NeurIPS 2026 Papers

Medicine is inherently pluralistic. Principles such as autonomy, beneficence, nonmaleficence, and justice routinely conflict, and such ethical dilemmas often sharply divide reasonable physicians. Good clinical practice navigates these tensions in concert with each patient's values rather than imposing a single ethical stance. The ethical values that large language models bring to medical advice, however, have not been systematically examined. We present a framework for auditing value pluralism in medical AI, comprising a benchmark of clinician-verified dilemmas and an attribution method that recovers value priorities directly from decisions. The ecosystem of frontier models spans physician-level value heterogeneity, and models discuss competing values in their reasoning (Overton pluralism) before committing to a decision. However, individual model decisions are near-deterministic across repeated sampling and semantic variations, failing to reproduce the distributional pluralism of the physician panel. Across benchmark cases, these consistent decisions reflect committed, systematic value preferences. While most model priorities fall within the natural range of inter-physician variation, some significantly underweight patient autonomy. A single LLM deployed without regard for its value priorities could amplify those priorities at scale to every patient it serves. Without explicit efforts to balance ethical perspectives with one or multiple models, these tools risk replacing clinical pluralism with a deployment monoculture.

There has been a plethora of algorithms proposed that leverage Wasserstein gradient flows or forward-only diffusion processes to perform sampling tasks. These approaches are often characterized by theoretical guarantees of exponentially fast convergence to the target distribution. In this work, we study the mixing behavior of this family of sampling methods. By invoking the Jordan--Kinderlehrer--Otto scheme and Otto calculus, we first establish that Wasserstein gradient flow and forward diffusion-based samplers share the same density evolution. Consequently, their convergence can be characterized by studying the convergence behavior of the associated diffusion process, which has been extensively analyzed in nonequilibrium statistical physics. We perform two independent and well-established analyses for this purpose, namely spectral analysis and mean first-passage time analysis. We show that, although the sampling distributions converge to the target distribution exponentially fast, the presence of multimodality can lead to exponentially long mixing times associated with small spectral gaps. Further analysis elucidates that even when combined with annealing, this family of samplers still requires impractically long time to sample multimodal distributions. We discuss the origin of this behavior as a consequence of the local (i.e., gradient-driven) dynamics underlying this class of samplers, and highlight the need for non-local mechanisms to facilitate the transport of probability mass across modes, enabling efficient exploration in multimodal settings.

Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.g., SVGD), which suffers from variance collapse in high dimensions and mode collapse on multimodal targets—pathologies caused by the absence of global transport structure. We introduce entropic transport descent (ETD), a ParVI family that frames each particle update as an entropy-regularized optimal transport problem. Derived from the JKO proximal scheme by lifting to the space of couplings and relaxing via the KL chain rule, each ETD iteration reduces to a Sinkhorn computation. The resulting transport plan provides global coordination, guiding each particle to nearby high-density proposals and naturally preserving multimodal structure. ETD can operate entirely score-free, requiring only pointwise evaluations of the unnormalized target density. Experiments on variance-collapse diagnostics, Bayesian logistic regression, neural networks, and molecular Boltzmann distributions show that ETD matches or outperforms SVGD, AGF-SVGD, and SGLD, with the largest gains in high-dimensional and multimodal settings.

Sampling from a softmax distribution is a fundamental operation in machine learning, but its linear complexity in the number of items makes exact sampling impractical at scale. Two-level softmax (2LS) sampling is a popular alternative enabling sublinear-time sampling. Assuming items are partitioned into clusters, 2LS first samples a cluster and then an item within it. In this paper, we show that, despite its advantages, 2LS introduces systematic and undesirable sampling biases, which arise from misweighting clusters by ignoring both cluster size imbalance and intra-cluster similarity dispersion. We propose two sampling methods, Size-Corrected 2LS (S-2LS) and Size- and Dispersion-Corrected 2LS (SD-2LS), which correct these biases and provide provably better softmax approximations with negligible to non-existent computational overhead. In-depth experiments on five large-scale datasets validate the improved sampling properties of our methods. We recommend their consistent use in place of standard 2LS in future work.

Diffusion models generate samples by denoising along the score of a perturbed target distribution. In practice, one trains a neural diffusion model, which is computationally expensive. Recent work suggests that score matching implicitly smooths the empirical score, and that this smoothing bias promotes generalization by capturing low-dimensional data geometry. We propose moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD), a training-free interacting particle sampler that enforces the target moments throughout the sampling trajectory. We prove that, in the large-particle limit, the empirical particle density converges to a deterministic limit whose one-particle stationary marginal is a Gibbs--Boltzmann density obtained by exponentially tilting a naive score-smoothed diffusion target. The mean and covariance of this distribution agree with the empirical moments of the training data. Experiments on 2D distributions and latent-space image generation show that MM-SOLD enables fast, robust, training-free sampling on CPUs, with sample fidelity and diversity competitive with neural diffusion baselines.

We study regret minimization in finite-horizon episodic Markov Decision Processes (MDPs). While minimax-optimal algorithms are known, tractable approaches to instance-dependent optimality are still lacking. Motivated by this gap, we introduce $\pi_0$-PSRL, a variant of PSRL that uses posterior samples to decide when exploration is needed, while following a fixed reference policy $\pi_0$ during exploration episodes. This decouples the test for exploration, triggered when the sampled and empirical MDPs have different optimal policies, from the choice of the policy used to gather information. The resulting design addresses a limitation of standard PSRL, where the sampled optimal policy may not be the optimal choice for exploration. We prove instance-dependent regret bounds for $\pi_0$-PSRL, identifying the logarithmic exploration cost induced by $\pi_0$ and taking a step toward matching asymptotic lower bounds for episodic RL. Our proof techniques showcase a novel proof structure to derive problem-dependent regret bounds in episodic MDPs, and concentration results for Dirichlet random variables, that may be of independent interest.

Data selection for language model pretraining faces a fundamental tension between quality and diversity. While quality filtering is empirically effective, it often induces diversity collapse: by favoring texts similar to high-quality reference corpora (e.g., educational or QA-style data), it systematically excludes valuable data from underrepresented domains. In contrast, diversified selection preserves domain balance and encourages robust downstream performance, yet existing methods either focus on coverage-oriented objectives that indirectly enhance diversity, or directly optimize for diversity via costly covariance matrix recomputation that limits scalability. To address these issues, we introduce \textbf{Leverage Score Sampling (Lev)}, which iteratively selects samples that maximally expand the determinantal volume of the embedded data via leverage scores, a computationally efficient criterion that eliminates matrix recomputation and enables scalable selection. Empirically, Lev delivers up to $65\times$ speedup and improves dataset diversity, measured by the Vendi score, by $9.2\%$ over the strong diversification baseline \textbf{DiSF}. On CommonCrawl (CC) web data selection, Lev improves accuracy across seven downstream tasks by up to $1.31\%$ over existing baselines. For domains where robust quality criteria are inherently difficult to define (e.g., code), Lev serves as an effective unsupervised curation alternative: on StarCoderData, the selected subset reduces bits-per-byte by $3.08\%$ over DiSF. Notably, we uncover a cross-domain collapse of quality filtering: CC data filtered by DCLM-fastText fail to retain sufficient code-related content, yielding inferior code performance relative to Lev-selected data. These findings advocate for integrating diversity-aware practices into quality filtering for more effective data curation in language model pretraining.

We study best-arm identification in large-scale stochastic dueling bandits under the sole assumption that a Condorcet winner exists, i.e., an arm that wins each noisy pairwise comparison with probability at least $1/2$. We introduce a new identification procedure that exploits the full gap matrix $\Delta_{i,j}=q_{i,j}-\tfrac12$ (where $q_{i,j}$ is the probability that arm $i$ beats arm $j$), rather than only the gaps between the Condorcet winner and the other arms. We derive high-probability, instance-dependent sample-complexity guarantees that (up to logarithmic factors) improve the best known ones by leveraging informative comparisons beyond those involving the winner. We complement these results with matching lower bounds that establish the optimality of our procedures in all regimes. Overall, our results reveal the general form of the sampling complexity, characterized by a trade-off between the cost of locating informative entries and the verification cost required to achieve the desired confidence. In particular, this complexity drastically differs from what is suggested by pure asymptotic results or by procedures that are tailored to Strongly Stochastic Transitive models.

Scientific discovery is constrained not only by what is true, but by what is cognitively available to the researchers currently exploring a field. Many directions are coherent in light of the literature yet unlikely to be proposed because no existing community occupies the right combination of concepts, methods, and intuitions. Modern language models inherit this bias, recombining high-density regions of the literature when prompted for novel ideas. We introduce a framework that targets the complementary region, which we call the \textbf{alien space of science}, where directions are plausible under the structure of existing knowledge but unlikely under the distribution of existing researchers. Our method first decomposes papers into granular conceptual units and clusters them into a shared vocabulary of \emph{idea atoms}. It then learns two complementary models over this vocabulary. A \emph{coherence model} scores whether a combination of atoms forms a viable research direction, and an \emph{availability model} scores whether any existing author community is positioned to produce a given combination. Sampling alien directions then reduces to ranking atom combinations that maximize coherence while minimizing availability. On a corpus of 16{,}068 peer-reviewed LLM papers from NeurIPS, ICLR, ICML, and major NLP venues, the resulting sampler explores a $3.5\text{--}7\times$ broader effective atom vocabulary than frontier LLM ideation baselines without sacrificing coherence, and produces ideas that match or exceed those baselines under blind LLM, human, and downstream experimental evaluation. By separating scientific plausibility from community availability, our framework points toward AI ideation that complements rather than merely accelerates human science, expanding exploration into coherent directions the current community is unlikely to pursue.

Diffusion models have achieved remarkable success as generative models. However, even a well-trained model can accumulate errors throughout the generation process. These errors become particularly problematic when arbitrary guidance is applied to steer samples toward desired properties, which often breaks sample fidelity. In this paper, we propose a general solution to address the off-manifold phenomenon observed in diffusion models. Our approach leverages a time predictor to estimate deviations from the desired data manifold at each timestep, identifying that a larger time gap is associated with reduced generation quality. We then design a novel guidance mechanism, `Temporal Alignment Guidance' (TAG), attracting the samples back to the desired manifold at every timestep during generation. Through extensive experiments, we demonstrate that TAG consistently produces samples closely aligned with the desired manifold at each timestep, leading to significant improvements in generation quality across various downstream tasks.

Best-of-N sampling is a simple inference-time scaling strategy for large language models, yet its behavior under incomplete reward models remains poorly understood. We study Best-of-N as a competition between the extreme reward tails of correct and incorrect responses. This view shows that success depends not only on the probability of sampling a correct response, but also on whether correct responses dominate incorrect ones in the upper tail. Using extreme value theory, we characterize three asymptotic regimes: correct-tail-dominant, incorrect-tail-dominant, and critical explaining both monotonic gains and reward-hacking-induced degradation. We further derive finite-sample scaling laws for representative reward distributions, showing that, under Gaussian rewards, incorrect responses with sufficiently large variance can dominate selection even when their mean reward is lower. Unlike oracle selection, convergence with an incomplete selector can be polynomial rather than exponential. Finally, we propose a lightweight tail-tension criterion to estimate when additional sampling may become harmful. Experiments on synthetic data and real reward model scores validate the predicted regimes, scaling laws, and diagnostic behavior, suggesting that tail competition provides a unified lens on Best-of-N sampling for verifiable problems.

Uniform-noise discrete diffusion and flow models generate sequences non-autoregressively through iterative, context-dependent token replacements. However, these models are typically formulated as time-inhomogeneous CTMC/DTMC processes, sampled using independent Bernoulli change decisions per discretization step. This induces Poisson-binomial variance in per-position jump counts that grows with the number of required edits, leading to the common under-editing (residual noise) and over-editing (cascading substitutions) failure modes that degrade sample quality, especially under tight discretization budgets. We identify this sampler-induced variance as an orthogonal source of degradation, distinct from model-side errors and addressable purely at inference time. We propose Systematic Hazard Sampling (SHS), a training-free, drop-in, and hyperparameter-free inference principle for any sampler that admits a stay-vs.-replace decomposition. SHS models per-token edits as events driven by cumulative hazard (CTMC) or jump mass (DTMC) and triggers an edit whenever this quantity exceeds unit-spaced thresholds with a single random phase per position. For any fixed cumulative mass, this preserves the expected jump count while achieving the minimum conditional variance possible among unbiased integer estimators (at most \(1/4\)), without altering per-jump destination sampling. Experiments on four uniform-noise discrete diffusion and flow language models spanning $\sim$110M to $\sim$3B parameters show that SHS consistently improves sample quality across NFE budgets, with the gains growing with NFE as predicted by the variance gap.

Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic Generative Flow Networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.

Large Language Models (LLMs) are typically evaluated for safety under single-shot or low-budget adversarial prompting, which underestimates real-world risk. In practice, attackers can exploit large-scale parallel sampling to repeatedly probe a model until a harmful response is produced. While recent work shows that attack success increases with repeated sampling, principled methods for predicting large-scale adversarial risk remain limited. We propose a scaling-aware Best-of-N estimation of risk, SABER, for modeling jailbreak vulnerability under Best-of-N sampling. We model sample-level success probabilities using a Beta distribution, the conjugate prior of the Bernoulli distribution, and derive an analytic scaling law that enables reliable extrapolation of large-N attack success rates from small-budget measurements. Using only n=200 samples, our anchored estimator predicts ASR@1000 with a mean absolute error of 1.44, compared to 6.58 for the baseline, which is a 78.1% reduction in estimation error. Our results reveal heterogeneous risk scaling profiles and show that models appearing robust under standard evaluation can experience rapid nonlinear risk amplification under parallel adversarial pressure. This work provides a low-cost, scalable methodology for realistic LLM safety assessment. We provide our code in the Supplementary Material.

We propose a stable algorithm for solving maximum coverage problems under a cardinality constraint of $k$ in a record-level stability model, where adjacent instances $I\sim I'$ differ by the incidence of one universe element. Our algorithm computes a negative-entropy-regularized maximizer of the capped concave relaxation over the hypersimplex and rounds it with a common-seed rounding map from hypersimplex correlated sampling. The resulting sensitivity bound is $\min\{2k, \alpha_k k/\lambda\}$, where $\lambda$ is the regularization parameter and $\alpha_k = O(\log k)$. For utility, the expected coverage has approximation factor $1-\frac{1}{e}$ with an additive error of order $O(\lambda k \log \frac{m}{k})$, where $m$ is the number of input sets. We also report experiments on synthetic and real-world instances.

We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on $(\mathbb S^{d-1})^L$ both decompose into posterior-weighted tangent sums that differ only by per-token scalar weights. This gives access to both ODE and predictor-corrector (PC) sampling. The posterior is the only learned object, trained by a cross-entropy loss. Experiments compare the vMF path against geodesic and Euclidean alternatives. The combination of vMF and PC sampling significantly improves results on Sudoku and language modeling.

We study the query and communication complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to polynomial approximation barriers and a characteristic $\sqrt{\kappa}$ dependence on the condition number. We show that this barrier disappears when the sampler is allowed to query \emph{smoothed gradients}, namely scores of Gaussian-convolved distributions. For a Gaussian target with precision $\Lambda$, a smoothed-score query at noise level $\tau$ gives access to the resolvent $(\Lambda+\tau^{-1}I)^{-1}$. Combining geometrically spaced noise levels with sinc-quadrature rational approximation, we obtain a sampler with $$ q = O\left( \left(\log\kappa+\log(\sqrt d/\varepsilon)\right) \log(\sqrt d/\varepsilon) \right) $$ smoothed-gradient queries for total variation error $\varepsilon$, improving the condition-number dependence from $\sqrt{\kappa}$ to logarithmic. We also study finite-bit gradient oracles. Using coordinatewise quantization of the transformed smoothed-gradient answers and a final dithering step, we obtain a sampling scheme whose total communicated gradient information is polylogarithmic in $\kappa$; in particular, for fixed dimension and accuracy, the bit complexity is $O(\log^2\kappa)$. To complement these upper bounds, we introduce a channel-synthesis, or reverse-Shannon, converse technique for sampling lower bounds. This converts total-variation simulation guarantees into communication requirements and yields an $\Omega(\log\kappa)$ lower bound on the required gradient information. Together, these results identify smoothed gradients as a strictly more powerful oracle for sampling and give nearly matching upper and lower bounds for its finite-bit complexity.

The performance of machine learning models depends on discovering features in the data that are relevant to solving the given task while ignoring irrelevant variation. To check and visualize whether this is the case, we propose ‘invariance auditing’, a diagnostic tool to analyze feature extractors. Invariance auditing generates diverse inputs which all yield the same features as a given query input, and are therefore treated as identical by the model. Using external knowledge about the task at hand, this enables assessing if the learned invariances do or do not conform to the task's required semantics. Unlike existing work where a dedicated generative model is trained for each feature extractor, our algorithm is training-free and exploits a pretrained diffusion or flow-matching model to sample invariant inputs. Our fiber loss -- which penalizes feature mismatch -- guides the denoising process so the output shares the same representation as the query input. This replaces days of training with a single guided generation procedure at the same quality. Experiments on popular datasets and model types demonstrate that our auditing method reveals invariances spanning very desirable and concerning behavior. For instance, it detects cases where Qwen-2B places patients with situs inversus (heart on the right side) in the same fiber as typical anatomy.

Generative models are increasingly central to many de novo discovery pipelines, in which designs are generated at scale and filtered through virtual screens to determine a set of candidates to experimentally validate. While Bayesian optimization (BO) is a natural fit for this setting, as it uses past evaluations to guide future proposals, the computational overhead required for its sequential decision-making becomes a bottleneck when virtual screens are relatively cheap. We make BO practical in this regime by exploiting the unique combination of a linear model constrained to a spherical domain where high-dimensional latents concentrate. We build off recent work justifying the use of linear surrogates, while deriving nearly closed-form solutions to the surrogate modelling and acquisition problems that exploit spherical symmetry. The result is a $100\times$ speedup over state-of-the-art baselines, with matching or improved performance across molecular and image generation benchmarks. Altogether, our method makes BO a practical drop-in for de novo pipelines where it was previously too slow to consider.