NeurIPS 2025 Papers

Data integration approaches are increasingly used to enhance the efficiency and generalizability of studies. However, a key limitation of these methods is the assumption that outcome measures are identical across datasets -- an assumption that often does not hold in practice. Consider the following opioid use disorder (OUD) studies: the XBOT trial and the POAT study, both evaluating the effect of medications for OUD on withdrawal symptom severity (not the primary outcome of either trial). While XBOT measures withdrawal severity using the subjective opiate withdrawal scale, POAT uses the clinical opiate withdrawal scale. We analyze this realistic yet challenging setting where outcome measures differ across studies and where neither study records both types of outcomes. Our paper studies whether and when integrating studies with disparate outcome measures leads to efficiency gains. We introduce three sets of assumptions -- with varying degrees of strength -- linking both outcome measures. Our theoretical and empirical results highlight a cautionary tale: integration can improve asymptotic efficiency only under the strongest assumption linking the outcomes. However, misspecification of this assumption leads to bias. In contrast, a milder assumption may yield finite-sample efficiency gains, yet these benefits diminish as sample size increases. We illustrate these trade-offs via a case study integrating the XBOT and POAT datasets to estimate the comparative effect of two medications for opioid use disorder on withdrawal symptoms. By systematically varying the assumptions linking the SOW and COW scales, we show potential efficiency gains and the risks of bias. Our findings emphasize the need for careful assumption selection when fusing datasets with differing outcome measures, offering guidance for researchers navigating this common challenge in modern data integration.

Uncertainty-aware meta-learning aims not only for rapid adaptation to new tasks but also for reliable uncertainty estimation under limited supervision. Neural Processes (NPs) offer a flexible solution by learning implicit stochastic processes directly from data, often using a global latent variable to capture functional uncertainty. However, we empirically find that variational posteriors for this global latent variable are frequently miscalibrated, limiting both predictive accuracy and the reliability of uncertainty estimates. To address this issue, we propose Test Time Scaling for Neural Processes (TTSNPs), a sequential inference framework based on Sequential Monte Carlo Sampler (SMCS) that refines latent samples at test time without modifying the pre-trained NP model. TTSNPs iteratively transform variational samples into better approximations of the true posterior using neural transition kernels, significantly improving both prediction quality and uncertainty calibration. This makes NPs more robust and trustworthy, extending applicability to various scenarios requiring well-calibrated uncertainty estimates.

Counterfactual inference aims to estimate the counterfactual outcome at the individual level given knowledge of an observed treatment and the factual outcome, with broad applications in fields such as epidemiology, econometrics, and management science. Previous methods rely on a known structural causal model (SCM) or assume the homogeneity of the exogenous variable and strict monotonicity between the outcome and exogenous variable. In this paper, we propose a principled approach for identifying and estimating the counterfactual outcome. We first introduce a simple and intuitive rank preservation assumption to identify the counterfactual outcome without relying on a known structural causal model. Building on this, we propose a novel ideal loss for theoretically unbiased learning of the counterfactual outcome and further develop a kernel-based estimator for its empirical estimation. Our theoretical analysis shows that the rank preservation assumption is not stronger than the homogeneity and strict monotonicity assumptions, and shows that the proposed ideal loss is convex, and the proposed estimator is unbiased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed method.

The goal of Root Cause Analysis (RCA) is to explain why an anomaly occurred by identifying where the fault originated. Several recent works model the anomalous event as resulting from a change in the causal mechanism at the root cause, i.e., as a soft intervention. RCA is then the task of identifying which causal mechanism changed. In real-world applications, one often has either few or only a single sample from the post-intervention distribution: a severe limitation for most methods, which assume one knows or can estimate the distribution. However, even those that do not are statistically ill-posed due to the need to probe regression models in regions of low probability density. In this paper, we propose simple, efficient methods to overcome both difficulties in the case where there is a single root cause and the causal graph is a polytree. When one knows the causal graph, we give guarantees for a traversal algorithm that requires only marginal anomaly scores and does not depend on specifying an arbitrary anomaly score cut-off. When one does not know the causal graph, we show that the heuristic of identifying root causes as the variables with the highest marginal anomaly scores is causally justified. To this end, we prove that anomalies with small scores are unlikely to cause those with larger scores in polytrees and give upper bounds for the likelihood of causal pathways with non-monotonic anomaly scores.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

We consider the problem of validating whether a neural posterior estimate $q(\theta \mid x)$ is an accurate approximation to the true, unknown true posterior $p(\theta \mid x)$. Existing methods for evaluating the quality of an NPE estimate are largely derived from classifier-based tests or divergence measures, but these suffer from several practical drawbacks. As an alternative, we introduce the *Conditional Localization Test* (**CoLT**), a principled method designed to detect discrepancies between $p(\theta \mid x)$ and $q(\theta \mid x)$ across the full range of conditioning inputs. Rather than relying on exhaustive comparisons or density estimation at every $x$, CoLT learns a localization function that adaptively selects points $\theta_l(x)$ where the neural posterior $q$ deviates most strongly from the true posterior $p$ for that $x$. This approach is particularly advantageous in typical simulation-based inference settings, where only a single draw $\theta \sim p(\theta \mid x)$ from the true posterior is observed for each conditioning input, but where the neural posterior $q(\theta \mid x)$ can be sampled an arbitrary number of times. Our theoretical results establish necessary and sufficient conditions for assessing distributional equality across all $x$, offering both rigorous guarantees and practical scalability. Empirically, we demonstrate that CoLT not only performs better than existing methods at comparing $p$ and $q$, but also pinpoints regions of significant divergence, providing actionable insights for model refinement. These properties position CoLT as a state-of-the-art solution for validating neural posterior estimates.

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the _state-space point process_ (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.

Neural processes (NPs) are probabilistic meta-learning models that map sets of observations to posterior predictive distributions, enabling inference at arbitrary domain points. Their capacity to handle variable-sized collections of unstructured observations, combined with simple maximum-likelihood training and uncertainty-aware predictions, makes them well-suited for modeling data over continuous domains. Since their introduction, several variants have been proposed. Early approaches typically represented observed data using finite-dimensional summary embeddings obtained through aggregation schemes such as mean pooling. However, this strategy fundamentally mismatches the infinite-dimensional nature of the generative processes that NPs aim to capture. Convolutional conditional neural processes (ConvCNPs) address this limitation by constructing infinite-dimensional functional embeddings processed through convolutional neural networks (CNNs) to enforce translation equivariance. Yet CNNs with local spatial kernels struggle to capture long-range dependencies without resorting to large kernels, which impose significant computational costs. To overcome this limitation, we propose the Spectral ConvCNP (SConvCNP), which performs global convolution in the frequency domain. Inspired by Fourier neural operators (FNOs) for learning solution operators of partial differential equations (PDEs), our approach directly parameterizes convolution kernels in the frequency domain, leveraging the relatively compact yet global Fourier representation of many natural signals. We validate the effectiveness of SConvCNP on both synthetic and real-world datasets, demonstrating how ideas from operator learning can advance the capabilities of NPs.

Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling and fine-tuning of diffusion models.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: *MultALMC*, which uses multiscale annealed Langevin dynamics, and *MultCDiff*, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student’s t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Inference in both brains and machines can be formalized by optimizing a shared objective: maximizing the evidence lower bound (ELBO) in machine learning, or minimizing variational free energy ($\mathcal{F}$) in neuroscience (ELBO = $-\mathcal{F}$). While this equivalence suggests a unifying framework, it leaves open how inference is implemented in neural systems. Here, we introduce FOND (*Free energy Online Natural-gradient Dynamics*), a framework that derives neural inference dynamics from three principles: (1) natural gradients on $\mathcal{F}$, (2) online belief updating, and (3) iterative refinement. We apply FOND to derive iP-VAE (*iterative Poisson variational autoencoder*), a recurrent spiking neural network that performs variational inference through membrane potential dynamics, replacing amortized encoders with iterative inference updates. Theoretically, iP-VAE yields several desirable features such as emergent normalization via lateral competition, and hardware-efficient integer spike count representations. Empirically, iP-VAE outperforms both standard VAEs and Gaussian-based predictive coding models in sparsity, reconstruction, and biological plausibility, and scales to complex color image datasets such as CelebA. iP-VAE also exhibits strong generalization to out-of-distribution inputs, exceeding hybrid iterative-amortized VAEs. These results demonstrate how deriving inference algorithms from first principles can yield concrete architectures that are simultaneously biologically plausible and empirically effective.

Diffusion models have made significant advancements in recent years. However, their performance often deteriorates when trained or fine-tuned on imbalanced datasets. This degradation is largely due to the disproportionate representation of majority and minority data in image-text pairs. In this paper, we propose a general fine-tuning approach, dubbed PoGDiff, to address this challenge. Rather than directly minimizing the KL divergence between the predicted and ground-truth distributions, PoGDiff replaces the ground-truth distribution with a Product of Gaussians (PoG), which is constructed by combining the original ground-truth targets with the predicted distribution conditioned on a neighboring text embedding. Experiments on real-world datasets demonstrate that our method effectively addresses the imbalance problem in diffusion models, improving both generation accuracy and quality.

In machine learning, a critical class of decision-making problems involves *Avoiding Undesired Future* (AUF): given a predicted undesired outcome, how can one make decision about actions to prevent it? Recently, the *rehearsal learning* framework has been proposed to address AUF problem. While existing methods offer reliable decisions for single-round success, this paper considers long-term settings that involve coordinating multiple future outcomes, which is often required in real-world tasks. Specifically, we generalize the AUF objective to characterize a long-term decision target that incorporates cross-temporal relations among variables. As directly optimizing the *AUF probability* $\mathbb{P}_{\operatorname{AUF}}$ over this objective remains challenging, we derive an explicit expression for the objective and further propose a quadratic programming (QP) reformulation that transforms the intractable probabilistic AUF optimization into a tractable one. Under mild assumptions, we show that solutions to the QP reformulation are equivalent to those of the original AUF optimization, based on which we develop two novel rehearsal learning methods for long-term decision-making: (i) a *greedy* method that maximizes the single-round $\mathbb{P}_{\operatorname{AUF}}$ at each step, and (ii) a *far-sighted* method that accounts for future consequences in each decision, yielding a higher overall $\mathbb{P}_{\operatorname{AUF}}$ through an $L/(L+1)$ variance reduction in the AUF objective. We further establish an $\mathcal{O}(1/\sqrt{N})$ excess risk bound for decisions based on estimated parameters, ensuring reliable practical applicability with finite data. Experiments validate the effectiveness of our approach.

Many causal inference frameworks rely on a staticity assumption, where repeated interventions are expected to yield consistent outcomes, often summarized by metrics like the Average Treatment Effect (ATE). This assumption, however, frequently fails in dynamic environments where interventions can alter the system's underlying causal structure, rendering traditional `static' ATE insufficient or misleading. Recent works on meta-causal models (MCM) offer a promising avenue by enabling qualitative reasoning over evolving relationships. In this work, we propose a specific class of MCM with desirable properties for explicitly modeling and predicting intervention outcomes under meta-causal dynamics, together with a first method for meta-causal analysis. Through expository examples in high-impact domains of medical treatment and judicial decision-making, we highlight the severe consequences that arise when system dynamics are neglected and demonstrate the successful application of meta-causal strategies to navigate these challenges.

In decision-making processes, an intelligent agent with causal knowledge can optimize action spaces to avoid unnecessary exploration. A *structural causal bandit* framework provides guidance on how to prune actions that are unable to maximize reward by leveraging prior knowledge of the underlying causal structure among actions. A key assumption of this framework is that the agent has access to a fully-specified causal diagram representing the target system. In this paper, we extend the structural causal bandits to scenarios where the agent leverages a Markov equivalence class. In such cases, the causal structure is provided to the agent in the form of a *partial ancestral graph* (PAG). We propose a generalized framework for identifying potentially optimal actions within this graph structure, thereby broadening the applicability of structural causal bandits.

In human-AI interaction, effective communication relies on aligning the AI agent’s model with the human user’s mental model -- a process known as model reconciliation. However, existing model reconciliation approaches predominantly assume deterministic models, overlooking the fact that human knowledge is often uncertain or probabilistic. To bridge this gap, we present a probabilistic model reconciliation framework that resolves inconsistencies in MPE outcome probabilities between an agent’s and a user’s models. Our approach is built on probabilistic logic programming (PLP) using ProbLog, where explanations are generated as cost-optimal model updates that reconcile these probabilistic differences. We develop two search algorithms - a generic baseline and an optimized version. The latter is guided by theoretical insights and further extended with greedy and weighted variants to enhance scalability and efficiency. Our approach is validated through a user study on explanation types and computational experiments showing that the optimized version consistently outperforms the generic baseline.

We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based on a local score matching technique which uses simulations from a localized region around each parameter iterate. By employing a linear parameterization for the surrogate score model, our technique admits a closed-form, least-squares solution. This approach yields a fast, flexible, and efficient approximation to the Fisher score, effectively smoothing the likelihood objective and mitigating the challenges posed by complex likelihood landscapes. We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by the smoothing. Empirical results on a range of synthetic and real-world problems demonstrate the superior performance of our method compared to existing benchmarks.

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in scale, the corresponding covariance and kernel matrices become increasingly large, often reaching magnitudes that make their direct formation impractical or impossible. Existing techniques typically rely on matrix-vector products, which can provide efficient approximations, if the matrix spectrum behaves well. However, in settings like distributed learning, or when the matrix is defined only indirectly, access to the full data set can be restricted to only very small sub-matrices of the original matrix. In these cases, the matrix of nominal interest is not even available as an implicit operator, meaning that even matrix-vector products may not be available. In such settings, the matrix is "impalpable", in the sense that we have access to only masked snapshots of it. We draw on principles from free probability theory to introduce a novel method of "free decompression" to estimate the spectrum of such matrices. Our method can be used to extrapolate from the empirical spectral densities of small submatrices to infer the eigenspectrum of extremely large (impalpable) matrices (that we cannot form or even evaluate with full matrix-vector products). We demonstrate the effectiveness of this approach through a series of examples, comparing its performance against known limiting distributions from random matrix theory in synthetic settings, as well as applying it to submatrices of real-world datasets, matching them with their full empirical eigenspectra.

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods for conformal prediction of causal effects are limited to binary/discrete treatments and make highly restrictive assumptions, such as known propensity scores. In this work, we provide a novel conformal prediction method for potential outcomes of continuous treatments. We account for the additional uncertainty introduced through propensity estimation so that our conformal prediction intervals are valid even if the propensity score is unknown. Our contributions are three-fold: (1) We derive finite-sample validity guarantees for prediction intervals of potential outcomes of continuous treatments. (2) We provide an algorithm for calculating the derived intervals. (3) We demonstrate the effectiveness of the conformal prediction intervals in experiments on synthetic and real-world datasets. To the best of our knowledge, we are the first to propose conformal prediction for continuous treatments when the propensity score is unknown and must be estimated from data.