NeurIPS 2026 Papers

Bayesian Reinforcement Learning (BRL), a subclass of Meta-Reinforcement Learning (Meta-RL), provides a principled framework for generalisation by explicitly incorporating Bayesian task parameters into transition and reward models. However, classical BRL methods assume known forms of transition and reward models. While recent deep BRL methods incorporate model learning to address this, applying neural networks directly to joint data and task parameters necessitates variational inference. This often yields indistinct task representations, compromising the resulting BRL policies. To overcome these limitations, we introduce Generalised Linear Models in Deep Bayesian RL with Learnable Basis Functions (GLiBRL). Our approach features fully tractable Bayesian inference over task parameters and model noise, alongside exact marginal likelihood evaluation for learning transition and reward models. The permutation-invariant nature of exact Bayesian inference in GLiBRL enables seamless integration with both on-policy and off-policy RL algorithms. We further show that GLiBRL admits a closed-form relationship between the $\mathcal{L}_2$ distance of its task representations and empirical kernel-based correspondence between task samples, which is to our knowledge the first such structural result for online deep BRL. GLiBRL is compared against representative and recent Meta-RL methods, and improves state-of-the-art performance on both MuJoCo and MetaWorld benchmarks by up to 1.8$\times$.

Linear interpolation between fine-tuned checkpoints has been shown to trace the Pareto front between competing objectives, but whether extrapolative weight averaging can extend such frontiers to new checkpoints useful at inference time, without additional RL training, remains unclear. We study this question in RL for competitive programming, where hidden unit tests under time and memory limits enforce both functional correctness and computational efficiency. Starting from a shared initialization, we train checkpoints under nested unit-test coverage: low-coverage rewards require passing smaller-input tests, while high-coverage rewards require passing progressively larger tests up to the full suite. This sweep reveals the emergence of a correctness–efficiency frontier: on hard problems, higher-coverage reward reduces optimization failures but increases correctness failures, leaving solve rate nearly unchanged. Interpolation between low- and high-coverage checkpoints recovers this frontier, while extrapolation extends it beyond the trained endpoints. Both the frontier and its extrapolative continuation appear across three inference settings, pure reasoning, tool use, and agentic coding, and across two model scales, 32B and 7B. At the problem level, moving along the frontier changes which problems are solved, making extrapolated checkpoints complementary policies in inference-time scaling: ensembles with extrapolative weight averaging broaden coverage and improve pass@250 on LCB/hard by 3.3\% over the best single checkpoint at matched sample budget. These results show that nested unit-test coverage in code RL induces a frontier that extrapolative weight averaging can navigate, extend, and exploit.

We study zeroth-order optimisation under context distributional uncertainty, a setting commonly tackled using Bayesian optimisation (BO). A prevailing strategy to make BO more robust to the complex and noisy nature of data is to employ an ensemble as the surrogate model, thereby mitigating the weaknesses of any single model. In this study, we propose a novel algorithm for Ensemble Distributionally Robust Bayesian Optimisation that remains computationally tractable while managing continuous context. We obtain theoretical sublinear regret bounds, improving current state-of-the-art results. We show that our method’s empirical behaviour aligns with its theoretical guarantees.

Guiding pretrained flow-based generative models for conditional generation or to produce samples with desired target properties enables solving diverse tasks without retraining on paired data. We present ESS-Flow, a gradient-free method that leverages the Gaussian prior of the source distribution in flow-based models to perform Bayesian inference directly in the source space using Elliptical Slice Sampling. ESS-Flow only requires forward passes through the generative model and observation process, making it applicable even when gradients are unavailable, such as with non-differentiable simulation-based observations or quantization in the generation process. We demonstrate its effectiveness on scientific applications including designing materials with desired target properties and predicting protein structures from sparse inter-residue distance measurements.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach learns the posterior inference over the dynamic block length, block formations and growth, and block decoding order within a unified Bayesian inference framework to jointly reason about how much to grow, where to grow, and how to organize content structurally. At each window expansion step, the method integrates local uncertainty with structural signals to (i) dynamically expand the sequence via adaptive length growth, (ii) infer block boundaries through Chinese Restaurant Process (CRP)-style partitioning, and (iii) allocate different number of decoding steps for different blocks and determine block decoding order via context-aware scheduling. This yields a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

In modern deep learning, weight decay is often credited with "stabilizing" training dynamics, diverging from its classical role as a static regularization penalty. We investigate a fundamental question: does weight decay stabilize training dynamics, and if so, through which mechanism? Indeed, training stability is understood through different but related notions in the literature. We consider how weight decay affects the parameter-space dynamics and loss sharpness by analyzing its effects at the Edge of Stability (EoS). We show that weight decay robustly slows progressive sharpening. Furthermore, we uncover a striking architecture-dependent phase transition. In CNNs, weight decay dampens the oscillations at the EoS, while in MLPs, increasing weight decay causes a phase transition in which the sharpness stabilizes at a threshold significantly below the theoretical $\frac{2}{\eta}$ boundary. We develop a mathematical framework that accurately models these phenomena and identify the global alignment of the parameter vector and the sharpness gradient as the mechanistic driver of the phase transition. Importantly, we show that these phenomena translate into stability in terms of search in function-space (NTK).

Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM$_{2.5}$ spatial interpolation from real-world air quality sensors, DnNPs reduces RMSE by up to 43% and NLL by up to 80% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes optimal predictor under noisy inputs belongs to the DnNPs model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNPs provably avoids.

Preferential Bayesian Optimization (PBO) aims to find a decision-maker’s most preferred solution in as few pairwise comparisons as possible. Existing approaches rely on Gaussian Process (GP) surrogates, which provide strong performance but limited interpretability. This limits real-world usability in high-stakes domains, such as healthcare, where interpretability and trust are essential. We propose DT-PBO, a novel tree-based surrogate model for PBO that is inherently interpretable while capturing preference uncertainty. Specifically, we introduce a novel splitting heuristic that constructs interpretable shallow decision trees directly from pairwise comparison data, and use Laplace approximation to obtain probabilistic estimates within each leaf. This enables efficient preference modeling without sacrificing interpretability. Across eight benchmark functions, our method achieves competitive convergence to GP-based PBO, particularly on functions with rugged optimization landscapes. Additional experiments show robustness against noise and a fast computational running time. Experiments on four real-world datasets further demonstrate that our model provides interpretable insights into decision-maker preferences that remain opaque under GP-based approaches.

We present Correlated Latent Uncertainty Estimation (CLUE), a single-pass deep uncertainty quantification framework that combines efficient amortized neural prediction with Bayesian-style information propagation across inputs. CLUE introduces a kernel-based prior, allowing cross-input dependence over latent variables while preserving test-time inference efficiency. CLUE requires neither posterior sampling nor ensembles, and avoids matrix inversion during inference, yet recovers posterior contraction behavior analogous to conventional Bayesian models. In the white-noise limit of the kernel, CLUE reduces to standard evidential deep learning (EDL). This limiting case reveals standard EDL as amortized variational inference with an independent latent structure, providing a probabilistic explanation for several pathologies of EDL identified in prior work. Empirically, CLUE exhibits consistent Bayesian-like uncertainty contraction and improved uncertainty quality across synthetic and real-world benchmarks, while maintaining competitive predictive accuracy and fast single-pass inference.

This paper studies the problem of semi-supervised edge classification, which aims to identify edge relations using both labeled and unlabeled data. This problem is highly challenging due to the inherent asymmetry of edge relations and strong prediction biases from imbalanced homophilous and heterophilous edges. Towards this end, this paper proposes a novel approach named Complementary Tripartite Play with Bayesian CaLibration (CLEAR) for semi-supervised edge classification. The core of our CLEAR is to incorporate asymmetric semantic branches and a meta-teacher into a tripartite-play framework, enabling reliable guidance and optimization under label scarcity. In particular, our CLEAR introduces a topological branch and a contextual branch which extracts graph semantics, generating pseudo-labels in complementary views. To improve the reliability of pseudo-labels, we filter low-quality pseudo-labels using epistemic uncertainty, and then calibrate posterior distributions using the priors induced by neighborhood information. More importantly, we utilize a meta-consoler to guide the optimization of two branches by outputting the objective coefficients, ensuring a reliable pseudo-labeling process in a tripartite play framework. Extensive experiments on benchmark datasets validate the superiority of the proposed CLEAR in comparison to various baselines. Our code is available at https://anonymous.4open.science/r/CLEAR-D1D7/.

Many scientific and combinatorial problems admit multiple correct solutions, not a single label. Standard supervised learning resolves this ambiguity by choosing one solution as the target, but this hidden selector can be arbitrary, discontinuous, and harder to learn than the underlying solution set. We study bifurcation models, a weight-tied dynamical view in which different initializations can converge to different stable equilibria, so the model represents an attractor landscape rather than one chosen branch. We prove that broad set-valued maps with locally Lipschitz branches can be represented by regular equilibrium dynamics and that the induced selectors are almost everywhere regular, while manual selectors can be arbitrarily irregular. Experiments on frustrated Ising models show that such dynamics can discover multiple valid equilibria without branch labels and outperform single-branch supervision. Allen-Cahn experiments further show that diversity is not automatic: it can be encouraged explicitly, but with an accuracy--diversity tradeoff.

Reward models are central to aligning language models with human preferences via reinforcement learning (RL). As RL is increasingly applied to settings such as verifiable rewards and multi-objective alignment, RMs are expected to encode more complex and multifaceted preference distributions. However, classifier RMs remain static once trained, limiting their adaptability at test time. We propose Variational In-Context Reward Modeling (ICRM), a novel Bayesian reward modeling objective that enables test-time steerability via in-context preference demonstrations. ICRM casts reward modeling as amortized variational inference over a latent preference probability under the Bradley-Terry model using a conjugate Beta prior. We show that ICRM adapts to unseen preference distributions at test time for both single and multi-objective settings. With more demonstrations, ICRM improves RM-Bench accuracy from 60.5 to 70.8, achieves lower calibration error than a generative judge on moral dilemma preferences, and expands the attainable Pareto frontier under conflicting preferences. We further study the practical applicability of ICRM for RL training, showing that it can effectively encode verifiable rewards by outperforming a conventional RM in math reasoning. Finally, we provide theoretical guarantees that the variational objective admits a global interior optimum with finite confidence, and we analyze how KL regularization mitigates reward over-optimization.

Membership inference attacks (MIAs) aim to determine whether a sample was used during the training of a target model. The most effective MIAs rely on reference (or shadow) models to estimate target-conditional score distributions, but training such ensembles is computationally prohibitive for modern large-scale Vision--Language Models (VLMs). In this work, we propose a scalable alternative that replaces explicit reference-model training with a Bayesian approximation over low-rank adaptation parameters. Leveraging parameter-efficient fine-tuning, we model uncertainty only within the LoRA subspace and construct a posterior from a single training run, from which we sample a diverse set of virtual reference models. We instantiate this approach using stochastic weight averaging Gaussian (SWAG), enabling efficient approximation of target-conditional score distributions at a fraction of the cost of conventional shadow-model ensembles. We evaluate the resulting attack on three downstream-adapted VLMs across two privacy-sensitive visual question answering tasks, namely Document VQA and medical VQA. To isolate the effect of pretraining knowledge, we additionally introduce a controlled synthetic dataset. Our approach outperforms standard reference-based attacks while requiring only a single trained reference model, demonstrating that accurate and scalable membership inference is feasible even for large VLMs.

Bayesian causal inference quantifies uncertainty in treatment effects under a specified causal model. This uncertainty is often interpreted as evidence that the resulting causal conclusion is robust. We argue these are distinct targets: a posterior over a treatment effect may be tightly concentrated above zero while the corresponding causal claim is fragile to small violations of ignorability, overlap, or target-population assumptions. We introduce Bayesian causal stress testing (BCS), a framework that assigns a posterior fragility score $F_\alpha$ with a threshold $\alpha\in(0,1)$ to a causal conclusion by measuring the smallest calibrated stress under which the posterior probability of the claim falls below $\alpha$. We give a stress-map formulation, decision and composition results for claim-level stress, a calibration theorem showing that $F_{0.5}$ asymptotically recovers the partial-correlation form of the Cinelli-Hazlett robustness value in the linear-Gaussian flat-prior limit, and a proposition formalizing why posterior precision and posterior fragility can decouple. We evaluate BCS on IHDP, TWINS, and ACIC-cov+Hill, a semi-synthetic benchmark built from the ACIC 2016 covariate matrix, under BART, BCF-style, Bayesian linear, and Bayesian-bootstrap AIPW posteriors. On the linear Bayesian posterior, $F_{0.5}^2$ matches the Cinelli-Hazlett $RV_{0.5}^{\mathrm{CH}}$ to RMS $0.001$ on both IHDP and ACIC-cov+Hill across all $20$ configurations; the BART and BCF-style posteriors show larger deviations in small-effect configurations. Across estimators, posterior $95$% interval widths vary by up to $50$% but $F_{0.5}$ remains within $0.05$, illustrating that posterior precision is not a robustness certificate. A controlled-DGP calibration experiment with a hidden confounder of known partial correlation $\gamma_{\mathrm{true}}$ confirms that $F_{0.5}$ tracks the required flip-stress to mean absolute error $0.03$.

Causal experimental design often assumes direct control over treatment assignment, but many experiments can only assign encouragements that affect treatment receipt indirectly. We formulate this as adaptive instrumental variable (IV) design under noncompliance: the experimenter chooses unit--instrument queries, observes stochastic treatment realizations and outcomes, and seeks the treatment-level conditional average treatment effect (CATE). This creates an acquisition mismatch: uncertainty in prospective feedback does not necessarily correspond to uncertainty in the target causal estimand, so outcome-predictive or marginal variance-based criteria may select queries weakly informative for CATE. We introduce instrumental variable information gain (IVIG), a Bayesian acquisition principle that scores queries by the expected information their joint treatment-realization and outcome feedback provides about CATE values over a target population. Under the working Bayesian posterior, IVIG is Bayes-risk aligned under logarithmic loss; we also characterize the residual information discarded by outcome-only acquisition and connect greedy IVIG-style acquisition to target posterior-variance reduction under a fixed-covariance analysis. To approximate IVIG, we use an empirical-Bayes Gaussian Process IV posterior approximation with first-stage treatment-realization modeling and treatment-realization-specific fantasy updates. Experiments on synthetic and two semi-synthetic IV benchmarks show improved CATE sample efficiency over adaptive-design baselines; a real-label diagnostic shows improved recovery of full-data CATE estimates from observed IV data.

Personalized federated continual learning (pFCL) alleviates catastrophic forgetting across tasks and data heterogeneity across clients. We view both challenges as interference between knowledge and propose Bayesian frameworks that define knowledge as posterior belief and quantify two types of interference: intra-model interference, measuring task-induced posterior drift, and inter-model interference, measuring aggregation-induced posterior drift. We show that such interference bounds catastrophic forgetting and data heterogeneity-induced loss, respectively. We then develop an interference-regularized local objective to guide personalization under catastrophic forgetting and data heterogeneity. The framework unifies standard FCL and pFL categories. Experiments on synthetic and real-world benchmarks demonstrate improved model performance over state-of-the-art pFCL methods.

High-dimensional Bayesian optimisation (HDBO) is an increasingly crowded field, with new methods proposed at every major conference, making it ever harder to answer a deceptively simple question: "Which method is currently state-of-the-art?" In this paper, we question the efficacy of benchmarking practices in the field, and find them to be systematically ineffective. Specifically, multiple published works fail to benchmark against the strongest baselines available at the time of writing, or even include incorrect implementations of key methods. As a remedy, we introduce BO-Arena, an actively maintained and extensible package providing canonical implementations of state-of-the-art algorithms, designed to streamline building new methods and rigorously benchmark against existing approaches. We use the package to ask what currently drives performance in HDBO, and find that the answer is even simpler than previously thought. Following these simple principles, we propose a new algorithm which achieves state-of-the-art performance on problems with large numbers of observations, outperforming considerably more complex recent methods. Finally, we question whether there is currently sufficient evidence to suggest that a simple Gaussian process baseline is outperformed by any more complex methods for HDBO.

Approximate Bayesian inference has driven significant advances in probabilistic machine learning at the basis of modern generative modelling. However, many successful Bayesian methods, such as variational inference or sequential Monte Carlo, often struggle in discrete domains with complex structure. In particular, their application to the challenges of neurosymbolic AI, i.e. learning and reasoning under uncertainty, is largely unexplored. Our contributions are twofold. First, we show that the majority of neurosymbolic problems are problems of posterior inference motivating the use of approximate Bayesian inference for neurosymbolic AI. Second, we adapt variational inference to the neurosymbolic setting by exploiting available symbolic structure. Moreover, we outline what properties a reasonable variational approximation to a neurosymbolic problem should have and how to enforce these properties by connecting to statistical estimation and statistical representation theorems. The result is a principled approach to learning and reasoning at scale that maintains statistical guarantees at test time. This work illustrates the opportunities at the intersection of approximate Bayesian inference, and learning and reasoning under uncertainty.

Bayesian neural networks (BNNs) offer principled uncertainty quantification, yet sampling from their posteriors via Hamiltonian Monte Carlo (HMC) remains challenging. While recent work theoretically identified the efficiency degradation of ReLU-based networks, smooth unbounded activations (_e.g.,_ GELU, Swish, Mish), which are prevalent in modern architectures, were assumed to be efficient due to their smoothness. In this work, we challenge this existing justification by deriving explicit local error formulas for the leapfrog integrator. Our analyses reveal that, in addition to differentiability, third-order curvatures of the potential energy also have a significant influence on HMC efficiency of BNNs inference. Empirically, we found that even smooth unbounded activations may degrade sampling performance as severely as piecewise linear activations. Thus, optimally tuning the step size for these networks may require a comparable empirical step size scaling as their piecewise counterparts. This result sheds light on the implications for architectural design in Bayesian deep learning.