NeurIPS 2025 Papers

In recommendation systems, implicit feedback data can be automatically recorded and is more common than explicit feedback data. However, implicit feedback poses two challenges for relevance prediction, namely (a) positive-unlabeled (PU): negative feedback does not necessarily imply low relevance and (b) missing not at random (MNAR): items that are popular or frequently recommended tend to receive more clicks than other items, even if the user does not have a significant interest in them. Existing methods either overlook the MNAR issue or fail to account for the inherent mechanism of the PU issue. As a result, they may lead to inaccurate relevance predictions or inflated biases and variances. In this paper, we formulate the implicit feedback problem as a counterfactual estimation problem with missing treatment variables. Prediction of the relevance in implicit feedback is equivalent to answering the counterfactual question that ``whether a user would click a specific item if exposed to it?". To solve the counterfactual question, we propose the Counterfactual Implicit Feedback (Counter-IF) prediction approach that divides the user-item pairs into four disjoint groups, namely definitely positive (DP), highly exposed (HE), highly unexposed (HU), and unknown (UN) groups. Specifically, Counter-IF first performs missing treatment imputation with different confidence levels from raw implicit feedback, then estimates the counterfactual outcomes via causal representation learning that combines pointwise loss and pairwise loss based on the user-item pairs stratification. Theoretically the generalization bound of the learned model is derived. Extensive experiments are conducted on publicly available datasets to demonstrate the effectiveness of our approach. The code is available at https://github.com/zhouchuanCN/NeurIPS25-Counter-IF.

Human annotations play a crucial role in evaluating the performance of GenAI models. Two common challenges in practice, however, are missing annotations (the response variable of interest) and cluster dependence among human-AI interactions (e.g., questions asked by the same user may be highly correlated). Reliable inference must address both issues to achieve unbiased estimation and appropriately quantify uncertainty when estimating average scores from human annotations. In this paper, we analyze the doubly robust estimator, a widely used method in missing data analysis and causal inference, applied to this setting and establish novel theoretical properties under cluster dependence. We further illustrate our findings through simulations and a real-world conversation quality dataset. Our theoretical and empirical results underscore the importance of incorporating cluster dependence in missing response problems to perform valid statistical inference.

Randomized controlled trials (RCTs) often exhibit limited inferential efficiency in estimating treatment effects due to small sample sizes. In recent years, the combination of external controls has gained increasing attention as a means of improving the efficiency of RCTs. However, external controls are not always comparable to RCTs, and direct borrowing without careful evaluation can introduce substantial bias and reduce the efficiency of treatment effect estimation. In this paper, we propose a novel influence-based adaptive sample borrowing approach that effectively quantifies the "comparability'' of each sample in the external controls using influence function theory. Given a selected set of borrowed external controls, we further derive a semiparametric efficient estimator under an exchangeability assumption. Recognizing that the exchangeability assumption may not hold for all possible borrowing sets, we conduct a detailed analysis of the asymptotic bias and variance of the proposed estimator under violations of exchangeability. Building on this bias-variance trade-off, we further develop a data-driven approach to select the optimal subset of external controls for borrowing. Extensive simulations and real-world applications demonstrate that the proposed approach significantly enhances treatment effect estimation efficiency in RCTs, outperforming existing approaches.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

Most expressive variational families---such as normalizing flows---lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for constructing tuning-free, asymptotically exact variational flows on *arbitrary* state spaces from involutive MCMC kernels. The core methodological component is a novel representation of general involutive MCMC kernels as invertible, measure- preserving iterated random function systems, which act as the flow maps of our variational flows. This leads to three new variational families with provable total variation convergence. Our framework resolves key practical limitations of existing variational families with similar guarantees (e.g., MixFlows), while requiring substantially weaker theoretical assumptions. Finally, we demonstrate the competitive performance of our flows across tasks including posterior approximation, Monte Carlo estimates, and normalization constant estimation, outperforming or matching No-U-Turn sampler (NUTS) and black-box normalizing flows.

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to the number of classes and underutilize the rich prototype information available at intermediate hierarchical levels. We introduce deep taxonomic networks, a novel deep latent variable approach designed to bridge these gaps. Our method optimizes a large latent taxonomic hierarchy, specifically a complete binary tree structured mixture-of-Gaussian prior within a variational inference framework, to automatically discover taxonomic structures and associated prototype clusters directly from unlabeled data without assuming true label sizes. We analytically show that optimizing the ELBO of our method encourages the discovery of hierarchical relationships among prototypes. Empirically, our learned models demonstrate strong hierarchical clustering performance, outperforming baselines across diverse image classification datasets using our novel evaluation mechanism that leverages prototype clusters discovered at all hierarchical levels. Qualitative results further reveal that deep taxonomic networks discover rich and interpretable hierarchical taxonomies, capturing both coarse-grained semantic categories and fine-grained visual distinctions.

While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications, caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context learning performing predictive Bayesian inference opens the avenue for Bayesian uncertainty estimation, particularly for decomposing uncertainty into epistemic uncertainty due to lack of in-context data and aleatoric uncertainty inherent in the in-context prediction task. However, the decomposition idea remains under-explored due to the intractability of the latent parameter posterior from the underlying Bayesian model. In this work, we introduce a variational uncertainty decomposition framework for in-context learning without explicitly sampling from the latent parameter posterior, by optimising auxiliary inputs as probes to obtain an upper bound to the aleatoric uncertainty of an LLM's in-context learning procedure. Through experiments on synthetic and real-world tasks, we show quantitatively and qualitatively that the decomposed uncertainties obtained from our method exhibit desirable properties of epistemic and aleatoric uncertainty.

Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially problematic in applications like program fuzzing, where one wants to generate diverse and valid program inputs for testing purposes. We propose a new constrained sampling framework based on Markov Chain Monte Carlo (MCMC) that simultaneously satisfies three core desiderata: constraint satisfying (every sample satisfies the constraint), monotonically converging (the sampling process converges to the true conditional distribution), and efficient (high-quality samples emerge in few steps). Our method constructs a proposal distribution over valid outputs and applies a Metropolis-Hastings acceptance criterion based on the LM’s likelihood, ensuring principled and efficient exploration of the constrained space. Empirically, our sampler outperforms existing methods on both synthetic benchmarks and real-world program fuzzing tasks.

We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging Jarzynski’s equality and developing algorithms based on a weighted version of the unadjusted Langevin algorithm (ULA) with recursively updated weights. Adapting this for latent variable models, we develop a sequential Monte Carlo (SMC) method that provides the maximum marginal likelihood estimate of the parameters, termed JALA-EM. Under suitable regularity assumptions on the marginal likelihood, we provide a nonasymptotic analysis of the JALA-EM scheme implemented with stochastic gradient descent and show that it provably converges to the maximum marginal likelihood estimate. We demonstrate the performance of JALA-EM on a variety of latent variable models and show that it performs comparably to existing methods in terms of accuracy and computational efficiency. Importantly, the ability to recursively estimate marginal likelihoods—an uncommon feature among scalable methods—makes our approach particularly suited for model selection, which we validate through dedicated experiments.

We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using approximate score functions, they can suffer from accumulating errors due to time discretization and imperfect score estimation. In this work, we introduce a principled SMC framework that formalizes diffusion-based samplers as proposals while systematically correcting for their biases. The core idea is to construct informative intermediate target distributions that progressively steer the sampling trajectory toward the final target distribution. Although ideal intermediate targets are intractable, we develop \emph{exact approximations} using quantities from the score estimation-based proposal, without requiring additional model training or inference overhead. The resulting sampler, termed \textit{\ourmethodfull}, enables consistent sampling and unbiased estimation of the target's normalization constant under mild conditions. We demonstrate the effectiveness of our method on a range of synthetic targets and real-world Bayesian inference problems.

Latent Gaussian variables have been popularised in probabilistic machine learning. In turn, gradient estimators are the machinery that facilitates gradient-based optimisation for models with latent Gaussian variables. The reparameterisation trick is often used as the default estimator as it is simple to implement and yields low-variance gradients for variational inference. In this work, we propose the R2-G2 estimator as the Rao-Blackwellisation of the reparameterisation gradient estimator. Interestingly, we show that the local reparameterisation gradient estimator for Bayesian MLPs is an instance of the R2-G2 estimator and Rao-Blackwellisation. This lets us extend benefits of Rao-Blackwellised gradients to a suite of probabilistic models. We show that initial training with R2-G2 consistently yields better performance in models with multiple applications of the reparameterisation trick.

The expressiveness of flow-based models combined with stochastic variational inference (SVI) has expanded the application of optimization-based Bayesian inference to highly complex problems. However, despite the importance of multi-model Bayesian inference, defined over a transdimensional joint model and parameter space, flow-based SVI has been limited to problems defined over a fixed-dimensional parameter space. We introduce CoSMIC normalizing flows (COntextually-Specified Masking for Identity-mapped Components), an extension to neural autoregressive conditional normalizing flow architectures that enables use of a single amortized variational density for inference over a transdimensional (multi-model) conditional target distribution. We propose a combined stochastic variational transdimensional inference (VTI) approach to training CoSMIC flows using ideas from Bayesian optimization and Monte Carlo gradient estimation. Numerical experiments show the performance of VTI on challenging problems that scale to high-cardinality model spaces.

Uncertainty quantification (UQ) is essential for safe deployment of generative AI models such as large language models (LLMs), especially in high-stakes applications. Conformal prediction (CP) offers a principled uncertainty quantification framework, but classical methods focus on regression and classification, relying on geometric distances or softmax scores--tools that presuppose structured outputs. We depart from this paradigm by studying CP in a query-only setting, where prediction sets must be constructed solely from finite queries to a black-box generative model, introducing a new trade-off between coverage, test-time query budget, and informativeness. We introduce **Conformal Prediction with Query Oracle** (CPQ), a framework characterizing the optimal interplay between these objectives. Our finite-sample algorithm is built on two core principles: one governs the optimal query policy, and the other defines the optimal mapping from queried samples to prediction sets. Remarkably, both are rooted in the classical **missing mass problem** in statistics. Specifically, the optimal query policy depends on the rate of decay--or the derivative--of the missing mass, for which we develop a novel estimator. Meanwhile, the optimal mapping hinges on the missing mass itself, which we estimate using Good-Turing estimators. We then turn our focus to implementing our method for language models, particularly in open-ended LLM tasks involving question answering, multi-step reasoning, and structured information extraction, where outputs are vast, variable, and often under-specified. Fine-grained experiments on three real-world open-ended tasks and two LLMs, show CPQ's applicability to **any black-box LLM** and highlight: (1) individual contribution of each principle to CPQ’s performance, and (2) CPQ's ability to yield significantly more informative prediction sets than existing conformal methods for language uncertainty quantification.

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.

We propose the Distance-informed Neural Process (DNP), a novel variant of Neural Processes that improves uncertainty estimation by combining global and distance-aware local latent structures. Standard Neural Processes (NPs) often rely on a global latent variable and struggle with uncertainty calibration and capturing local data dependencies. DNP addresses these limitations by introducing a global latent variable to model task-level variations and a local latent variable to capture input similarity within a distance-preserving latent space. This is achieved through bi-Lipschitz regularization, which bounds distortions in input relationships and encourages the preservation of relative distances in the latent space. This modeling approach allows DNP to produce better-calibrated uncertainty estimates and more effectively distinguish in- from out-of-distribution data. Empirical results demonstrate that DNP achieves strong predictive performance and improved uncertainty calibration across regression and classification tasks.

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a fully probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input–output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods.

Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty---due to incomplete knowledge---requires richer representations than those offered by classical probability. Imprecise probability (IP) theory offers such models, capturing ambiguity and partial belief. This has driven growing interest in imprecise probabilistic machine learning (IPML), where inference and decision-making rely on broader uncertainty models---highlighting the need for metrics beyond classical probability. This work introduces the Integral Imprecise Probability Metric (IIPM) framework, a Choquet integral-based generalisation of classical Integral Probability Metric to the setting of capacities---a broad class of IP models encompassing many existing ones, including lower probabilities, probability intervals, belief functions, and more. Theoretically, we establish conditions under which IIPM serves as a valid metric and metrises a form of weak convergence of capacities. Practically, IIPM not only enables comparison across different IP models but also supports the quantification of epistemic uncertainty~(EU) within a single IP model. In particular, by comparing an IP model with its conjugate, IIPM gives rise to a new class of epistemic uncertainty measures---Maximum Mean Imprecision (MMI) ---which satisfy key axiomatic properties proposed in the Uncertainty Quantification literature. We validate MMI through selective classification experiments, demonstrating strong empirical performance against established EU measures, and outperforming them when classical methods struggle to scale to a large number of classes. Our work advances both theory and practice in Imprecise Probabilistic Machine Learning, offering a principled framework for comparing and quantifying epistemic uncertainty under imprecision.

Federated Learning (FL) incurs high communication costs in both uplink and downlink. The literature largely focuses on lossy compression of model updates in deterministic FL. In contrast, stochastic (Bayesian) FL considers distributions over parameters, enabling uncertainty quantification, better generalization, and, crucially, inherent communication-regularized training through a mirror-descent structure. In this paper, we consider both uplink and downlink communication in stochastic FL, and propose a communication framework based on remote source generation. Employing Minimal Random Coding (MRC) for remote generation, we allow the server and the clients to sample from local and global posteriors (sources), respectively, rather than transmitting locally sampled updates. The framework encompasses communication-regularized local optimization and principled compression of model updates, leveraging gradually updated prior distributions as side information. Through extensive simulations, we show that our method achieves $5-32\times$ reduction in total communication cost while preserving accuracy. We further analyze the communication cost, refining existing MRC bounds and enabling precise quantification of uplink and downlink trade-offs. We also extend our method to conventional FL via stochastic quantization and prove a contraction property for the biased MRC compressor to facilitate convergence analysis.