Causal graphs play a crucial role in AI research as they reveal the data generation processes underlying real-world machine learning and computer vision tasks. Recent studies have leveraged causal graphs to develop more robust and interpretable models. However, limited or biased data often lead to inaccurate causal graph estimation, reducing a model's transferability to unseen domains. To address this challenge, we propose a novel framework that performs Bayesian inference over causal graphs to capture potential underlying causal relations and identify invariant causal features for DG prediction. The key advantage of our framework lies in its ability to quantify causal graph uncertainty in the context of prediction tasks and incorporate it into the prediction process. Our proposed uncertainty provides valuable insights into (i) the reliability of our method on specific datasets, (ii) the alignment between learned causal graphs and unseen test domains, and (iii) the confidence of our predictions. In particular, we go beyond merely quantifying uncertainty and leverage it as weighting factors in a weighted Bayesian inference scheme. Empirical results on multiple benchmark distribution-shift datasets show that our algorithm, **C**ausal **G**raph **U**ncertainty-guided **Bayes**ian Inference (CGU-Bayes), outperforms existing DG methods on challenging datasets and achieves state-of-the-art performance overall.
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From Passive Metric to Active Signal: The Evolving Role of Uncertainty Quantification in Large Language Models
PDF ↗While Large Language Models (LLMs) show remarkable capabilities, their unreliability remains a critical barrier to deployment in high-stakes domains. This survey charts a functional evolution in addressing this challenge: the evolution of uncertainty from a passive diagnostic metric to an active control signal guiding real-time model behavior. We demonstrate how uncertainty is leveraged as an active control signal across three frontiers: in advanced reasoning to optimize computation and trigger self-correction; in autonomous agents to govern metacognitive decisions about tool use and information seeking; and in reinforcement learning to mitigate reward hacking and enable self-improvement via intrinsic rewards. By grounding these advancements in emerging theoretical frameworks like Bayesian methods and Conformal Prediction, we provide a unified perspective on this transformative trend. This survey provides a comprehensive overview, critical analysis, and practical design patterns, arguing that mastering the new trend of uncertainty is essential for building the next generation of scalable, reliable, and trustworthy AI.
Existing information extraction (IE) tasks increasingly adopt in-context learning (ICL) with large language models. However, current approaches either show inconsistent performance across model scales or lack systematic optimization and generalizability. Building on this, we propose BCL-IE (Bayesian In-Context Learning Framework for Information Extraction), the first optimization framework that uses particle filtering with Bayesian updates to systematically refine label representations across IE tasks. Through four steps—initialization, observation, weight update, and resampling, BCL-IE generalizes to both sequence labeling and relation classification paradigms. Extensive experiments demonstrate substantial improvements over existing approaches (up to 30%), achieving prior performance while other methods either fail to generalize or show limited effectiveness.
Automated negotiation in complex, multi-party and multi-issue settings critically depends on accurate opponent modeling. However, conventional numerical-only approaches fail to capture the qualitative information embedded in natural language interactions, resulting in unstable and incomplete preference estimation. Although Large Language Models (LLMs) enable rich semantic understanding of utterances, it remains challenging to quantitatively incorporate such information into a consistent opponent modeling. To tackle this issue, we propose a novel preference estimation method integrating natural language information into a structured Bayesian opponent modeling framework. Our approach leverages LLMs to extract qualitative cues from utterances and converts them into probabilistic formats for dynamic belief tracking. Experimental results on a multi-party benchmark demonstrate that our framework improves the full agreement rate and preference estimation accuracy by integrating probabilistic reasoning with natural language understanding.
Balancing Fidelity and Plasticity: Aligning Mixed-Precision Fine-Tuning with Linguistic Hierarchies
PDF ↗Deploying and fine-tuning Large Language Models (LLMs) on resource-constrained edge devices requires navigating a strict trade-off between memory footprint and task performance. Existing quantization-aware fine-tuning methods typically decouple weight precision and adapter capacity, overlooking that a layer’s ability to adapt is constrained by the information preserved in its frozen weights. Layers that are highly sensitive to quantization—whether due to representational specialization or accumulated error propagation—can become bottlenecks that adapter rank alone cannot recover. To address this issue, we introduce QR-Adaptor, a unified framework that jointly optimizes per-layer quantization bit-width and LoRA rank. We formulate resource allocation as a multi-objective discrete search guided by empirical layer-wise sensitivity, and implement it with a three-stage pipeline comprising KL-based sensitivity profiling, evolutionary exploration, and Bayesian refinement. Extensive experiments across LLaMA and Qwen models, including modern instruction tuning on OpenOrca and comparisons with strong PEFT baselines such as QDoRA, show that QR-Adaptor establishes a strong Pareto frontier: under a strict 4-bit memory budget, it matches or approaches 16-bit baselines while using substantially less memory.
Bayesian Active Learning with Gaussian Processes Guided by LLM Relevance Scoring for Dense Passage Retrieval
PDF ↗While Large Language Models (LLMs) exhibit exceptional zero-shot relevance modeling, their high computational cost necessitates framing passage retrieval as a budget-constrained global optimization problem. Existing approaches passively rely on first-stage dense retrievers, which leads to two limitations: (1) failing to retrieve relevant passages in semantically distinct clusters, and (2) failing to propagate relevance signals to the broader corpus. To address these limitations, we propose Bayesian Active Learning with Gaussian Processes guided by LLM relevance scoring (BAGEL), a novel framework that propagates sparse LLM relevance signals across the embedding space to guide global exploration. BAGEL models the multimodal relevance distribution across the entire embedding space with a query-specific Gaussian Process (GP) based on LLM relevance scores. Subsequently, it iteratively selects passages for scoring by strategically balancing the exploitation of high-confidence regions with the exploration of uncertain areas. Extensive experiments across four benchmark datasets and two LLM backbones demonstrate that BAGEL effectively explores and captures complex relevance distributions and outperforms LLM reranking methods under the same LLM budget on all four datasets.
Generative-to-Discriminative Test-Time Adaptation via Manifold-Aware Diffusion and Bayesian Distillation
PDF ↗Multimodal Sentiment Analysis (MSA) models typically suffer significant performance degradation under domain shifts. While Test-Time Adaptation (TTA) aims to mitigate this, existing discriminative approaches often succumb to “confident but wrong” predictions on out-of-distribution samples. Conversely, generative models offer robust calibration but incur prohibitive computational costs. To bridge this gap, we propose GD-Adapt (Generative-Discriminative Adaptation), a novel TTA framework that harmonizes the robustness of generative diffusion models with the efficiency of discriminative regression networks via Bayesian Diffusion Distillation (BDD). Specifically, we introduce Auxiliary Generative Regularization (AGR) during pretraining to enforce manifold-aware feature learning. Extensive experiments across five cross-domain scenarios demonstrate our method’s superiority. For instance, on the challenging MOSI to SIMS shift, GD-Adapt reduces Mean Absolute Error (MAE) from 0.6872 to 0.5673 and boosts binary accuracy by 5.81 percentage points (reaching 57.33%). Notably, in scenarios such as SIMS to MOSI, we achieve an 11.18-point gain over the non-adapted baseline.
Verifiable Parameterization of Bayesian Networks from Scientific Literature: Unlocking Unstructured Empirical Evidence
PDF ↗Learning Bayesian Networks typically requires access to raw tabular data to estimate conditional probabilities. However, in many scientific domains, raw data is unavailable due to privacy concerns or general lack of access, while structured statistical summaries are increasingly accessible through large language models and published literature. We propose and evaluate five distinct strategies to reconstruct local conditional probability tables solely from statistical summaries in order to parameterize Bayesian Networks. Our comprehensive evaluation across mixed-type synthetic networks demonstrates that copula-based methods significantly outperform standard baselines, offering a viable path for knowledge integration from heterogeneous sources – unlocking the wealth of published knowledge for causal modeling while ensuring transparency and verifiability.
Fine-tuning large language models (LLMs) for downstream tasks remains expensive, even with parameter-efficient methods like Low-Rank Adaptation (LoRA). In this regard, meta-learning approaches such as Model-Agnostic Meta-Learning for LLMs (MAML-en-LLM) and Amortized Bayesian Meta-Learning for LoRA (ABMLL) have emerged as promising solutions for rapid downstream LLM adaptation. However, these methods fundamentally couple two distinct objectives: learning generalizable initializations and enabling efficient task adaptation. We argue that this coupling limits both the quality of learned representations and adaptation efficiency. In this paper, we introduce **DeGAML-LLM** (**De**coupled **G**eneralization and **A**daptation in **M**eta-**L**earning for **LLM**s), a novel framework that explicitly separates these two objectives through dedicated parameter spaces. Specifically, we maintain a generalization module that learns task-agnostic representations across the task distribution, and an adaptation module that specializes in rapid task-specific adjustment. Extensive experiments on common-sense reasoning, mathematics, logic, social, medical and coding benchmarks across model scales demonstrate that DeGAML-LLM outperforms existing meta-learning and standard multi-task baselines.
Test-time scaling evaluates reasoning LLMs by sampling multiple outputs per prompt, but ranking models in this regime remains underexplored. We formalize dense benchmark ranking under test-time scaling and introduce Scorio, a library that implements statistical ranking methods such as paired-comparison models, item response theory (IRT) models, voting rules, and graph- and spectral-based methods. Across 20 reasoning models on four Olympiad-style math benchmarks (AIME’24, AIME’25, HMMT’25, and BrUMO’25; up to N = 80 trials), most full-trial rankings agree closely with the Bayesian gold standard Bayes_𝒰@80 (mean Kendall’s τ_b = 0.93–0.95), and 19–34 methods recover exactly the same ordering. In the single-trial regime, the best methods reach τ_b ≈ 0.86.Using greedy decoding as an empirical prior (Bayes_R₀@N) reduces variance at N = 1 by 16–52%, but can bias rankings when greedy and stochastic sampling disagree. These results identify reliable ranking methods for both high- and low-budget test-time scaling. We release Scorio as an open-source library at https://github.com/mohsenhariri/scorio.
Decisive: Guiding User Decisions with Optimal Preference Elicitation from Unstructured Documents
PDF ↗Decision-making is a cognitively intensive task that requires synthesizing relevant information from multiple unstructured sources, weighing competing factors, and incorporating subjective user preferences. Existing methods, including large language models and traditional decision-support systems, fall short: they often overwhelm users with information or fail to capture nuanced preferences accurately. We present Decisive, an interactive decision-making framework that combines document-grounded reasoning with Bayesian preference inference. Our approach grounds decisions in an objective option-scoring matrix extracted from source documents, while actively learning a user’s latent preference vector through targeted elicitation. Users answer pairwise tradeoff questions adaptively selected to maximize information gain over the final decision. This process converges efficiently, minimizing user effort while ensuring recommendations remain transparent and personalized. Through extensive experiments, we demonstrate that our approach significantly outperforms both general-purpose LLMs and existing decision-making frameworks achieving up to 20% improvement in decision accuracy over strong baselines across domains.
The rise of Large Audio-Language Models (LAMs) brings both potential and risks, as their audio outputs may contain harmful or unethical content. However, current research lacks a systematic, quantitative evaluation of LAM safety, especially against jailbreak attacks, which are challenging due to the temporal and semantic nature of speech. To bridge this gap, we introduce AJailBench, the first benchmark specifically designed to evaluate jailbreak vulnerabilities in LAMs. We begin by constructing -Base, a dataset of 1,495 adversarial audio prompts spanning 10 policy-violating categories. Using this dataset, we evaluate several state-of-the-art LAMs and reveal that none exhibit consistent robustness across attacks. To further strengthen jailbreak testing and simulate more realistic attack conditions, we propose a method to generate dynamic adversarial variants. Our Audio Perturbation Toolkit (APT) applies targeted distortions across time, frequency, and amplitude domains. To preserve the original jailbreak intent, we enforce a semantic consistency constraint and employ Bayesian optimization to efficiently search for perturbations that are both subtle and highly effective. This results in AJailBench-APT+, an extended dataset of optimized adversarial audio samples. Our findings demonstrate that even small, semantically preserved perturbations can significantly reduce the safety performance of leading LAMs, underscoring the need for more robust and semantically aware defense mechanisms. We release AJailBench to facilitate future research: https://anonymous.4open.science/r/AudioJailbreak-4262/
Modeling Human-Like Cognition for Stance Detection: Integrating Intuitive Judgment and Analytical Reasoning
PDF ↗Stance detection aims to identify the attitude expressed in text towards a given target, with applications in public opinion analysis and misinformation mitigation. Despite recent advances in large language models (LLMs), two key challenges remain: (1) spurious correlations between superficial features and stance labels, and (2) lack of cognitive modeling that simulates the transition from intuitive perception to deliberate reasoning. To address these issues, we propose Cognitive-Driven Stance Detection (CDSD), inspired by Kahneman’s Dual-Process Theory. CDSD integrates fast intuitive judgment (System 1) and analytical reasoning (System 2), enhanced by three key modules: attention-based cognitive alignment to compare system focus, uncertainty-aware belief update using Bayesian inference, and self-doubt-triggered counterfactual reasoning for re-evaluation under low consistency or high uncertainty. Experimental results on SEM16, P-Stance, and VAST show that CDSD outperforms state-of-the-art methods across multiple LLMs. Notably, CDSD exhibits strong robustness against textual perturbations such as emotional word removal and rhetorical restructuring. By integrating cognitive theory with NLP, our work provides a promising path toward more reliable and interpretable stance detection systems.
Quantifying Aleatoric Uncertainty of In-Context Learning for Robust Measure of LLM Prediction Confidence
PDF ↗In-Context Learning (ICL) allows large language models to adapt to new tasks from a few demonstrations, but its reliability remains a concern: predictions are highly sensitive to both prompt design and the model’s ability to understand the context, obscuring whether failures arise from data properties or model limitations. Uncertainty decomposition—separating aleatoric from epistemic sources—is particularly crucial in this setting, yet existing methods, designed for standard generation tasks, fail to capture the unique dynamics of ICL. To address this, we introduce a concept of self-function vectors, built upon Bayesian views and the mechanistic interpretability of ICL. These vectors leverage internal model representations to model the latent concept learned during in-context prompting, thereby enabling a direct estimation of aleatoric uncertainty within a Bayesian framework and circumventing the reliance on brittle input or decoding manipulations. Given the lack of established benchmarks and suitable evaluation protocols, we also propose the first and rigorous evaluation framework, initially grounded in synthetic tasks for conceptual development and subsequently extended to real-world datasets, in which aleatoric and epistemic uncertainty can be quantified separately under controlled settings. Moreover, we show it can be used as a practical tool for trustworthy-related applications, such as hallucination detection. Our findings pave a new direction for connecting the quantitative view of uncertainty with the mechanistic understanding of model behavior.
Probabilistic Methods · Bayesian Models and Methods
Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian mechanism for feature sparsity via marginal likelihood optimization. Yet, its reliance on a homoscedastic noise model renders it sensitive to data contaminations such as outliers or misspecified noise, harming model fit and predictions. Instead, we propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification via a single Bayesian objective. This symmetric pruning of model and data offers a natural extension that preserves conjugacy, admits closed-form updates for standard optimization procedures, and aligns with perspectives from robust regression and influence functions. Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
Probabilistic Methods · Bayesian Models and Methods
Generalized Bayesian Inference (GBI) tempers a loss with a temperature $\beta>0$ to mitigate overconfidence and improve robustness under model misspecification, but existing GBI methods typically rely on costly MCMC or SDE-based samplers and must be re-run for each new dataset and each $\beta$-value. We give the first fully amortized variational approximation to the tempered posterior family $p_\beta(\theta\! \mid\! x) \propto \pi(\theta)p(x\! \mid\! \theta)^\beta$ by training a single $\beta$-conditioned neural posterior estimator $q_\phi(\theta \mid x, \beta)$ that enables sampling in a single forward pass, without simulator calls or inference-time MCMC. We introduce two complementary training routes: (i) synthesizes off-manifold samples $(\theta, x) \sim \pi(\theta)p(x \mid \theta)^\beta$ and (ii) reweights a fixed base dataset $\pi(\theta)p(x \mid \theta)$ using self-normalized importance sampling (SNIS), where we show that the SNIS-weighted objective provides a consistent forward-KL fit to the tempered posterior with finite weight variance. Across four standard simulation-based inference (SBI) benchmarks—including the chaotic Lorenz–96 system—our $\beta$-amortized estimator achieves competitive posterior approximations, in standard two-sample metrics, with non-amortized MCMC-based power-posterior samplers over a wide range of temperatures.
Probabilistic Methods · Gaussian Processes
Bayesian optimization (BO) selects evaluation points for expensive black-box objectives using Gaussian process (GP) predictive distributions. Kernel choice and hyperparameter selection can lead to miscalibrated predictive distributions, which can distort the exploration--exploitation trade-off. In the minimization setting, sampling criteria such as expected improvement (EI) depend on the predictive lower tail and can therefore be sensitive to miscalibration. This article studies goal-oriented calibration of GP predictive distributions below a low threshold $t$ in the noiseless setting, complementing standard GP modeling with hyperparameters selected by maximum likelihood. A framework for predictive reliability below $t$ is introduced, based on two notions of spatial calibration: occurrence calibration over the design space and thresholded $\mu$-calibration on the sublevel set $\lbrace x\in\mathbb{X}, f(x)\le t \rbrace$. Building on this framework, we propose tcGP, a post-hoc method that calibrates GP predictive distributions below $t$, and we establish a convergence result for the resulting EI-based global optimization algorithm. Experiments on standard benchmarks show improved lower-tail calibration and BO performance relative to standard GP models and global calibration GP models.
Probabilistic Methods · Bayesian Models and Methods
Epistemic uncertainty quantification (UQ) for deep neural networks (DNNs) is a requirement for safe adoption of AI in mission-critical settings. Several leading methods for UQ linearize DNNs to form Bayesian Generalized Linear Models (GLMs), where epistemic uncertainty is modeled via the predictive posterior distribution. Linearizing around the parameters of the *final connected layer* of a DNN is a commonly used approximation for reducing the computational burden of such GLMs, though it is often believed to come at the cost of degraded performance. In this work, we compare GLMs arising from full-network and last-layer linearization using both theoretical and empirical approaches. We first employ tools from random matrix theory to conduct a theoretical comparison; this analysis reveals no meaningful improvement in the UQ capabilities of full linearization. Coupled with a large-scale empirical evaluation across a range of modern machine learning tasks, we arrive at the following conclusion: a last-layer approximation yields comparable UQ performance while offering substantially improved computational efficiency.
Multi-fidelity (MF) regression often operates in regimes of extreme data imbalance, where the commonly-used Gaussian-process surrogates struggle with cubic scaling costs and overfit to sparse high-fidelity observations, limiting efficiency and generalization in real-world applications. We introduce FIRE, a training-free MF framework that couples tabular foundation models (TFMs) to perform zero-shot in-context Bayesian inference via a high-fidelity correction model conditioned on the low-fidelity model's posterior predictive distributions. This cross-fidelity information transfer via distributional summaries captures heteroscedastic errors, enabling robust residual learning without model retraining. Across 31 benchmark problems spanning synthetic functions and real-world tasks (e.g., DrivAerNet, LCBench), FIRE delivers a stronger performance–time trade-off than seven state-of-the-art GP-based or deep learning MF regression methods, ranking highest in accuracy and uncertainty quantification with runtime advantages. Limitations include context window constraints and dependence on the quality of the pre-trained TFM’s.
Probabilistic Methods · Monte Carlo and Sampling Methods
Hamiltonian Monte Carlo and underdamped Langevin Monte Carlo are state-of-the-art methods for taking samples from high-dimensional distributions with a differentiable density function. To generate samples, they numerically integrate Hamiltonian or Langevin dynamics. This numerical integration introduces an asymptotic bias in Monte Carlo estimators of expectation values, which can be eliminated by adjusting the dynamics with a Metropolis-Hastings (MH) proposal step. Alternatively, one can trade bias for variance by avoiding MH, and select an integration step size that ensures sufficiently small asymptotic bias, relative to the variance inherent in a finite set of samples. Such \emph{unadjusted} methods often significantly outperform their adjusted counterparts in high-dimensional problems where sampling would otherwise be prohibitively expensive, yet are rarely used in statistical applications due to the absence of an automated way of choosing a step size. We propose just such an automatic tuning scheme that takes a user-provided asymptotic bias tolerance and selects a step size that ensures it. The key to the method is a relationship we establish between the energy change during integration and the asymptotic bias. We show that this procedure rigorously bounds the asymptotic bias for Gaussian target distributions. We then numerically show that the procedure works beyond Gaussians. To demonstrate the practicality of the proposed scheme, we provide a comprehensive comparison of adjusted and unadjusted samplers on Bayesian inference problems and on a statistical physics model in more than one million parameters. With our tuning scheme, the unadjusted methods achieve close to optimal performance, significantly and consistently outperforming their adjusted counterparts.