NeurIPS 2026 论文列表

Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.

Chain-of-thought (CoT) prompting and related strategies that elicit intermediate reasoning traces have fundamentally changed how language models are used, evaluated, and developed. CoT now touches many areas of contemporary research beyond prompting, from advanced test-time inference and model tuning to interpretability, yet much of this work treats CoT traces in task-specific ways, without a shared formal account of what they are or how they compose and support inference. We argue that probabilistic programs — ordinary programs extended with stochastic choices and probabilistic conditioning — provide a natural framework for modeling CoT reasoning. To demonstrate this, we derive a small discrete probabilistic programming language for CoT in which reasoning steps are stochastic choices, branches encode dependencies, trace likelihoods score executions, and answers are return values. Even with a minimal reachability-based semantics, this language enables a first-principles analysis of trace likelihood, exposing why likelihood alone can be a misleading model of reasoning. Motivated by this limitation, we add differentiable operators for composing scores and feedback over CoT traces. The resulting framework links several uses of CoT — scoring, evidence aggregation, feedback propagation, model tuning, and step-level sensitivity analysis — within a single probabilistic program. Through case studies, we show how this approach yields new analysis techniques and test-time inference strategies, offering a promising direction for programming-language-based approaches to language-model reasoning.

Conformal prediction (CP) for language models is typically evaluated under a \emph{matched} protocol, in which calibration and deployment use the same post-training inference configuration, such as quantization mode and inference temperature. In deployment, these choices often differ from those used at calibration to meet memory or throughput constraints or serving policies. We argue that this exposes a limitation in current CP evaluation protocols for language models. We formalize the underlying phenomenon as \emph{inference-time model shift}: a change in the conformal score distribution induced by inference configuration rather than by the input--label distribution, and theoretically characterize how it breaks split-conformal exchangeability even when the task distribution and trained model are unchanged. We then evaluate its consequences across $8$ language models, $4$ finite-label benchmarks, and $12$ inference configurations. We find that matched evaluation can substantially overstate deployment-time coverage, and that the effect is heterogeneous across models and datasets. We argue that inference configuration should be reported as a first-class experimental axis in CP evaluations for language-model systems.

Online forecasters sometimes know a regime boundary before any post-boundary labels arrive. Standard adaptive conformal methods still react through later coverage errors, so they can pay a detection-delay cost even when the boundary is public. We study conformal prediction with an announced partition of the stream and separate two post-break audits. The reset empirical quantile in segmented split-CP attains the minimax per-time probability-gap rate $\Theta(M^{-1/2})$ after $M$ post-reset scores, with a matching Le Cam lower bound. A pure bounded constant-step announced-break ACI recursion attains an $O(M^{-1})$ time-averaged empirical-frequency gap by telescoping, but this is a realized-frequency statement, not a guarantee for the next interval. The practical AB-ACI implementation used in experiments adds burn-in and projection, so its rate claim includes explicit correction terms and is not unconditional. Synthetic experiments recover both slopes and show short-window gains when the break is large. Two real-data applications are null under leakage-free protocols. ERCOT RTC+B gives 0.863 post-reform coverage for AB-ACI versus 0.880 for ACI, and FOMC yield breaks give 0.892 versus 0.900. The message is diagnostic: use the reset empirical quantile for per-prediction reliability, use AB-ACI only for long-run frequency audits, and expect gains only when the realized score shift is large enough to make detection delay costly.

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce *affine tracing*, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.

Neural dynamics are a central feature of biological neural systems. In the visual cortex, the functional role of neural dynamics is poorly understood, particularly for static stimuli. The statistics of still natural images have long been used by models that successfully predict firing in the early visual cortex. Those models assume that neurons represent inferences about latent image features, but they often ignore the dynamics of said inference. Here, we test if inferential dynamics for images explain visual-cortical dynamics. To do so, we present a biologically plausible model of cortical computation that assumes the inference of features is coupled with inference about how those features are organized into meaningful parts, also known as segmentation. Given an input image, our model iterates between inferring the features and the segments, through recurrence, thus inducing dynamics in the feature representation. We make theoretical and exact predictions for the induced neural dynamics. Our model predicts both gain and variability in evoked responses to natural images, and we show that it captures classical single-neuron experimental findings such as gain dynamics and variability decay during stimulus presentation. The model also predicts that those metrics are more heterogeneous than previously thought, reflecting the complexity of inference for natural scenes, and that their population-level organization reflects the inferred segments. Finally, our analytical formulation provides a clear interpretation of those results. Insights from our normative model could generalize to segmentation problems in other experimental modalities, and help address the cost of inference in artificial networks.

Linear structural causal models (SCMs) are used to analyze relationships among random variables. In these models, directed edges encode direct causal effects, while bidirected edges capture latent confounding. The problem of generically identifying the hidden parameters from observed correlations remains open in causal inference. The half-trek criterion by Foygel, Draisma, and Drton [2012] and its generalization to the edge-wise criterion are important criteria for generic identification in linear SCMs, since the half-trek criterion can be efficiently decided by an algorithm with running time $\mathcal{O}(n^5)$. We here develop a new criterion that is equivalent to the edgewise criterion. Utilizing this criterion, we design a faster randomized algorithm for deciding the half-trek criterion with running time $\mathcal{O}(n^4)$. For sparse graphs, our algorithm even works in $\mathcal{O}(n^3)$. We show that the algorithm is useful in practice by providing an implementation that outperforms the implementation of HTC in the state-of-the art R package SEMID.