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General Machine Learning · Probabilistic Methods

Jonas Arruda, Vikas Pandey, Catherine Sherry, Margarida Barroso, Xavier Intes, Jan Hasenauer, Stefan Radev

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.

Deep Learning · Algorithms

Moritz Akiya Zanger, Pascal R Van der Vaart, Wendelin Boehmer, Matthijs T. J. Spaan

Uncertainty quantification is a critical aspect of reinforcement learning and deep learning, with numerous applications ranging from efficient exploration and stable offline reinforcement learning to outlier detection in medical diagnostics. The scale of modern neural networks, however, complicates the use of many theoretically well-motivated approaches such as full Bayesian inference. Approximate methods like deep ensembles can provide reliable uncertainty estimates but still remain computationally expensive. In this work, we propose contextual similarity distillation, a novel approach that explicitly estimates the variance of an ensemble of deep neural networks with a single model, without ever learning or evaluating such an ensemble in the first place. Our method builds on the predictable learning dynamics of wide neural networks, governed by the neural tangent kernel, to derive an efficient approximation of the predictive variance of an infinite ensemble. Specifically, we reinterpret the computation of ensemble variance as a supervised regression problem with kernel similarities as regression targets. The resulting model can estimate predictive variance at inference time with a single forward pass, and can make use of unlabeled target-domain data or data augmentations to refine its uncertainty estimates. We empirically validate our method across a variety of out-of-distribution detection benchmarks and sparse-reward reinforcement learning environments. We find that our single-model method performs competitively and sometimes superior to ensemble-based baselines and serves as a reliable signal for efficient exploration. These results, we believe, position contextual similarity distillation as a principled and scalable alternative for uncertainty quantification in reinforcement learning and general deep learning.

General Machine Learning · Probabilistic Methods

Tommy Rochussen, Vincent Fortuin

One of the core facets of Bayesianism is in the updating of prior beliefs in light of new evidence$\textemdash$so how can we maintain a Bayesian approach if we have no prior beliefs in the first place? This is one of the central challenges in the field of Bayesian deep learning, where it is not clear how to represent beliefs about a prediction task by prior distributions over model parameters. Bridging the fields of Bayesian deep learning and probabilistic meta-learning, we introduce a way to $\textit{learn}$ a weights prior from a collection of datasets by introducing a way to perform per-dataset amortised variational inference. The model we develop can be viewed as a neural process whose latent variable is the set of weights of a BNN and whose decoder is the neural network parameterised by a sample of the latent variable itself. This unique model allows us to study the behaviour of Bayesian neural networks under well-specified priors, use Bayesian neural networks as flexible generative models, and perform desirable but previously elusive feats in neural processes such as within-task minibatching or meta-learning under extreme data-starvation.

Theory · Probabilistic Methods

Madi Matymov, Ba-Hien Tran, Michael Kampffmeyer, Markus Heinonen, Maurizio Filippone

Data Augmentation (DA) has become an essential tool to improve robustness and generalization of modern machine learning. However, when deciding on DA strategies it is critical to choose parameters carefully, and this can be a daunting task which is traditionally left to trial-and-error or expensive optimization based on validation performance. In this paper, we counter these limitations by proposing a novel framework for optimizing DA. In particular, we take a probabilistic view of DA, which leads to the interpretation of augmentation parameters as model (hyper)-parameters, and the optimization of the marginal likelihood with respect to these parameters as a Bayesian model selection problem. Due to its intractability, we derive a tractable ELBO, which allows us to optimize augmentation parameters jointly with model parameters. We provide extensive theoretical results on variational approximation quality, generalization guarantees, invariance properties, and connections to empirical Bayes. Through experiments on computer vision and NLP tasks, we show that our approach improves calibration and yields robust performance over fixed or no augmentation. Our work provides a rigorous foundation for optimizing DA through Bayesian principles with significant potential for robust machine learning.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Forough Fazeliasl, Michael Minyi Zhang, Linglong Kong, Bei Jiang

A fundamental challenge in data synthesis is protecting the fairness and privacy of the individual, particularly in data-scarce environments where underrepresented groups are at risk of further marginalization by reproducing the biases inherent in the data modeling process. We introduce a privacy- and fairness-aware for a class of generative models, which fuses the conditional generator within the framework of Bayesian nonparametric learning (BNPL). This conditional structure imposes fairness constraints in our generative model by minimizing the mutual information between generated outcomes and protected attributes. Unlike existing methods that primarily focus on sensitive binary-valued attributes, our framework extends seamlessly to non-binary attributes. Moreover, our method provides a systematic solution to class imbalance, ensuring adequate representation of underrepresented protected groups. Our proposed approach offers a scalable, privacy-preserving framework for ethical and equitable data generation, which we demonstrate by theoretical guarantees and extensive experiments on sensitive empirical examples.

Theory · Interpretability and Visualization

Hongxu Liu, Jing Ma, Xiaojie Wang, Caixia YUAN, Fangxiang Feng

Figuring out how neural language models comprehend syntax acts as a key to revealing how they understand languages. We systematically analyzed methods for finding syntax structures in models, namely _probing_, and found limitations yet widely exist in previous probing practice. We proposed a method capable of estimating mutual information (MI) and extracting dependency trees from attention scores in a mathematical-rigorous way, requiring no additional network training effort. Compared with previous approaches, it has a much simpler model, while being able to probe more complex dependency trees, also transparent for fine-grained explanation. We tested our method on several open-source LLMs and demonstrated its effectiveness by systematically comparing it with a great many competitive baselines. Several informative conclusions can be drawn by further analysis of the results, shedding light on our method’s explanatory potential. Our code is released at https://github.com/ChristLBUPT/IPBP.

General Machine Learning · Probabilistic Methods

Yang Yang, Severi Rissanen, Paul Chang, Nasrulloh Satrio, Daolang Huang, Arno Solin, Markus Heinonen, Luigi Acerbi

Amortized simulator-based inference offers a powerful framework for tackling Bayesian inference in computational fields such as engineering or neuroscience, increasingly leveraging modern generative methods like diffusion models to map observed data to model parameters or future predictions. These approaches yield posterior or posterior-predictive samples for new datasets without requiring further simulator calls after training on simulated parameter-data pairs. However, their applicability is often limited by the prior distribution(s) used to generate model parameters during this training phase. To overcome this constraint, we introduce *PriorGuide*, a technique specifically designed for diffusion-based amortized inference methods. PriorGuide leverages a novel guidance approximation that enables flexible adaptation of the trained diffusion model to new priors at test time, crucially without costly retraining. This allows users to readily incorporate updated information or expert knowledge post-training, enhancing the versatility of pre-trained inference models.

General Machine Learning · Probabilistic Methods

Conor Hassan, Nasrulloh Satrio, Cen-You Li, Daolang Huang, Paul Chang, Yang Yang, Francesco Silvestrin, Samuel Kaski, Luigi Acerbi

Set-based transformer models for amortized probabilistic inference and meta-learning, such as neural processes, prior-fitted networks, and tabular foundation models, excel at single-pass _marginal_ prediction. However, many applications require _joint distributions_ over multiple predictions. Purely autoregressive architectures generate these efficiently but sacrifice flexible set-conditioning. Obtaining joint distributions from set-based models requires re-encoding the entire context at each autoregressive step, which scales poorly. We introduce a _causal autoregressive buffer_ that combines the strengths of both paradigms. The model encodes the context once and caches it; a lightweight causal buffer captures dependencies among generated targets, with each new prediction attending to both the cached context and all previously predicted targets added to the buffer. This enables efficient batched autoregressive sampling and joint predictive density evaluation. Training integrates set-based and autoregressive modes through masked attention at minimal overhead. Across synthetic functions, EEG time series, a Bayesian model comparison task, and tabular regression, our method closely matches the performance of full context re-encoding while delivering up to $20\times$ faster joint sampling and density evaluation, and up to $7\times$ lower memory usage.

Optimization · Zero-order and Black-box Optimization

Nicolas Menet, Aleksandar Terzic, Michael Hersche, Andreas Krause, Abbas Rahimi

Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by directly parameterizing the probability that a candidate yields the maximum reward. Our approach, *Thompson Sampling via Fine-Tuning* (ToSFiT) leverages the prior knowledge embedded in prompt-conditioned large language models, and incrementally adapts them toward the posterior. Theoretically, we derive a novel regret bound for a variational formulation of Thompson Sampling that matches the strong guarantees of its standard counterpart. Our analysis reveals the critical role of careful adaptation to the posterior probability of maximality—a principle that underpins our ToSFiT algorithm. Empirically, we validate our method on three diverse tasks: FAQ response refinement, thermally stable protein search, and quantum circuit design. Within a collection of methods covering in-context Bayesian optimization, reinforcement learning, and evolutionary search, ToSFiT exhibits both state-of-the-art sample efficiency and computational efficiency.

General Machine Learning · Probabilistic Methods

Kaiyu Li, Yiming Yang, Xiaoyuan Cheng, Yi He, Zhuo Sun

Control variates are variance reduction techniques for Monte Carlo estimators. They play a critical role in improving Monte Carlo estimators in scientific and machine learning applications that involve computationally expensive integrals. We introduce \emph{multilevel control functionals} (MLCFs), a novel and widely applicable extension of control variates that combines non-parametric Stein-based control variates with multi-fidelity methods. We show that when the integrand and the density are smooth, and when the dimensionality is not very high, MLCFs enjoy a faster convergence rate. We provide both theoretical analysis and empirical assessments on differential equation examples, including Bayesian inference for ecological models, to demonstrate the effectiveness of our proposed approach. Furthermore, we extend MLCFs for variational inference, and demonstrate improved performance empirically through Bayesian neural network examples.

General Machine Learning · Probabilistic Methods

Mona Schirmer, Dan Zhang, Eric Nalisnick

Distribution shifts between training and test data are inevitable over the lifecycle of a deployed model, leading to performance decay. Adapting a model on test samples can help mitigate this drop in performance. However, most test-time adaptation methods have focused on synthetic corruption shifts, leaving a variety of distribution shifts underexplored. In this paper, we focus on distribution shifts that evolve gradually over time, which are common in the wild but challenging for existing methods, as we show. To address this, we propose STAD, a Bayesian filtering method that adapts a deployed model to temporal distribution shifts by learning the time-varying dynamics in the last set of hidden features. Without requiring labels, our model infers time-evolving class prototypes that act as a dynamic classification head. Through experiments on real-world temporal distribution shifts, we show that our method excels in handling small batch sizes and label shift.

Gabriel Grand, Valerio Pepe, Joshua B Tenenbaum, Jacob Andreas

Many emerging applications of AI—from scientific discovery to medical diagnosis—require agents to seek information strategically: forming hypotheses, asking targeted questions, and making decisions under uncertainty. In high-stakes settings with limited resources, do language models (LMs) behave like rational agents? Drawing on insights from human cognition, we develop methods to evaluate and enhance agentic information-seeking. First, we introduce a decision-oriented dialogue task called Collaborative Battleship, in which a Captain must balance exploration (asking questions) and action (taking shots), while a Spotter must supply accurate, contextually-grounded answers. Compared to human players (N=42), we find that many LM agents struggle to ask informative questions, produce accurate answers, and identify high-utility actions. To address these gaps, we develop novel Monte Carlo inference strategies for LMs inspired by Bayesian Experimental Design (BED). For Spotter agents, our approach boosts accuracy by up to 14.7% absolute over LM-only baselines; for Captain agents, it raises expected information gain (EIG) by up to 0.227 bits (94.2% of the achievable noise ceiling). Combined, these components yield sharper targeting (+0.303–0.374 F1), and enable weaker LMs, such as Llama-4-Scout, to outperform both humans (8% → 82% win rate) and frontier models (0% → 67% win rate vs. GPT-5) at ≈1% of GPT-5's cost. We replicate these findings on Guess Who?, where our methods significantly boost accuracy (+28.3–42.4 p.p.), demonstrating their general applicability for building information-seeking agents.

Applications · Neuroscience, Cognitive Science

Gabriel Grand, Valerio Pepe, Joshua B Tenenbaum, Jacob Andreas

Many emerging applications of AI—from scientific discovery to medical diagnosis—require agents to seek information strategically: forming hypotheses, asking targeted questions, and making decisions under uncertainty. In high-stakes settings with limited resources, do language models (LMs) behave like rational agents? Drawing on insights from human cognition, we develop methods to evaluate and enhance agentic information-seeking. First, we introduce a decision-oriented dialogue task called Collaborative Battleship, in which a Captain must balance exploration (asking questions) and action (taking shots), while a Spotter must supply accurate, contextually-grounded answers. Compared to human players (N=42), we find that many LM agents struggle to ask informative questions, produce accurate answers, and identify high-utility actions. To address these gaps, we develop novel Monte Carlo inference strategies for LMs inspired by Bayesian Experimental Design (BED). For Spotter agents, our approach boosts accuracy by up to 14.7% absolute over LM-only baselines; for Captain agents, it raises expected information gain (EIG) by up to 0.227 bits (94.2% of the achievable noise ceiling). Combined, these components yield sharper targeting (+0.303–0.374 F1), and enable weaker LMs, such as Llama-4-Scout, to outperform both humans (8% → 82% win rate) and frontier models (0% → 67% win rate vs. GPT-5) at ≈1% of GPT-5's cost. We replicate these findings on Guess Who?, where our methods significantly boost accuracy (+28.3–42.4 p.p.), demonstrating their general applicability for building information-seeking agents.

General Machine Learning · Probabilistic Methods

Anastasia Nastya Krouglova, Hayden Johnson, Basile Confavreux, Michael Deistler, Pedro J Goncalves

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high accuracy) to the phenomena under study being often preferable. However, inferring parameters of high-fidelity models via simulation-based inference is challenging, especially when the simulator is computationally expensive. We introduce a multifidelity approach to neural posterior estimation that uses transfer learning to leverage inexpensive low-fidelity simulations to efficiently infer parameters of high-fidelity simulators. Our method applies the multifidelity scheme to both amortized and non-amortized neural posterior estimation. We further improve simulation efficiency by introducing a sequential variant that uses an acquisition function targeting the predictive uncertainty of the density estimator to adaptively select high-fidelity parameters. On established benchmark and neuroscience tasks, our approaches require up to two orders of magnitude fewer high-fidelity simulations than current methods, while showing comparable performance. Overall, our approaches open new opportunities to perform efficient Bayesian inference on computationally expensive simulators.

Optimization · Zero-order and Black-box Optimization

Giang Ngo, Dat Phan Trong, Dang Nguyen, Sunil Gupta, Svetha Venkatesh

Bayesian Optimization critically depends on the choice of acquisition function, but no single strategy is universally optimal; the best choice is non-stationary and problem-dependent. Existing adaptive portfolio methods often base their decisions on past function values while ignoring richer information like remaining budget or surrogate model characteristics. To address this, we introduce LMABO, a novel framework that casts a pre-trained Large Language Model (LLM) as a zero-shot, online strategist for the BO process. At each iteration, LMABO uses a structured state representation to prompt the LLM to select the most suitable acquisition function from a diverse portfolio. In an evaluation across 50 benchmark problems, LMABO demonstrates a significant performance improvement over strong static, adaptive portfolio, and other LLM-based baselines. We show that the LLM's behavior is a comprehensive strategy that adapts to real-time progress, proving its advantage stems from its ability to process and synthesize the complete optimization state into an effective, adaptive policy.

Applications · Chemistry and Drug Discovery

Alston Lo, Connor Coley, Wojciech Matusik

Inspired by the effectiveness of genetic algorithms and the importance of synthesizability in molecular design, we present SynGA, a simple genetic algorithm that operates directly over synthesis routes. Our method features custom crossover and mutation operators that explicitly constrain it to synthesizable molecular space. By modifying the fitness function, we demonstrate the effectiveness of SynGA on a variety of design tasks, including synthesizable analog search and sample-efficient property optimization, for both 2D and 3D objectives. Furthermore, by coupling SynGA with a machine learning-based filter that focuses the building block set, we boost SynGA to state-of-the-art performance. For property optimization, this manifests as a model-based variant SynGBO, which employs SynGA and block filtering in the inner loop of Bayesian optimization. Since SynGA is lightweight and enforces synthesizability by construction, our hope is that SynGA can not only serve as a strong standalone baseline but also as a versatile module that can be incorporated into larger synthesis-aware workflows in the future.

Deep Learning · Generative Models and Autoencoders

Yingzhi Xia, Setthakorn Tanomkiattikun, Liangli Zhen, ZAIWANG GU

Diffusion models (DMs) have recently shown remarkable performance on inverse problems (IPs). Optimization-based methods can fast solve IPs using DMs as powerful regularizers, but they are susceptible to local minima and noise overfitting. Although DMs can provide strong priors for Bayesian approaches, enforcing measurement consistency during the denoising process leads to manifold infeasibility issues. We propose Noise-space Hamiltonian Monte Carlo (N-HMC), a posterior sampling method that treats reverse diffusion as a deterministic mapping from initial noise to clean images. N-HMC enables comprehensive exploration of the solution space, avoiding local optima. By moving inference entirely into the initial-noise space, N-HMC keeps proposals on the learned data manifold. We provide a comprehensive theoretical analysis of our approach and extend the framework to a noise-adaptive variant (NA-NHMC) that effectively handles IPs with unknown noise type and level. Extensive experiments across four linear and three nonlinear inverse problems demonstrate that NA-NHMC achieves superior reconstruction quality with robust performance across different hyperparameters and initializations, significantly outperforming recent state-of-the-art methods. The code is available at https://github.com/NA-HMC/NA-HMC.

Alana Renda, Jillian Ross, Jacob Andreas

Real-world settings where language models (LMs) are deployed --- in domains spanning healthcare, finance, and other forms of knowledge work --- require models to grapple with incomplete information and reason under uncertainty. Yet most LM evaluations focus on problems with well-defined answers and success criteria. This gap exists in part because natural problems involving uncertainty are difficult to construct: given that LMs have access to most of the same knowledge as humans, it is non-trivial to design questions for which LMs will struggle to produce correct answers. As a result, LM performance on reasoning under uncertainty remains poorly characterized. To address this gap, we introduce \textsc{OpenEstimate}, an extensible, multi-domain benchmark for evaluating LMs on probabilistic estimation tasks that require models to synthesize knowledge from pretraining and express predictions as Bayesian priors. We assess these priors for accuracy and calibration. Across six frontier models, we find that LM-elicited priors are worth the equivalent of about five samples from the underlying data distribution, and that posteriors computed using LM priors tend to be more accurate than those computed using a naive prior. At the same time, the relationship between model accuracy and confidence is weak across the board, indicating the value of developing new methods to improve calibration. The \textsc{OpenEstimate} benchmark thus offers a challenging evaluation for frontier LMs and a platform for developing models that are better at probabilistic estimation and reasoning under uncertainty.

Zairah Mustahsan

As large language models (LLMs) and agentic systems advance, the field increasingly depends on fine-grained evaluation to compare models, guide research directions, and make deployment decisions. Yet evaluation pipelines often treat LLMs as deterministic functions, even though they are fundamentally stochastic systems with variability arising from sampling methods, hardware nondeterminism, environmental randomness, and evaluation procedures. This mismatch leads to unstable benchmarks, unreliable model comparisons, inconsistent agent outcomes, and significant uncertainty when using LLMs as judges. Recent research has begun to quantify this instability and propose statistical techniques, from frequentist error bars to Bayesian latent-state models, reliability metrics, and large-scale variance audits. But adoption is uneven, and the field lacks a cohesive statistical framework for evaluating stochastic intelligence. This post synthesizes existing research into a unified perspective and outlines practical recommendations for improving evaluation practice. The goal is not to introduce new methods, but to demonstrate that the tools already exist and that incorporating statistical thinking is both feasible and urgently needed.

Maxine Perroni-Scharf, Zachary Ferguson, Thomas Butruille, Carlos M. Portela, Mina Konakovic-Lukovic

Triply periodic minimal surfaces (TPMS) are a class of metamaterials with a variety of applications and well-known primitive morphologies. We present a new method for discovering novel microscale TPMS structures with exceptional energy-dissipation capabilities, achieving double the energy absorption of the best existing TPMS primitive structure. Our approach employs a parametric representation, allowing seamless interpolation between structures and representing a rich TPMS design space. As simulations are intractable for efficiently optimizing microscale hyperelastic structures, we propose a sample-efficient computational strategy for rapid discovery with limited empirical data from 3D-printed and tested samples that ensures high-fidelity results. We achieve this by leveraging a predictive uncertainty-aware Deep Ensembles model to identify which structures to fabricate and test next. We iteratively refine our model through batch Bayesian optimization, selecting structures for fabrication that maximize exploration of the performance space and exploitation of our energy-dissipation objective. Using our method, we produce the first open-source dataset of hyperelastic microscale TPMS structures, including a set of novel structures that demonstrate extreme energy dissipation capabilities, and show several potential applications of these structures.