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Probabilistic Methods · Bayesian Models and Methods

Katarzyna Kobalczyk, Zhiyuan Jerry Lin, Benjamin Letham, Zhuokai Zhao, Maximilian Balandat, Eytan Bakshy

Many real-world optimization problems are guided by complex, subjective preferences that are difficult to express as explicit closed-form objectives. In response, we introduce Language-in-the-Loop Optimization (LILO), a Bayesian optimization (BO) framework that employs a large language model (LLM) to translate free-form natural language feedback and prior knowledge from a decision maker into structured preference signals, going beyond the restrictive scalar or pairwise feedback formats typically assumed in preferential BO. The LLM-derived preferences are integrated by a Gaussian process proxy model, enabling principled acquisition-driven exploration with calibrated uncertainty. By placing the LLM in a supporting role rather than as the optimizer itself, LILO preserves the sample efficiency and stability of BO while providing a flexible and expressive feedback interface. Across synthetic and real-world benchmarks, LILO consistently outperforms both conventional preference-based BO methods and LLM-only optimizers, with particularly strong gains in feedback-limited regimes.

Probabilistic Methods · Bayesian Models and Methods

Sherman Khoo, Dennis Prangle, Song Liu, Mark Beaumont

Simulation-based inference (SBI) enables amortized Bayesian inference by first training a neural posterior estimator (NPE) on prior-simulator pairs, typically through low-dimensional summary statistics, which can then be cheaply reused for fast inference by querying it on new test observations. Because NPE is estimated under the training data distribution, it is susceptible to misspecification when observations deviate from the training distribution. Many robust SBI approaches address this by modifying NPE training or introducing error models, coupling robustness to the inference network and compromising amortization and modularity. We introduce minimum-distance summaries, a plug-in robust NPE method that adapts queried test-time summaries independently of the pretrained NPE. Leveraging the maximum mean discrepancy (MMD) as a distance between observed data and a summary-conditional predictive distribution, the adapted summary inherits strong robustness properties from the MMD. We demonstrate that the algorithm can be implemented efficiently with random Fourier feature approximations, yielding a lightweight, model-free test-time adaptation procedure. We provide theoretical guarantees for the robustness of our algorithm and empirically evaluate it on a range of synthetic and real-world tasks, demonstrating substantial robustness gains with minimal additional overhead.

Probabilistic Methods · Bayesian Models and Methods

SongEun Kim, Seungyoo Lee, Edwin Fong, Hyungi Lee, Juho Lee

Large language models (LLMs) are often hypothesized to perform implicit Bayesian inference, yet a key coherence condition—the martingale property of predictive beliefs—has been shown to fail in controlled synthetic in-context learning settings. We revisit this question in a more typical usage regime: generic multiple-choice question answering. Exploiting the discrete answer space, we compute exact predictive distributions and study belief dynamics induced by autoregressive answer resampling. We introduce prompted predictive resampling (PPR), where an LLM generates a sequence of answers to the same question. Empirically, PPR reveals early-stage belief drift, indicating martingale violations. However, after sufficient resampling steps, the belief process self-stabilizes and converges to a coherent predictive distribution. Based on this observation, we further propose (i) a seed-answer prompting strategy to accelerate stabilization, and (ii) a self-consistency loss that amortizes early-stage drift into the model via fine-tuning. Experiments on multiple-choice QA benchmarks show that our methods substantially reduce belief drift and improve predictive coherence without sacrificing accuracy.

Deep Learning · Foundation Models

Reihaneh Zohrabi, Hosein Hasani, Akshita Gupta, Mahdieh Baghshah, Anna Rohrbach, Marcus Rohrbach

Large vision-language models can produce object hallucinations in image descriptions, highlighting the need for effective detection and mitigation strategies. Prior work commonly relies on the model's attention weights on visual tokens as a detection signal. We reveal that coarse-grained attention-based analysis is unreliable due to hidden confounders, specifically token position and object repetition in a description. This leads to Simpson’s paradox: the attention trends reverse when statistics are aggregated. Based on this observation, we introduce HaloProbe, a Bayesian framework that factorizes external description statistics and internal decoding signals to estimate token-level hallucination probabilities. HaloProbe uses balanced training to isolate internal evidence and combines it with learned prior over external features to recover the true posterior. While intervention-based mitigation methods often degrade utility or fluency by modifying models’ internals, we use HaloProbe as an external scoring signal for non-invasive mitigation. Our experiments show that HaloProbe guided decoding reduces hallucinations more effectively than state-of-the-art intervention-based methods while preserving utility.

Probabilistic Methods · Monte Carlo and Sampling Methods

Emanuel Sommer, David Rügamer

The practical adoption of sampling-based inference (SAI) in Bayesian neural networks (BNNs) remains limited, partly due to persistent misconceptions about the feasibility and efficiency of sampling. This position paper argues that SAI has achieved computational parity with optimization-based methods and is at the verge of superseding such methods for effective and efficient inference in BNNs. This development should be in the interest of the whole community, promoting BNNs as a principled paradigm with its long-standing yet unfulfilled promise of providing principled uncertainty quantification for neural networks. SAI can even do more—yielding superior prediction performance through model averaging, serving as the foundation for a plethora of possible downstream tasks, and providing crucial insights into the landscape of BNNs. In order to make such a change happen and unfold the potential of sampling, overcoming current misconceptions is a necessary first step. The next step is to realign research efforts toward addressing remaining challenges in SAI. In particular, the community must focus on two core problems: sufficient exploration of the posterior landscape and high-fidelity distillation of posterior samples for efficient downstream inference. By addressing conceptual and practical obstacles, we can unlock the full potential of SAI and establish it as a central tool in Bayesian deep learning.

General Machine Learning · Scalable Algorithms

Haolin Yu, Guojun Zhang, Hongliang Li, Pascal Poupart

Federated representation learning (FRL) aims to learn personalized federated models with effective feature extraction from local data. FRL algorithms that share the majority of the model parameters face significant challenges with huge communication overhead. This overhead stems from the millions of neural network parameters and slow aggregation progress of the averaging heuristic. To reduce the overhead, we propose FedLog, which shares sufficient data summaries instead of raw model parameters. The data summaries encode minimal sufficient statistics of an exponential family, and Bayesian inference is utilized for global aggregation. FedLog helps reduce message sizes and communication frequency. We prove that the shared messages are minimal sufficient statistics and theoretically analyze the convergence rate of FedLog. To further ensure formal privacy guarantees, we extend FedLog with the differential privacy framework. Empirical results demonstrate high learning accuracy with low communication overhead of our method.

Deep Learning · Generative Models and Autoencoders

Daniel Geyfman, Felix Draxler, Jan Groeneveld, Hyunsoo Lee, Theofanis Karaletsos, Stephan Mandt

Test-time guidance is a widely used mechanism for steering pre-trained diffusion models toward outcomes specified by a reward function. Existing approaches, however, focus on reward maximization rather than sampling from the true Bayesian posterior, leading to miscalibrated inference. In this work, we show that common test-time guidance methods do not recover the correct posterior distribution and identify the structural approximations responsible for this failure. We then propose consistent alternative estimators that enable calibrated sampling from the Bayesian posterior. Across Bayesian inference and inverse problems, our approach yields substantially improved posterior calibration.

Probabilistic Methods · Bayesian Models and Methods

Gyeonghun Kang, Changwoo Lee, Xiang Cheng

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds of the approximated PPD in terms of attention depth and bin resolution. Based on these results, we further demonstrate the key role of normalization and the choice of attention depth in enabling the extrapolation abilities of transformers beyond the pretraining sample size range. We conduct simulations that corroborate our findings, providing insight into the expressivity of PFNs targeting PPDs and how architectural choices may influence generalization capabilities.

Probabilistic Methods · Bayesian Models and Methods

Luwei Wang, Dagmara Panas, Ke Wang, Sohan Seth, Bruce Guthrie

Constrained clustering incorporates prior knowledge in the form of pairwise constraints to guide data partitioning. While effective, existing Bayesian approaches are often limited in scalability to large datasets and provide weak interpretability due to the lack of explicit feature relevance modeling. We propose BASIL, a scalable Bayesian semi-supervised clustering framework that leverages stochastic variational inference to jointly infer cluster assignments and feature importance weights. This joint formulation enables the identification of discriminative features consistent with the imposed constraints. To robustly handle noisy or inconsistent supervision, BASIL introduces an adaptive constraint-weighting mechanism that down-weights unreliable constraints. Experiments on synthetic and real-world benchmarks demonstrate that our approach achieves competitive clustering performance while improving scalability and interpretability over existing baselines. We further demonstrate applicability to large-scale health data, including medical imaging and electronic health records.

Probabilistic Methods · Bayesian Models and Methods

Weifeng Zhang, Wenyuan Zhao, Amir Hossein Rahmati, Yucheng Wang, Zhiyuan Wang, Chao Tian, Xiaoning Qian

Principled uncertainty quantification (UQ) is increasingly recognized as essential for trustworthy artificial general intelligence (AGI). Bayesian Low-Rank Adaptation (LoRA) provides a principled mechanism for uncertainty-aware fine-tuning of large language models (LLMs). However, existing techniques either face scalability constraints, e.g. Laplace-LoRA, or rely on approximate inference schemes that lead to poorly calibrated posterior uncertainty, often manifesting as overconfident predictions under distribution shift. To address this challenge, we propose GPan-LoRA, the first scalable Gaussian Process (GP)-based framework for Bayesian LoRA, which integrates neural network-based sparse GP approximations with amortized variational inference. By preserving the Bayesian function prior and posterior semantics intrinsic to GPs, GPan-LoRA achieves a faithful balance between computational scalability and principled UQ. Empirically, GPan-LoRA produces well-calibrated uncertainty that remains reliable under distribution shift, mitigating overconfident failures while preserving competitive task performance.

Probabilistic Methods · Everything Else

Mengqi Chen, Thomas Berrett, Theodoros Damoulas, Michele Caprio

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

Probabilistic Methods · Monte Carlo and Sampling Methods

Emanuel Sommer, Kangning Diao, Jakob Robnik, Uros Seljak, David Rügamer

Scaling inference methods such as Markov chain Monte Carlo to high-dimensional models remains a central challenge in Bayesian deep learning. A promising recent proposal, microcanonical Langevin Monte Carlo, has shown state-of-the-art performance across a wide range of problems. However, its reliance on full-dataset gradients makes it prohibitively expensive for large-scale problems. This paper addresses a fundamental question: Can microcanonical dynamics effectively leverage mini-batch gradient noise? We provide the first systematic study of this problem, establishing a novel continuous-time theoretical analysis of stochastic-gradient microcanonical dynamics. We reveal two critical failure modes: a theoretically derived bias due to anisotropic gradient noise and numerical instabilities in complex high-dimensional posteriors. To tackle these issues, we propose a principled gradient noise preconditioning scheme shown to significantly reduce this bias and develop a novel, energy-variance-based adaptive tuner that automates step size selection and dynamically informs numerical guardrails. The resulting algorithm is a robust and scalable microcanonical Monte Carlo sampler that achieves state-of-the-art performance on challenging high-dimensional inference tasks like Bayesian neural networks. Combined with recent ensemble techniques, our work unlocks a new class of stochastic microcanonical Langevin ensemble (SMILE) samplers for large-scale Bayesian inference.

Qiru Li, Ao Zhou, Zhiwei Jiang, Zifeng Cheng, Cong Wang, Yafeng Yin, Qing Gu

Vision--language models such as CLIP have shown strong zero-shot performance, but their reliability degrades in realistic multi-label settings under distribution shift. Standard test-time adaptation (TTA) methods either rely on costly gradient-based updates or adopt lightweight statistical schemes that implicitly assume label independence. The latter is particularly harmful in multi-label scenarios, where visually dominant classes suppress semantically correlated yet weaker labels, leading to severe recall loss. We revisit multi-label TTA from a Bayesian perspective and propose Bayesian Conditional Priors~(BCP) estimation, a backpropagation-free framework that injects label dependencies into CLIP's zero-shot predictions. Treating the zero-shot scores as approximate marginal posteriors, BCP derives an anchor-conditioned Bayesian refinement in which each logit is corrected by a term determined solely by the conditional prior $P(c_i=1 \mid c_a=1)$. These conditional priors are estimated online via second-order co-occurrence statistics over the test stream and instantiated as closed-form, monotonic logit transformations, without backpropagation or architectural changes. Experiments on multi-label benchmarks show that this structure-aware adaptation consistently improves mean average precision over entropy-based and retrieval-augmented TTA baselines, while incurring negligible computational overhead.

General Machine Learning · Transfer, Multitask and Meta-learning

Siyang Guo, Junbo Wang, Zibin Zheng

As pre-trained models evolve rapidly, transferring fine-tuning knowledge to updated models without retraining has become a critical challenge. Most existing methods reuse parameter updates, yet the same dataset can induce substantially different updates across base models due to mismatched local loss landscapes, making such transfer unstable. We instead adopt a Bayesian-updating perspective: a base model defines a prior, while fine-tuning contributes a task-update factor that is prior-agnostic, thereby making it feasible to reuse the update across base models. Specifically, we formalize a reusable task-update factor by requiring *invariance across base models* and *a fixed-dimensional parameterization*. Our main theoretical result shows that such reusable factors exist when the variational family is a half-space, and it is already maximal among convex families. In particular, an ideal regime arises when the priors and their Bayesian posteriors remain within a shared exponential family, as it always admits a reusable update factor. Building on this existence, we propose ***B**ayesian Task Update **Transfer*** (*BTransfer*), which extracts a reusable task-update factor from a single fine-tuning run and applies it to a new prior. For deep networks, we implement *BTransfer* with a ``lift–transfer–return'' pipeline: 1) lift model parameters to distributions; 2) transfer the extracted task-update factor in the exponential family distributions; and 3) return the updated posterior distribution to parameter space. Extensive experiments demonstrate that our approach effectively reuses fine-tuning knowledge across models without post-training.

General Machine Learning · Transfer, Multitask and Meta-learning

Zhiliang Chen, Gregory Kang Ruey Lau, Chuan Sheng Foo, Bryan Kian Hsiang Low

The performance of an LLM depends heavily on how well the training data matches the downstream evaluation task. However, in many practical settings, we typically do not know the data in the evaluation task (e.g., conversations between a chatbot and users are end-to-end encrypted). We refer to such tasks as unseen evaluation tasks. We can only deploy the LLM on these unseen evaluation tasks to gather multiple rounds of feedback on how well the model performs (e.g., gathering user ratings from a chatbot). In addition, this feedback can be noisy. How can we exploit such noisy feedback efficiently to optimize the LLM training data-mixture? Our paper presents DUET, a novel global-to-local algorithm that optimizes training data mixtures by interleaving data selection with Bayesian optimization to exploit coarse and noisy feedback from a downstream evaluation task. DUET is flexible enough to incorporate different data selection methods, each with different performance-compute tradeoffs. By analyzing DUET's cumulative regret, we theoretically show that DUET converges to the optimal training data mixture even without any fine-grained data information from an unseen task. Finally, our experiments across a variety of language tasks demonstrate that DUET attains substantial performance improvements over existing data selection and mixing methods in the unseen-task setting. Our library, which is flexible enough to optimize different LLM training ingredients, can be found at https://github.com/chenzhiliang94/BO-for-LLM.

Optimization · Optimization and Learning under Uncertainty

Rafael Oliveira, Dan Steinberg, Edwin Bonilla

We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables large batch scaling as generative sampling, optimization of non-continuous design spaces, and high-dimensional and combinatorial design. Inspired by the success of direct preference optimization (DPO), we show that one can train a generative model with noisy, simple utility values directly computed from observations to then form proposal distributions whose densities are proportional to the expected utility, i.e., BO's acquisition function values. Furthermore, this approach is generalizable beyond preference-based feedback to general types of reward signals and loss functions. This perspective avoids the construction of surrogate (regression or classification) models, common in previous methods that have used generative models for black-box optimization. Theoretically, we show that the generative models within the BO process follow a sequence of distributions which asymptotically approximate an optimal target under certain conditions. We also evaluate the performance through experiments on challenging optimization problems involving large batches in high dimensions.

Computer Vision · Everything Else

Jiyong Rao, Yu Wang, Shengjie Zhao

Category-agnostic pose estimation (CAPE) aims to localize keypoints on query images from arbitrary categories, using only a few annotated support examples for guidance. Recent approaches either treat keypoints as isolated entities or rely on manually defined skeleton priors, which are costly to annotate and inherently inflexible across diverse categories. Such oversimplification limits the model’s capacity to capture instance-wise structural cues critical for accurate pixel-level localization. To overcome these limitations, we propose \textbf{GenCape}, a \textbf{Gen}erative-based framework for \textbf{CAPE} that infers keypoint relationships solely from image-based support inputs, without additional textual descriptions or predefined skeletons. Our framework consists of two principal components: an iterative Structure-aware Variational Autoencoder (i-SVAE) and a Compositional Graph Transfer (CGT) module. The former infers soft, instance-specific adjacency matrices from support features through variational inference, embedded layer-wise into the Graph Transformer Decoder for progressive structural priors refinement. The latter adaptively aggregates multiple latent graphs into a query-aware structure via Bayesian fusion and attention-based reweighting, enhancing resilience to visual uncertainty and support-induced bias. This structure-aware design facilitates effective message propagation among keypoints and promotes semantic alignment across object categories with diverse keypoint topologies. Experimental results on the MP-100 dataset show that our method achieves substantial gains over graph-support baselines under both 1- and 5-shot settings, while maintaining competitive performance against text-support counterparts.

General Machine Learning · Transfer, Multitask and Meta-learning

De Cheng, Mingyue Zeng, Zhipeng Xu, Di Xu, Nannan Wang, Xinbo Gao

Incremental Object Detection (IOD) enables AI systems to continuously learn new object classes over time while retaining knowledge of previously learned categories. This capability is essential for adapting to dynamic environments without forgetting prior information. Although existing IOD methods have made progress in mitigating catastrophic forgetting, they usually lack explicit and quantitative modeling of information conflicts during knowledge preservation, making task boundaries ambiguous. Such conflicts often stem from the fact that a single image can contain objects belonging to previous, present, and future tasks, where unlabeled past and future objects are often mistakenly treated as background. In this paper, we propose a novel approach grounded in Elastic Weight Consolidation (EWC) to alleviate conflict knowledge preservation caused by task interference. Specifically, we introduce the Interference Knowledge Isolated Elastic Weight Consolidation (IKI-EWC) framework for IOD, which leverages the mispredictions of the old detector on new task data to estimate task conflicts and suppresses them at the parameter level. By reformulating the Bayesian posterior of model parameters, we derive a mathematical relationship between previously learned knowledge and interference knowledge, enabling targeted elimination of conflicts during model weight updates. In addition, we also propose a prototype-based knowledge calibration (PKC) mechanism to further preserve old knowledge during the training of the objector's classification head. This method employs a learnable projection layer to compensate semantic drift in old class prototypes, and then jointly trains the classification head using both calibrated prototypes and current task features, thereby mitigating forgetting caused by classifier updates. Extensive experiments on PASCAL VOC and MS-COCO benchmarks demonstrate the effectiveness of the proposed method, outperforming state-of-the-art approaches in various settings.

Applications · Chemistry and Drug Discovery

Kevin Tirta Wijaya, Bing Hu, Hans-Peter Seidel, Wojciech Matusik, Vahid Babaei

Accurate regression models are essential for scientific discovery, yet high-quality numeric labels are scarce and expensive. In contrast, rankings (especially pairwise) are easier to obtain from domain experts or artificial intelligence judges. We introduce RankRefine++, a novel plug-and-play method that improves a base regressor's prediction for a query by leveraging pairwise rankings between the query and reference items with known labels. RankRefine++ performs a Bayesian update that combines a Gaussian likelihood from the regressor and the Bradley-Terry likelihood from the ranker. This yields a strictly log-concave posterior with a unique maximum likelihood solution and fast Newton updates. We show that prior state-of-the-art is a special case of our framework, and we identify a fundamental failure mode: Bradley-Terry likelihoods suffer from scale mismatch and curvature dominance when the number of reference items is large, which can degrade performance. From this analysis, we derive a calibration method to adjust the information originating from the expert rankings. RankRefine++ shows a stunning 97.65\% median improvement across 12 datasets over previous state-of-the-art method using a realistically-accurate ranker, and runs efficiently on a consumer-grade CPU.

Social Aspects · Accountability, Transparency and Interpretability

Anjali Parashar, Yingke Li, Eric Yu, Fei Chen, James Neidhoefer, devesh upadhyay, Chuchu Fan

As autonomous systems such as drones, become increasingly deployed in high-stakes, human-centric domains, it is critical to evaluate the ethical alignment since failure to do so imposes imminent danger to human lives, and long term bias in decision-making. Automated ethical benchmarking of these systems is understudied due to the lack of ubiquitous, well-defined metrics for evaluation, and stakeholder-specific subjectivity, which cannot be modeled analytically. To address these challenges, we propose SEED-SET, a Bayesian experimental design framework that incorporates domain-specific objective evaluations, and subjective value judgments from stakeholders. SEED-SET models both evaluation types separately with hierarchical Gaussian Processes, and uses a novel acquisition strategy to propose interesting test candidates based on learnt qualitative preferences and objectives that align with the stakeholder preferences. We validate our approach for ethical benchmarking of autonomous agents on two applications and find our method to perform the best. Our method provides an interpretable and efficient trade-off between exploration and exploitation, by generating up to $2\times$ optimal test candidates compared to baselines, with $1.25\times$ improvement in coverage of high dimensional search spaces.