieving an average improvement of 0.7% with less than 90% activated parameters. Further analysis shows our model dispatches more experts to tasks requiring complex reasoning skills, like BBH, confirming its ability to dynamically allocate computational resources in alignment with the input's complexity. Our findings also highlight a variation in the number of experts needed across different layers of the transformer model, offering insights into the potential for designing heterogeneous MoE frameworks. The code and models are available at https://github.com/ZhenweiAn/Dynamic_MoE.

Can we teach Large Language Models (LLMs) to refrain from hallucinating factual statements? In this paper we present a fine-tuning strategy that we call ConfQA, which can reduce hallucination rate from 20-40% to under 5% across multiple factuality benchmarks. The core idea is simple: when the LLM answers a question correctly, it is trained to continue with the answer; otherwise, it is trained to admit "I am unsure". But there are two key factors that make the training highly effective. First, we introduce a dampening prompt "answer only if you are confident" to explicitly guide the behavior, without which hallucination remains high as 15%-25%. Second, we leverage simple factual statements, specifically attribute values from knowledge graphs, to help LLMs calibrate the confidence, resulting in robust generalization across domains and question types. Building on this insight, we propose the Dual Neural Knowledge framework, which seamlessly select between internally parameterized neural knowledge and externally recorded symbolic knowledge based on ConfQA's confidence. The framework enables potential accuracy gains to beyond 95%, while reducing unnecessary external retrievals by over 30%.

While large language models (LLMs) have demonstrated remarkable performance across diverse tasks, they fundamentally lack self-awareness and frequently exhibit overconfidence, assigning high confidence scores to incorrect predictions. Accurate confidence estimation is therefore critical for enhancing the trustworthiness and reliability of LLM-generated outputs. However, existing approaches suffer from coarse-grained scoring mechanisms that fail to provide fine-grained, continuous confidence estimates throughout the generation process. To address these limitations, we introduce FineCE, a novel confidence estimation method that delivers accurate, fine-grained confidence scores during text generation. Specifically, we first develop a comprehensive pipeline for constructing training data that effectively captures the underlying probabilistic distribution of LLM responses, and then train a model to predict confidence scores for arbitrary text sequences in a supervised manner. Furthermore, we propose a Backward Confidence Integration (BCI) strategy that leverages information from the subsequent text to enhance confidence estimation for the current sequence during inference. We also introduce three strategies for identifying optimal positions to perform confidence estimation within the generation process. Extensive experiments on multiple benchmark datasets demonstrate that FineCE consistently outperforms existing classical confidence estimation methods. Our code and all baselines used in the paper are available on GitHub.

Language models (LMs) should provide reliable confidence estimates to help users detect mistakes in their outputs and defer to human experts when necessary. Asking a language model to assess its confidence ("Score your confidence from 0-1.") is a natural way of evaluating its uncertainty. However, models struggle to provide absolute assessments of confidence (i.e. judging confidence in answering a question independent of other questions) and the coarse-grained scores they produce are not useful for evaluating the correctness of their answers. We propose relative confidence estimation, where we match up questions against each other and ask the model to make relative judgments of confidence ("Which question are you more confident in answering correctly?"). Treating each question as a "player" in a series of matchups against other questions and the model's preferences as match outcomes, we can use rank aggregation methods like Elo rating and Bradley-Terry to translate the model's confidence preferences into confidence scores. We evaluate relative confidence estimation against absolute confidence estimation and self-consistency confidence methods on five state-of-the-art LMs -- GPT-4, GPT-4o, Gemini 1.5 Pro, Claude 3.5 Sonnet, and Llama 3.1 405B -- across 14 challenging STEM, social science, and commonsense reasoning question answering tasks. Our results demonstrate that relative confidence estimation consistently provides more reliable confidence scores than absolute confidence estimation, with average gains of 3.5% in selective classification AUC over direct absolute confidence estimation methods and 1.7% over self-consistency approaches across all models and datasets.

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.

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.

Increasing test-time computation is a straightforward approach to enhancing the quality of responses in Large Language Models (LLMs). While Best-of-N sampling and Self-Consistency with majority voting are simple and effective, they require a fixed number of sampling responses for each query, regardless of its complexity. This could result in wasted computation for simpler questions and insufficient exploration for more challenging ones. In this work, we argue that model confidence of responses can be used for improving the efficiency of test-time scaling. Unfortunately, LLMs are known to be overconfident and provide unreliable confidence estimation. To address this limitation, we introduce Self-Calibration by distilling Self-Consistency-derived confidence into the model itself. This enables reliable confidence estimation at test time with one forward pass. We then design confidence-based efficient test-time scaling methods to handle queries of various difficulty, such as Early-Stopping for Best-of-N and Self-Consistency with calibrated confidence. Experiments on three LLMs across six datasets demonstrate the effectiveness of our approach. Specifically, applying confidence-based Early Stopping to Best-of-N improves MathQA accuracy from 81.0 to 83.6 with a sample budget of 16 responses, indicating the efficacy of confidence-based sampling strategy at inference time.

There is a growing literature on reasoning by large language models (LLMs), but the discussion on the uncertainty in their responses is still lacking. Our aim is to assess the extent of confidence that LLMs have in their answers and how it correlates with accuracy. Confidence is measured (i) qualitatively in terms of persistence in keeping their answer when prompted to reconsider, and (ii) quantitatively in terms of self-reported confidence score. We investigate the performance of three LLMs -- GPT4o, GPT4-turbo and Mistral -- on two benchmark sets of questions on causal judgement and formal fallacies and a set of probability and statistical puzzles and paradoxes. Although the LLMs show significantly better performance than random guessing, there is a wide variability in their tendency to change their initial answers. There is a positive correlation between qualitative confidence and accuracy, but the overall accuracy for the second answer is often worse than for the first answer. There is a strong tendency to overstate the self-reported confidence score. Confidence is only partially explained by the underlying token-level probability. The material effects of prompting on qualitative confidence and the strong tendency for overconfidence indicate that current LLMs do not have any internally coherent sense of confidence.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

Model evolution and constant availability of data are two common phenomena in large-scale real-world machine learning applications, e.g. ads and recommendation systems. To adapt, the real-world system typically retrain with all available data and online learn with recently available data to update the models periodically with the goal of better serving performance. In this paper, we propose a novel framework, named Confidence Ranking, which designs the optimization objective as a ranking function with two different models. Our confidence ranking loss allows direct optimization of the logits output for different convex surrogate functions of metrics, e.g. AUC and Accuracy depending on the target task and dataset. Armed with our proposed methods, our experiments show that the introduction of confidence ranking loss can outperform all baselines on the CTR prediction tasks of public and industrial datasets. This framework has been deployed in the advertisement system of JD.com to serve the main traffic in the fine-rank stage.

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.

Multi-agent debates have been introduced to improve the accuracy of Large Language Models (LLMs) by having multiple agents discuss solutions to a problem over several rounds of debate. However, models often generate incorrect yet confident-sounding responses, which can mislead others. This issue arises partly because agents do not consider how confident their peers are. To address this, we propose DebUnc, a debate framework that uses uncertainty metrics to assess agent confidence. Confidence is then conveyed through a modified attention mechanism that adjusts token weights, or through textual prompts. Evaluations across benchmarks show that attention-based methods are particularly effective and that performance continues to improve as uncertainty estimation becomes more reliable. The code is available at https://github.com/lukeyoffe/debunc.

Retrieval Augmented Generation (RAG) complements the knowledge of Large Language Models (LLMs) by leveraging external information to enhance response accuracy for queries. This approach is widely applied in several fields by taking its advantage of injecting the most up-to-date information, and researchers are focusing on understanding and improving this aspect to unlock the full potential of RAG in such high-stakes applications. However, despite the potential of RAG to address these needs, the mechanisms behind the confidence levels of its outputs remain underexplored, although the confidence of information is very critical in some domains, such as finance, healthcare, and medicine. Our study focuses the impact of RAG on confidence within the medical domain under various configurations and models. We evaluate confidence by treating the model's predicted probability as its output and calculating Expected Calibration Error (ECE) and Adaptive Calibration Error (ACE) scores based on the probabilities and accuracy. In addition, we analyze whether the order of retrieved documents within prompts calibrates the confidence. Our findings reveal large variation in confidence and accuracy depending on the model, settings, and the format of input prompts. These results underscore the necessity of optimizing configurations based on the specific model and conditions.

Language models have made significant progress in generating coherent text and predicting next tokens based on input prompts. This study compares the next-token prediction performance of two well-known models: OpenAI's GPT-2 and Meta's Llama-2-7b-chat-hf on Theory of Mind (ToM) tasks. To evaluate their capabilities, we built a dataset from 10 short stories sourced from the Explore ToM Dataset. We enhanced these stories by programmatically inserting additional sentences (infills) using GPT-4, creating variations that introduce different levels of contextual complexity. This setup enables analysis of how increasing context affects model performance. We tested both models under four temperature settings (0.01, 0.5, 1.0, 2.0) and evaluated their ability to predict the next token across three reasoning levels. Zero-order reasoning involves tracking the state, either current (ground truth) or past (memory). First-order reasoning concerns understanding another's mental state (e.g., "Does Anne know the apple is salted?"). Second-order reasoning adds recursion (e.g., "Does Anne think that Charles knows the apple is salted?"). Our results show that adding more infill sentences slightly reduces prediction accuracy, as added context increases complexity and ambiguity. Llama-2 consistently outperforms GPT-2 in prediction accuracy, especially at lower temperatures, demonstrating greater confidence in selecting the most probable token. As reasoning complexity rises, model responses diverge more. Notably, GPT-2 and Llama-2 display greater variability in predictions during first- and second-order reasoning tasks. These findings illustrate how model architecture, temperature, and contextual complexity influence next-token prediction, contributing to a better understanding of the strengths and limitations of current language models.

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.

Recent progress in large language models (LLMs) has enabled them to express their confidence in natural language, enhancing transparency and reliability. However, their confidence often exhibits overconfidence, the cause of which remains poorly understood. In this work, we conduct a detailed analysis of the dynamics underlying verbalized confidence and identify answer-independence as a key factor, defined as the model's failure to condition confidence on its own answer. To address this, we propose ADVICE (Answer-Dependent Verbalized Confidence Estimation), a fine-tuning framework that facilitates answer-grounded confidence estimation. Extensive experiments show that ADVICE substantially improves confidence calibration while preserving task performance. Further analyses confirm that ADVICE strengthens answer-groundedness, leading to more balanced and well-calibrated confidence distributions. Our findings shed light on the origin of overconfidence and establish a framework for more trustworthy confidence verbalization.

Large Language Models (LLMs) have acquired ubiquitous attention for their performances across diverse domains. Our study here searches through LLMs' cognitive abilities and confidence dynamics. We dive deep into understanding the alignment between their self-assessed confidence and actual performance. We exploit these models with diverse sets of questionnaires and real-world scenarios and extract how LLMs exhibit confidence in their responses. Our findings reveal intriguing instances where models demonstrate high confidence even when they answer incorrectly. This is reminiscent of the Dunning-Kruger effect observed in human psychology. In contrast, there are cases where models exhibit low confidence with correct answers revealing potential underestimation biases. Our results underscore the need for a deeper understanding of their cognitive processes. By examining the nuances of LLMs' self-assessment mechanism, this investigation provides noteworthy revelations that serve to advance the functionalities and broaden the potential applications of these formidable language models.

Reward models can significantly enhance the reasoning capabilities of large language models (LLMs), but they typically require extensive curated data and costly training. To mitigate these challenges, training-free approaches such as LLM-as-a-Judge leverage the intrinsic reasoning abilities of LLMs to evaluate responses, achieving promising results. Recent works have also indicated that model confidence can serve effectively as a reward metric, distinguishing between chain-of-thought (CoT) and non-CoT paths. However, the concept of using confidence as a reward has not been comprehensively studied. In this work, we systematically investigate Confidence-as-a-Reward (CRew), a simple yet powerful training-free method that utilizes token-level confidence in the model's final answers as a proxy for reward, especially suitable for close-ended tasks. Through extensive experiments on mathematical reasoning tasks, we demonstrate that CRew outperforms existing training-free reward approaches on the MATH500 and RewardMATH benchmarks, and even surpasses most trained reward models. We further identify a strong correlation between CRew scores and the actual reasoning performance of the model. Additionally, we find that CRew can effectively filter high-quality training data. Building upon these insights, we propose CRew-DPO, a training strategy that constructs preference data from confidence scores combined with correctness signals. Finetuning with CRew-DPO further enhances the model's judging capabilities and consistently outperforms existing self-training methods.

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.

Out-of-distribution (OOD) detection aims to identify OOD inputs from unknown classes, which is important for the reliable deployment of machine learning models in the open world. Various scoring functions are proposed to distinguish it from in-distribution (ID) data. However, existing methods generally focus on excavating the discriminative information from a single input, which implicitly limits its representation dimension. In this work, we introduce a novel perspective, i.e., employing different common corruptions on the input space, to expand that. We reveal an interesting phenomenon termed confidence mutation, where the confidence of OOD data can decrease significantly under the corruptions, while the ID data shows a higher confidence expectation considering the resistance of semantic features. Based on that, we formalize a new scoring method, namely, Confidence aVerage (CoVer), which can capture the dynamic differences by simply averaging the scores obtained from different corrupted inputs and the original ones, making the OOD and ID distributions more separable in detection tasks. Extensive experiments and analyses have been conducted to understand and verify the effectiveness of CoVer. The code is publicly available at: https://github.com/tmlr-group/CoVer.

Estimating uncertainty or confidence in the responses of a model can be significant in evaluating trust not only in the responses, but also in the model as a whole. In this paper, we explore the problem of estimating confidence for responses of large language models (LLMs) with simply black-box or query access to them. We propose a simple and extensible framework where, we engineer novel features and train a (interpretable) model (viz. logistic regression) on these features to estimate the confidence. We empirically demonstrate that our simple framework is effective in estimating confidence of flan-ul2, llama-13b and mistral-7b with it consistently outperforming existing black-box confidence estimation approaches on benchmark datasets such as TriviaQA, SQuAD, CoQA and Natural Questions by even over 10% (on AUROC) in some cases. Additionally, our interpretable approach provides insight into features that are predictive of confidence, leading to the interesting and useful discovery that our confidence models built for one LLM generalize zero-shot across others on a given dataset.

FOLD-RM is an explainable machine learning classification algorithm that uses training data to create a set of classification rules. In this paper we introduce CON-FOLD which extends FOLD-RM in several ways. CON-FOLD assigns probability-based confidence scores to rules learned for a classification task. This allows users to know how confident they should be in a prediction made by the model. We present a confidence-based pruning algorithm that uses the unique structure of FOLD-RM rules to efficiently prune rules and prevent overfitting. Furthermore, CON-FOLD enables the user to provide pre-existing knowledge in the form of logic program rules that are either (fixed) background knowledge or (modifiable) initial rule candidates. The paper describes our method in detail and reports on practical experiments. We demonstrate the performance of the algorithm on benchmark datasets from the UCI Machine Learning Repository. For that, we introduce a new metric, Inverse Brier Score, to evaluate the accuracy of the produced confidence scores. Finally we apply this extension to a real world example that requires explainability: marking of student responses to a short answer question from the Australian Physics Olympiad.

One of the most widely used methods to evaluate LLMs are Multiple Choice Question (MCQ) tests. MCQ benchmarks enable the testing of LLM knowledge on almost any topic at scale as the results can be processed automatically. To help the LLM answer, a few examples called few shots can be included in the prompt. Moreover, the LLM can be asked to answer the question directly with the selected option or to first provide the reasoning and then the selected answer, which is known as chain of thought. In addition to checking whether the selected answer is correct, the evaluation can look at the LLM-estimated probability of its response as an indication of the confidence of the LLM in the response. In this paper, we study how the LLM confidence in its answer depends on whether the model has been asked to answer directly or to provide the reasoning before answering. The results of the evaluation of questions on a wide range of topics in seven different models show that LLMs are more confident in their answers when they provide reasoning before the answer. This occurs regardless of whether the selected answer is correct. Our hypothesis is that this behavior is due to the reasoning that modifies the probability of the selected answer, as the LLM predicts the answer based on the input question and the reasoning that supports the selection made. Therefore, LLM estimated probabilities seem to have intrinsic limitations that should be understood in order to use them in evaluation procedures. Interestingly, the same behavior has been observed in humans, for whom explaining an answer increases confidence in its correctness.

Large language models (LLMs) are increasingly used in high-stakes settings, where overconfident responses can mislead users. Reliable confidence estimation has been shown to enhance trust and task accuracy. Yet existing methods face practical barriers: logits are often hidden, multi-sampling is computationally expensive, and verbalized numerical uncertainty (e.g., giving a 0-100 score) deviates from natural communication. We revisit linguistic confidence (LC), where models express uncertainty through hedging language (e.g., probably, might), offering a lightweight and human-centered alternative. To advance this direction, we (1) release the first diverse, large-scale dataset of hedging expressions with human-annotated confidence scores, and (2) propose a lightweight mapper that converts hedges into confidence scores at near-zero cost. Building on these resources, we (3) conduct the first systematic study of LC across modern LLMs and QA benchmarks, revealing that while most LLMs underperform in expressing reliable LC, carefully designed prompting achieves competitive calibration and discriminability. Finally, we (4) introduce a fine-tuning framework that further improves LC reliability. Taken together, our work positions linguistic confidence as a scalable, efficient, and human-aligned approach to LLM uncertainty estimation, and calls for deeper exploration of this promising yet underexplored direction.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

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.

Large language models (LLMs) often generate inaccurate or fabricated information and generally fail to indicate their confidence, which limits their broader applications. Previous work elicits confidence from LLMs by direct or self-consistency prompting, or constructing specific datasets for supervised finetuning. The prompting-based approaches have inferior performance, and the training-based approaches are limited to binary or inaccurate group-level confidence estimates. In this work, we present the advanced SaySelf, a training framework that teaches LLMs to express more accurate fine-grained confidence estimates. In addition, beyond the confidence scores, SaySelf initiates the process of directing LLMs to produce self-reflective rationales that clearly identify gaps in their parametric knowledge and explain their uncertainty. This is achieved by using an LLM to automatically summarize the uncertainties in specific knowledge via natural language. The summarization is based on the analysis of the inconsistency in multiple sampled reasoning chains, and the resulting data is utilized for supervised fine-tuning. Moreover, we utilize reinforcement learning with a meticulously crafted reward function to calibrate the confidence estimates, motivating LLMs to deliver accurate, high-confidence predictions and to penalize overconfidence in erroneous outputs. Experimental results in both in-distribution and out-of-distribution datasets demonstrate the effectiveness of SaySelf in reducing the confidence calibration error and maintaining the task performance. We show that the generated self-reflective rationales are reasonable and can further contribute to the calibration. The code is made public at https://github.com/xu1868/SaySelf.

For large language models (LLMs) to be trusted by humans they need to be well-calibrated in the sense that they can accurately assess and communicate how likely it is that their predictions are correct. Recent work has focused on the quality of internal LLM confidence assessments, but the question remains of how well LLMs can communicate this internal model confidence to human users. This paper explores the disparity between external human confidence in an LLM's responses and the internal confidence of the model. Through experiments involving multiple-choice questions, we systematically examine human users' ability to discern the reliability of LLM outputs. Our study focuses on two key areas: (1) assessing users' perception of true LLM confidence and (2) investigating the impact of tailored explanations on this perception. The research highlights that default explanations from LLMs often lead to user overestimation of both the model's confidence and its' accuracy. By modifying the explanations to more accurately reflect the LLM's internal confidence, we observe a significant shift in user perception, aligning it more closely with the model's actual confidence levels. This adjustment in explanatory approach demonstrates potential for enhancing user trust and accuracy in assessing LLM outputs. The findings underscore the importance of transparent communication of confidence levels in LLMs, particularly in high-stakes applications where understanding the reliability of AI-generated information is essential.

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.

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.

Next token prediction paradigm has been prevailing for autoregressive models in the era of LLMs. The current default sampling choice for popular LLMs is temperature scaling together with nucleus sampling to balance diversity and coherence. Nevertheless, such approach leads to inferior performance in various NLP tasks when the model is not certain about testing questions. To this end, we propose a brand new training-free decoding strategy, dubbed as Cautious Next Token Prediction (CNTP). In the decoding process, if the model has comparatively high prediction entropy at a certain step, we sample multiple trials starting from the step independently and stop when encountering any punctuation. Then we select the trial with the lowest perplexity score viewed as the most probable and reliable trial path given the model's capacity. The trial number is negatively correlated with the prediction confidence, i.e., the less confident the model is, the more trials it should sample. This is consistent with human beings' behaviour: when feeling uncertain or unconfident, one tends to think more creatively, exploring multiple thinking paths, to cautiously select the path one feels most confident about. Extensive experiments on both LLMs and MLLMs show that our proposed CNTP approach outperforms existing standard decoding strategies consistently by a clear margin. Moreover, the integration of CNTP with self consistency can further improve over vanilla self consistency. We believe our proposed CNTP has the potential to become one of the default choices for LLM decoding. Code is available at https://github.com/wyzjack/CNTP.

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

Cascades are a classical strategy to enable inference cost to vary adaptively across samples, wherein a sequence of classifiers are invoked in turn. A deferral rule determines whether to invoke the next classifier in the sequence, or to terminate prediction. One simple deferral rule employs the confidence of the current classifier, e.g., based on the maximum predicted softmax probability. Despite being oblivious to the structure of the cascade -- e.g., not modelling the errors of downstream models -- such confidence-based deferral often works remarkably well in practice. In this paper, we seek to better understand the conditions under which confidence-based deferral may fail, and when alternate deferral strategies can perform better. We first present a theoretical characterisation of the optimal deferral rule, which precisely characterises settings under which confidence-based deferral may suffer. We then study post-hoc deferral mechanisms, and demonstrate they can significantly improve upon confidence-based deferral in settings where (i) downstream models are specialists that only work well on a subset of inputs, (ii) samples are subject to label noise, and (iii) there is distribution shift between the train and test set.

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%.

Recent work in open-domain question answering (ODQA) has shown that adversarial poisoning of the input contexts can cause large drops in accuracy for production systems. However, little to no work has proposed methods to defend against these attacks. To do so, we introduce a new method that uses query augmentation to search for a diverse set of retrieved passages that could answer the original question. We integrate these new passages into the model through the design of a novel confidence method, comparing the predicted answer to its appearance in the retrieved contexts (what we call Confidence from Answer Redundancy, e.g. CAR). Together these methods allow for a simple but effective way to defend against poisoning attacks and provide gains of 5-20% exact match across varying levels of data poisoning.

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.

To maintain user trust, large language models (LLMs) should signal low confidence on examples where they are incorrect, instead of misleading the user. The standard approach of estimating confidence is to use the softmax probabilities of these models, but as of November 2023, state-of-the-art LLMs such as GPT-4 and Claude-v1.3 do not provide access to these probabilities. We first study eliciting confidence linguistically -- asking an LLM for its confidence in its answer -- which performs reasonably (80.5% AUC on GPT-4 averaged across 12 question-answering datasets -- 7% above a random baseline) but leaves room for improvement. We then explore using a surrogate confidence model -- using a model where we do have probabilities to evaluate the original model's confidence in a given question. Surprisingly, even though these probabilities come from a different and often weaker model, this method leads to higher AUC than linguistic confidences on 9 out of 12 datasets. Our best method composing linguistic confidences and surrogate model probabilities gives state-of-the-art confidence estimates on all 12 datasets (84.6% average AUC on GPT-4).

Major cloud providers have employed advanced AI-based solutions like large language models to aid humans in identifying the root causes of cloud incidents. Despite the growing prevalence of AI-driven assistants in the root cause analysis process, their effectiveness in assisting on-call engineers is constrained by low accuracy due to the intrinsic difficulty of the task, a propensity for LLM-based approaches to hallucinate, and difficulties in distinguishing these well-disguised hallucinations. To address this challenge, we propose to perform confidence estimation for the predictions to help on-call engineers make decisions on whether to adopt the model prediction. Considering the black-box nature of many LLM-based root cause predictors, fine-tuning or temperature-scaling-based approaches are inapplicable. We therefore design an innovative confidence estimation framework based on prompting retrieval-augmented large language models (LLMs) that demand a minimal amount of information from the root cause predictor. This approach consists of two scoring phases: the LLM-based confidence estimator first evaluates its confidence in making judgments in the face of the current incident that reflects its ``grounded-ness" level in reference data, then rates the root cause prediction based on historical references. An optimization step combines these two scores for a final confidence assignment. We show that our method is able to produce calibrated confidence estimates for predicted root causes, validate the usefulness of retrieved historical data and the prompting strategy as well as the generalizability across different root cause prediction models. Our study takes an important move towards reliably and effectively embedding LLMs into cloud incident management systems.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

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.

Large language models (LLMs) produce outputs with varying levels of uncertainty, and, just as often, varying levels of correctness; making their practical reliability far from guaranteed. To quantify this uncertainty, we systematically evaluate four approaches for confidence estimation in LLM outputs: VCE, MSP, Sample Consistency, and CoCoA (Vashurin et al., 2025). For the evaluation of the approaches, we conduct experiments on four question-answering tasks using a state-of-the-art open-source LLM. Our results show that each uncertainty metric captures a different facet of model confidence and that the hybrid CoCoA approach yields the best reliability overall, improving both calibration and discrimination of correct answers. We discuss the trade-offs of each method and provide recommendations for selecting uncertainty measures in LLM applications.

This paper presents a novel technique for accelerating inference in large, pre-trained language models (LLMs) by introducing early exits during inference. The computational demands of these models, used across a wide range of applications, can be substantial. By capitalizing on the inherent variability in token complexity, our approach enables selective acceleration of the inference process. Specifically, we propose the integration of early exit ''heads'' atop existing transformer layers, which facilitate conditional terminations based on a confidence metric. These heads are trained in a self-supervised manner using the model's own predictions as training data, thereby eliminating the need for additional annotated data. The confidence metric, established using a calibration set, ensures a desired level of accuracy while enabling early termination when confidence exceeds a predetermined threshold. Notably, our method preserves the original accuracy and reduces computational time on certain tasks, leveraging the existing knowledge of pre-trained LLMs without requiring extensive retraining. This lightweight, modular modification has the potential to greatly enhance the practical usability of LLMs, particularly in applications like real-time language processing in resource-constrained environments.

Learning exists in the context of data, yet notions of confidence typically focus on model predictions, not label quality. Confident learning (CL) is an alternative approach which focuses instead on label quality by characterizing and identifying label errors in datasets, based on the principles of pruning noisy data, counting with probabilistic thresholds to estimate noise, and ranking examples to train with confidence. Whereas numerous studies have developed these principles independently, here, we combine them, building on the assumption of a class-conditional noise process to directly estimate the joint distribution between noisy (given) labels and uncorrupted (unknown) labels. This results in a generalized CL which is provably consistent and experimentally performant. We present sufficient conditions where CL exactly finds label errors, and show CL performance exceeding seven recent competitive approaches for learning with noisy labels on the CIFAR dataset. Uniquely, the CL framework is not coupled to a specific data modality or model (e.g., we use CL to find several label errors in the presumed error-free MNIST dataset and improve sentiment classification on text data in Amazon Reviews). We also employ CL on ImageNet to quantify ontological class overlap (e.g., estimating 645 "missile" images are mislabeled as their parent class "projectile"), and moderately increase model accuracy (e.g., for ResNet) by cleaning data prior to training. These results are replicable using the open-source cleanlab release.

Language models are increasingly used in Brazil, but most evaluation remains English-centric. This paper presents Alvorada-Bench, a 4,515-question, text-only benchmark drawn from five Brazilian university entrance examinations. Evaluating twenty models under zero-shot, role-playing, and chain-of-thought prompting, producing 270,900 responses with structured self-reports of confidence, perceived difficulty, and Bloom level. The top models exceed 94% accuracy overall, but accuracy declines on Mathematics and on the engineering oriented IME and ITA exams, indicating persistent weaknesses in multi-step reasoning. Confidence is well calibrated and correlates with perceived difficulty, revealing that models can accurately assess their own certainty capabilities. A cost accuracy analysis shows that high accuracy is achievable at under $2 per 1K tokens. On ENEM 2024 the top model (O3) achieved perfect scores in Languages subject questions while even the weakest system (GPT-4.1 Nano) only underperforms humans in Mathematics. Through exams that distill decades of Brazilian educational priorities and assess millions of students yearly, Alvorada-Bench establishes whether language models can navigate the intersection of language, culture, and reasoning that defines academic readiness in Brazil.

Recent advances in handling long sequences have facilitated the exploration of long-context in-context learning (ICL). While much of the existing research emphasizes performance improvements driven by additional in-context examples, the influence on the trustworthiness of generated responses remains underexplored. This paper addresses this gap by investigating how increased examples influence predictive uncertainty, an essential aspect in trustworthiness. We begin by systematically quantifying the uncertainty of ICL with varying shot counts, analyzing the impact of example quantity. Through uncertainty decomposition, we introduce a novel perspective on performance enhancement, with a focus on epistemic uncertainty (EU). Our results reveal that additional examples reduce total uncertainty in both simple and complex tasks by injecting task-specific knowledge, thereby diminishing EU and enhancing performance. For complex tasks, these advantages emerge only after addressing the increased noise and uncertainty associated with longer inputs. Finally, we explore the evolution of internal confidence across layers, unveiling the mechanisms driving the reduction in uncertainty.

Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget varepsilon spent on training a model. Existing approaches derive confidence intervals for varepsilon from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for epsilon using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for varepsilon (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for varepsilon around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.

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.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

This study investigates GPT-4's assessment of its performance in healthcare applications. A simple prompting technique was used to prompt the LLM with questions taken from the United States Medical Licensing Examination (USMLE) questionnaire and it was tasked to evaluate its confidence score before posing the question and after asking the question. The questionnaire was categorized into two groups-questions with feedback (WF) and questions with no feedback(NF) post-question. The model was asked to provide absolute and relative confidence scores before and after each question. The experimental findings were analyzed using statistical tools to study the variability of confidence in WF and NF groups. Additionally, a sequential analysis was conducted to observe the performance variation for the WF and NF groups. Results indicate that feedback influences relative confidence but doesn't consistently increase or decrease it. Understanding the performance of LLM is paramount in exploring its utility in sensitive areas like healthcare. This study contributes to the ongoing discourse on the reliability of AI, particularly of LLMs like GPT-4, within healthcare, offering insights into how feedback mechanisms might be optimized to enhance AI-assisted medical education and decision support.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

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.

It is important for Large Language Models to be aware of the boundary of their knowledge, the mechanism of identifying known and unknown queries. This type of awareness can help models perform adaptive inference, such as invoking RAG, engaging in slow and deep thinking, or adopting the abstention mechanism, which is beneficial to the development of efficient and trustworthy AI. In this work, we propose a method to detect knowledge boundaries via Query-Level Uncertainty, which aims to determine if the model is able to address a given query without generating any tokens. To this end, we introduce a novel and training-free method called Internal Confidence, which leverages self-evaluations across layers and tokens. Empirical results on both factual QA and mathematical reasoning tasks demonstrate that our internal confidence can outperform several baselines. Furthermore, we showcase that our proposed method can be used for efficient RAG and model cascading, which is able to reduce inference costs while maintaining performance.

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.

We introduce a simple, yet novel entropy-based framework to drive token efficiency in large language models during reasoning tasks. Our approach uses Shannon entropy from token-level logprobs as a confidence signal to enable early stopping, achieving 25-50% computational savings while maintaining task accuracy. Crucially, we demonstrate that entropy-based confidence calibration represents an emergent property of advanced post-training optimization present in modern reasoning models but notably absent in standard instruction-tuned and pre-trained models (Llama 3.3 70B). We show that the entropy threshold to stop reasoning varies from model to model but can be calculated easily in one shot using only a few examples from existing reasoning datasets. Our results indicate that advanced reasoning models often know that they've gotten a correct answer early on, and that this emergent confidence awareness can be exploited to save tokens and reduce latency. The framework demonstrates consistent performance across reasoning-optimized model families with 25-50% computational cost reduction while preserving accuracy, revealing that confidence mechanisms represent a distinguishing characteristic of modern post-trained reasoning systems versus their predecessors.

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.

Active learning is a machine learning paradigm that aims to improve the performance of a model by strategically selecting and querying unlabeled data. One effective selection strategy is to base it on the model's predictive uncertainty, which can be interpreted as a measure of how informative a sample is. The sample's distance to the decision boundary is a natural measure of predictive uncertainty, but it is often intractable to compute, especially for complex decision boundaries formed in multiclass classification tasks. To address this issue, this paper proposes the {\it least disagree metric} (LDM), defined as the smallest probability of disagreement of the predicted label, and an estimator for LDM proven to be asymptotically consistent under mild assumptions. The estimator is computationally efficient and can be easily implemented for deep learning models using parameter perturbation. The LDM-based active learning is performed by querying unlabeled data with the smallest LDM. Experimental results show that our LDM-based active learning algorithm obtains state-of-the-art overall performance on all considered datasets and deep architectures.

We investigate the problem of determining the predictive confidence (or, conversely, uncertainty) of a neural classifier through the lens of low-resource languages. By training models on sub-sampled datasets in three different languages, we assess the quality of estimates from a wide array of approaches and their dependence on the amount of available data. We find that while approaches based on pre-trained models and ensembles achieve the best results overall, the quality of uncertainty estimates can surprisingly suffer with more data. We also perform a qualitative analysis of uncertainties on sequences, discovering that a model's total uncertainty seems to be influenced to a large degree by its data uncertainty, not model uncertainty. All model implementations are open-sourced in a software package.

This project aims to investigate a novel sequence generation method inspired by the AlphaGo paradigm, adapting it for use with large language models (LLMs). The proposed approach involves creating search trees of different possible completions and evaluating these completions based on model confidence. By considering various paths in the search tree and scoring them according to the model's confidence in each completion, we can generate diverse and high-quality sequences. This research explores the implementation of this paradigm by using confidence as a proxy for response quality akin to beam search vijayakumar2016diverse. The primary goal of this paper is to outline the paradigm and demonstrate its potential, rather than focusing on achieving perfect results. The paper will outline the reasons why we believe this paradigm has the potential to improve LLMs in the following manners: 1) increase output quality, 2) decrease errors, 3) eliminate or reduce the compound error problems, 4) generate diverse and creative completions, 5) allow for iterative problem-solving, and 6) self-training. We expect this approach to yield a set of diverse and coherent sequences, offering insights into balancing exploration and exploitation in sequence generation. Potential applications include creative text generation tasks, such as storytelling and content creation, as well as other natural language processing domains, like machine translation and automated summarization. The goal is that the model will be far more effective as it will be able to consider many possible variations allowing it to find the ideal completion. This research aims to contribute to the understanding of effective search strategies in sequence generation and their impact on generating high-quality, varied textual outputs.

Despite the remarkable success of deep neural networks in a myriad of settings, several works have demonstrated their overwhelming sensitivity to near-imperceptible perturbations, known as adversarial attacks. On the other hand, prior works have also observed that deep networks can be under-sensitive, wherein large-magnitude perturbations in input space do not induce appreciable changes to network activations. In this work, we study in detail the phenomenon of under-sensitivity in vision models such as CNNs and Transformers, and present techniques to study the geometry and extent of "equi-confidence" level sets of such networks. We propose a Level Set Traversal algorithm that iteratively explores regions of high confidence with respect to the input space using orthogonal components of the local gradients. Given a source image, we use this algorithm to identify inputs that lie in the same equi-confidence level set as the source image despite being perceptually similar to arbitrary images from other classes. We further observe that the source image is linearly connected by a high-confidence path to these inputs, uncovering a star-like structure for level sets of deep networks. Furthermore, we attempt to identify and estimate the extent of these connected higher-dimensional regions over which the model maintains a high degree of confidence. The code for this project is publicly available at https://github.com/SriramB-98/blindspots-neurips-sub

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.

Neural Radiance Fields (NeRF) exhibit remarkable performance for Novel View Synthesis (NVS) given a set of 2D images. However, NeRF training requires accurate camera pose for each input view, typically obtained by Structure-from-Motion (SfM) pipelines. Recent works have attempted to relax this constraint, but they still often rely on decent initial poses which they can refine. Here we aim at removing the requirement for pose initialization. We present Incremental CONfidence (ICON), an optimization procedure for training NeRFs from 2D video frames. ICON only assumes smooth camera motion to estimate initial guess for poses. Further, ICON introduces ``confidence": an adaptive measure of model quality used to dynamically reweight gradients. ICON relies on high-confidence poses to learn NeRF, and high-confidence 3D structure (as encoded by NeRF) to learn poses. We show that ICON, without prior pose initialization, achieves superior performance in both CO3D and HO3D versus methods which use SfM pose.

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.

Large Language Models (LLMs) are often augmented with external information as contexts, but this external information can sometimes be inaccurate or even intentionally misleading. We argue that robust LLMs should demonstrate situated faithfulness, dynamically calibrating their trust in external information based on their confidence in the internal knowledge and the external context. To benchmark this capability, we evaluate LLMs across several QA datasets, including a newly created dataset called RedditQA featuring in-the-wild incorrect contexts sourced from Reddit posts. We show that when provided with both correct and incorrect contexts, both open-source and proprietary models tend to overly rely on external information, regardless of its factual accuracy. To enhance situated faithfulness, we propose two approaches: Self-Guided Confidence Reasoning (SCR) and Rule-Based Confidence Reasoning (RCR). SCR enables models to self-access the confidence of external information relative to their own internal knowledge to produce the most accurate answer. RCR, in contrast, extracts explicit confidence signals from the LLM and determines the final answer using predefined rules. Our results show that for LLMs with strong reasoning capabilities, such as GPT-4o and GPT-4o mini, SCR outperforms RCR, achieving improvements of up to 24.2% over a direct input augmentation baseline. Conversely, for a smaller model like Llama-3-8B, RCR outperforms SCR. Fine-tuning SCR with our proposed Confidence Reasoning Direct Preference Optimization (CR-DPO) method improves performance on both seen and unseen datasets, yielding an average improvement of 8.9% on Llama-3-8B. In addition to quantitative results, we offer insights into the relative strengths of SCR and RCR. Our findings highlight promising avenues for improving situated faithfulness in LLMs. The data and code are released.

The ability to judge whether a caption correctly describes an image is a critical part of vision-language understanding. However, state-of-the-art models often misinterpret the correctness of fine-grained details, leading to errors in outputs such as hallucinating objects in generated captions or poor compositional reasoning. In this work, we explore Token-Level Confidence, or TLC, as a simple yet surprisingly effective method to assess caption correctness. Specifically, we fine-tune a vision-language model on image captioning, input an image and proposed caption to the model, and aggregate either algebraic or learned token confidences over words or sequences to estimate image-caption consistency. Compared to sequence-level scores from pretrained models, TLC with algebraic confidence measures achieves a relative improvement in accuracy by 10% on verb understanding in SVO-Probes and outperforms prior state-of-the-art in image and group scores for compositional reasoning in Winoground by a relative 37% and 9%, respectively. When training data are available, a learned confidence estimator provides further improved performance, reducing object hallucination rates in MS COCO Captions by a relative 30% over the original model and setting a new state-of-the-art.

Generative Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Recent research has introduced Multi-Agent Debate (MAD) systems, which leverage multiple LLMs to simulate human debate and thereby improve task performance. However, while some LLMs may possess superior knowledge or reasoning capabilities for specific tasks, they often struggle to clearly communicate this advantage during debates, in part due to a lack of confidence expression. Moreover, inappropriate confidence expression can cause agents in MAD systems to either stubbornly maintain incorrect beliefs or converge prematurely on suboptimal answers, ultimately reducing debate effectiveness and overall system performance. To address these challenges, we propose incorporating confidence expression into MAD systems to allow LLMs to explicitly communicate their confidence levels. To validate this approach, we develop ConfMAD, a MAD framework that integrates confidence expression throughout the debate process. Experimental results demonstrate the effectiveness of our method, and we further analyze how confidence influences debate dynamics, offering insights into the design of confidence-aware MAD systems.

Retrieval-augmented generation (RAG) has emerged as a popular solution to mitigate the hallucination issues of large language models. However, existing studies on RAG seldom address the issue of predictive uncertainty, i.e., how likely it is that a RAG model's prediction is incorrect, resulting in uncontrollable risks in real-world applications. In this work, we emphasize the importance of risk control, ensuring that RAG models proactively refuse to answer questions with low confidence. Our research identifies two critical latent factors affecting RAG's confidence in its predictions: the quality of the retrieved results and the manner in which these results are utilized. To guide RAG models in assessing their own confidence based on these two latent factors, we develop a counterfactual prompting framework that induces the models to alter these factors and analyzes the effect on their answers. We also introduce a benchmarking procedure to collect answers with the option to abstain, facilitating a series of experiments. For evaluation, we introduce several risk-related metrics and the experimental results demonstrate the effectiveness of our approach.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases are not always available and can be expensive to build in practice, researchers propose to automatically generate test cases to assess code solutions. However, when both code solutions and test cases are plausible and not reliable, selecting the best solution becomes challenging. Although some heuristic strategies have been proposed to tackle this problem, they lack a strong theoretical guarantee and it is still an open question whether an optimal selection strategy exists. Our work contributes in two ways. First, we show that within a Bayesian framework, the optimal selection strategy can be defined based on the posterior probability of the observed passing states between solutions and tests. The problem of identifying the best solution is then framed as an integer programming problem. Second, we propose an efficient approach for approximating this optimal (yet uncomputable) strategy, where the approximation error is bounded by the correctness of prior knowledge. We then incorporate effective prior knowledge to tailor code generation tasks. Both theoretical and empirical studies confirm that existing heuristics are limited in selecting the best solutions with plausible test cases. Our proposed approximated optimal strategy B4 significantly surpasses existing heuristics in selecting code solutions generated by large language models (LLMs) with LLM-generated tests, achieving a relative performance improvement by up to 50% over the strongest heuristic and 246% over the random selection in the most challenging scenarios. Our code is publicly available at https://github.com/ZJU-CTAG/B4.

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.

Quality estimation is omnipresent in machine translation, for both evaluation and generation. Unfortunately, quality estimation models are often opaque and computationally expensive, making them impractical to be part of large-scale pipelines. In this work, we tackle two connected challenges: (1) reducing the cost of quality estimation at scale, and (2) developing an inexpensive uncertainty estimation method for quality estimation. To address the latter, we introduce Instant Confidence COMET, an uncertainty-aware quality estimation model that matches the performance of previous approaches at a fraction of their costs. We extend this to Early-Exit COMET, a quality estimation model that can compute quality scores and associated confidences already at early model layers, allowing us to early-exit computations and reduce evaluation costs. We also apply our model to machine translation reranking. We combine Early-Exit COMET with an upper confidence bound bandit algorithm to find the best candidate from a large pool without having to run the full evaluation model on all candidates. In both cases (evaluation and reranking) our methods reduce the required compute by 50% with very little degradation in performance.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

In natural language processing, a recently popular line of work explores how to best report the experimental results of neural networks. One exemplar publication, titled "Show Your Work: Improved Reporting of Experimental Results," advocates for reporting the expected validation effectiveness of the best-tuned model, with respect to the computational budget. In the present work, we critically examine this paper. As far as statistical generalizability is concerned, we find unspoken pitfalls and caveats with this approach. We analytically show that their estimator is biased and uses error-prone assumptions. We find that the estimator favors negative errors and yields poor bootstrapped confidence intervals. We derive an unbiased alternative and bolster our claims with empirical evidence from statistical simulation. Our codebase is at http://github.com/castorini/meanmax.

Large language models (LLMs) have shown high agreement with human raters across a variety of tasks, demonstrating potential to ease the challenges of human data collection. In computational social science (CSS), researchers are increasingly leveraging LLM annotations to complement slow and expensive human annotations. Still, guidelines for collecting and using LLM annotations, without compromising the validity of downstream conclusions, remain limited. We introduce Confidence-Driven Inference: a method that combines LLM annotations and LLM confidence indicators to strategically select which human annotations should be collected, with the goal of producing accurate statistical estimates and provably valid confidence intervals while reducing the number of human annotations needed. Our approach comes with safeguards against LLM annotations of poor quality, guaranteeing that the conclusions will be both valid and no less accurate than if we only relied on human annotations. We demonstrate the effectiveness of Confidence-Driven Inference over baselines in statistical estimation tasks across three CSS settings--text politeness, stance, and bias--reducing the needed number of human annotations by over 25% in each. Although we use CSS settings for demonstration, Confidence-Driven Inference can be used to estimate most standard quantities across a broad range of NLP problems.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but their performance is highly sensitive to the prompts utilized. This variability poses challenges for accurate assessment and user satisfaction. Current research frequently overlooks instance-level prompt variations and their implications on subjective evaluations. To address these shortcomings, we introduce ProSA, a framework designed to evaluate and comprehend prompt sensitivity in LLMs. ProSA incorporates a novel sensitivity metric, PromptSensiScore, and leverages decoding confidence to elucidate underlying mechanisms. Our extensive study, spanning multiple tasks, uncovers that prompt sensitivity fluctuates across datasets and models, with larger models exhibiting enhanced robustness. We observe that few-shot examples can alleviate this sensitivity issue, and subjective evaluations are also susceptible to prompt sensitivities, particularly in complex, reasoning-oriented tasks. Furthermore, our findings indicate that higher model confidence correlates with increased prompt robustness. We believe this work will serve as a helpful tool in studying prompt sensitivity of LLMs. The project is released at: https://github.com/open-compass/ProSA .

The recent success of Large Language Models (LLMs) has catalyzed an increasing interest in their self-correction capabilities. This paper presents a comprehensive investigation into the intrinsic self-correction of LLMs, attempting to address the ongoing debate about its feasibility. Our research has identified an important latent factor - the "confidence" of LLMs - during the self-correction process. Overlooking this factor may cause the models to over-criticize themselves, resulting in unreliable conclusions regarding the efficacy of self-correction. We have experimentally observed that LLMs possess the capability to understand the "confidence" in their own responses. It motivates us to develop an "If-or-Else" (IoE) prompting framework, designed to guide LLMs in assessing their own "confidence", facilitating intrinsic self-corrections. We conduct extensive experiments and demonstrate that our IoE-based Prompt can achieve a consistent improvement regarding the accuracy of self-corrected responses over the initial answers. Our study not only sheds light on the underlying factors affecting self-correction in LLMs, but also introduces a practical framework that utilizes the IoE prompting principle to efficiently improve self-correction capabilities with "confidence". The code is available at https://github.com/MBZUAI-CLeaR/IoE-Prompting.git.

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.

Human evaluation is the gold-standard for evaluating text generation models. It is also expensive, and to fit budgetary constraints, a random subset of the test data is often chosen in practice. The randomly selected data may not accurately represent test performance, making this approach economically inefficient for model comparison. Thus, in this work, we develop a suite of selectors to get the most informative datapoints for human evaluation while taking the evaluation costs into account. We show that selectors based on variance in automated metric scores, diversity in model outputs, or Item Response Theory outperform random selection. We further develop an approach to distill these selectors to the scenario where the model outputs are not yet available. In particular, we introduce source-based estimators, which predict item usefulness for human evaluation just based on the source texts. We demonstrate the efficacy of our selectors in two common NLG tasks, machine translation and summarization, and show that up to only ~50% of the test data is needed to produce the same evaluation result as the entire data. Our implementations are published in the subset2evaluate package.

We give a new algorithm for best arm identification in linearly parameterised bandits in the fixed confidence setting. The algorithm generalises the well-known LUCB algorithm of Kalyanakrishnan et al. (2012) by playing an arm which minimises a suitable notion of geometric overlap of the statistical confidence set for the unknown parameter, and is fully adaptive and computationally efficient as compared to several state-of-the methods. We theoretically analyse the sample complexity of the algorithm for problems with two and three arms, showing optimality in many cases. Numerical results indicate favourable performance over other algorithms with which we compare.