NeurIPS 2026 Papers

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.

Multivariate weather time series are a central modality for forecasting and decision support, and the surrounding language increasingly mediates how numerical weather is consumed by users and downstream models. However, existing pipelines depend on closed-source language model ensembles with expert quality control or on retrieving human-curated text, while prior caption-RL rewards optimize cycle similarity or downstream-task utility, neither of which can tell a captioner that a confidently asserted phenomenon is contradicted by the data, so the absence of an executable, station-observable, and refutation-aware reward signal has blocked the application of self-play RL to this scientific modality. To address this, we propose AtmoZero, a post-training framework that trains a weather-time-series captioner without a single human-written caption, by aligning a language model with a library of seven station-observable scientific verifiers, pairing them with an explicit refutation channel that penalizes caption claims the data contradicts, and combining them with auxiliary reconstruction and forecaster-utility rewards under group-relative policy optimization. Extensive empirical results on a twelve-year ERA5 reanalysis corpus and real-world surface observations show that AtmoZero attains the lowest unsupported-claim rate and forecasting error at every horizon, outperforming closed-source captioners, dense-reward RL, and far-larger foundation models, with extensive analyses confirming that these gains arise from multiple complementary signals and are robust under distribution shift.

Open-set 3D macromolecule detection in cryogenic electron tomography eliminates the need for target-specific model retraining. However, strict VRAM constraints prohibit processing an entire 3D tomogram, forcing current methods to rely on slow sliding-window inference over extracted subvolumes. To overcome this, we propose FullTilt, an end-to-end framework that redefines 3D detection by operating directly on aligned 2D tilt-series. Because a tilt-series contains significantly fewer images than slices in a reconstructed tomogram, FullTilt eliminates redundant volumetric computation, accelerating inference by orders of magnitude. To process the entire tilt-series simultaneously, we introduce a tilt-series encoder to efficiently fuse cross-view information. We further propose a multiclass visual prompt encoder for flexible prompting, a tilt-aware query initializer to effectively anchor 3D queries, and an auxiliary geometric primitives module to enhance the model's understanding of multi-view geometry while improving robustness to adverse imaging artifacts. Extensive evaluations on three real-world datasets demonstrate that FullTilt achieves state-of-the-art zero-shot performance while drastically reducing runtime and VRAM requirements, paving the way for rapid, large-scale visual proteomics analysis. All code and data will be publicly available upon publication.

No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and (c) exact parameter gradients. Existing implementations handle only bivariate problems, low dimensional (i.e., $d \leq 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present acopula, a JAX-native framework that, given any Archimedean generator—classical or neural—evaluates exact nested-copula likelihoods and parameter gradients under arbitrary censoring masks in polynomial time. The mechanism is polynomial powering of Taylor-mode automatic differentiation output, which replaces per-family hand-derived partial Bell polynomial tables with a single differentiable computation that any user-defined generator can drive. We conduct extensive simulations to verify the correctness of acopula. We then demonstrate (a) per-variable censoring on $85,229$ MIMIC-IV ICU admissions in high dimensions with $d=53$, fit by both classical Archimedean families and nested neural Archimedean copulas; (b) an 11-sector hierarchical model on S&P 500 daily returns at $d=98$; (c) family-agnostic censored MLE across ten families, five of them with no prior implementation, on a retinopathy study; and (d) a $\sim650\times$ per-density speedup over R's nacLL at $d=35$, scaling quadratically to $d=8,000$.

Test-time scaling systems often choose how much to sample, which prompt to use, and which verifier or aggregation rule to trust after repeatedly inspecting a calibration set. Standard validation error bars are not valid after this adaptive selection. We model a test-time scaling recipe as a randomized predictor with a random cost and prove a time-uniform PAC-Bayes certificate that holds simultaneously over all calibration times, all posterior mixtures over recipes, and all data-dependent stopping rules. Thus the same event covers the recipe search that precedes deployment, not merely the fixed recipe finally reported. For a finite grid of budgets and verifiers, the penalty is the familiar $\log M/n$, while non-uniform priors and localized posterior mixtures give sharper certificates for structured searches. We specialize the result to self-consistency and show a complementary margin law: plurality voting improves exponentially in the sample budget only on examples where the correct answer is the generator's unique mode; otherwise more compute can provably amplify errors. The same margin analysis yields an oracle water-filling law for compute allocation. A synthetic audit quantifies the optimism caused by adaptive budget selection, and a 192-example GSM8K audit using gpt-4.1-mini generations illustrates risk-cost reporting for a real inference pipeline. The results give a lightweight, distribution-free way to report risk and compute claims for adaptive inference systems.

Kernel methods are widely used in machine learning and statistics for their flexibility and expressive power, yet their black-box nature limits adoption in high-stakes applications. Shapley value--based attribution methods such as SHAP, and kernel-specific adaptations including RKHS-SHAP, provide a principled framework for explainability---but exact computation of Shapley values is generally intractable, forcing existing approaches to rely on approximations that incur unavoidable estimation error. We introduce PKeX-Shapley, an algorithm that exploits the multiplicative structure of product kernels to compute exact Shapley values for all $d$ features in quadratic time in $d$. The method rests on a distribution-free removal operator intrinsic to the product-kernel structure: removing a feature replaces its kernel factor with the multiplicative identity. This yields a parameter-free value function---requiring no sampling and no density estimation---and uniquely determines a functional decomposition of the model. Building on this value function, we develop shared recursive formulations that evaluate all feature attributions jointly, achieving amortized linear time per feature with numerical stability. Beyond predictive modeling, the framework extends to widely used kernel-based discrepancies such as the Maximum Mean Discrepancy (MMD) and the Hilbert--Schmidt Independence Criterion (HSIC), providing new tools for interpretable statistical analysis.

Many inference-time language-model pipelines combine a cheap reward signal with an expensive verifier, such as exact answer checking in mathematical reasoning or hidden-test execution in code generation. We formalize this setting using a learning-theoretic lens as generative active search: a cost-sensitive first-positive search problem in which a policy adaptively samples candidates from an unknown distribution, observes cheap scores, and pays for verifier labels until it finds a positive example. For a fixed prompt, the generator and reward model induce two unknown objects: a distribution over reward scores and a score-conditioned success function. When these quantities are known, we characterize the distribution-aware optimal policy using a dynamic programming approach. In the realistic and practical setting where both the score distribution and success function are unknown, we propose ADAP, a shellwise adaptive generate-rank-verify algorithm that progressively increases the number of sampled responses and top-ranked verifications. Under the monotonicity assumption that higher reward scores are no less likely to pass verification, we show that ADAP achieves expected cost within a constant factor of the distribution-aware optimum. We complement this result with learning-theoretic lower bounds, based on a centered star number, showing that structural assumptions on the score--label relationship are necessary. Experiments on mathematical reasoning and competitive programming validate the predicted advantage over both fixed non-adaptive policies and difficulty-adaptive baselines.

We investigate the problem of scaling safe reinforcement learning to massively parallel training regimes, where a large number of environments are executed with short rollout horizons. Although this setting improves data throughput and wall-clock efficiency, it creates a mismatch with constrained Markov decision processes, whose safety constraints are defined over full-episode cost returns. We address this mismatch by analyzing staggered environment resets as a phase-mixture distribution over short trajectory segments. This analysis characterizes the bias induced by phase coverage and motivates a phase-aggregated cost estimator that reconstructs episode-level cost estimates from staggered short rollout batches. We further incorporate finite-sample uncertainty and distribution mismatch into a constraint-tightening framework, yielding a scalable Safe RL method compatible with on-policy optimization.Using an MJX-based implementation of Safety Gym, our experiments show that the proposed method achieves performance comparable to non-massively parallel implementations while substantially reducing wall-clock training time

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.

Atomic electron tomography (AET) aims to recover the three-dimensional arrangement, chemical identity, and temporal evolution of individual atoms. Yet most reconstruction methods are still evaluated primarily by voxel-level image similarity, such as PSNR, SSIM, or Fourier shell correlation. In this work, we show that this evaluation practice can select scientifically incorrect reconstructions: a volume that looks accurate can contain atoms that are shifted, merged, missed, hallucinated, chemically mislabeled, or assigned inconsistent identities through time. We introduce AET-Bench, a dataset and benchmark for atom-first evaluation of atomic electron tomography. AET-Bench contains 755 samples across a six-tier realism ladder, spanning clean analytical simulations, binary alloys, 4D atomic dynamics, multislice scattering, real experimental tilt series, and Brownian Pt nanocrystal trajectories. It defines four complementary tasks and evaluates 14 core method families with 21 logged method entries under a unified protocol. AET-Bench reveals a central failure mode hidden by voxel-only evaluation. On the AET-Sim-Mono tier, high-SSIM neural and Gaussian reconstructions can recover substantially fewer atoms than classical or sparsity-regularized methods: for example, 4D-GS achieves strong voxel similarity but only 43.9\% atom recall, while FISTA-TV reaches 95.1\% atom recall despite much lower SSIM. This inversion persists across atom-matching thresholds, showing that it is not an artifact of a single cutoff. On more realistic multislice and real tiers, atom recovery further degrades, exposing a physics gap between visually plausible volumes and reference atomic models. For 4D reconstruction, we find that smooth temporal density fields do not guarantee persistent atom identities. AET-Bench establishes atom-level fidelity as a necessary evaluation axis for AET. Our results suggest that future AET methods should not be judged only by how reconstructions look, but by whether they recover the atoms, species, and trajectories that scientists actually use.

Large Language Models (LLMs) present a novel paradigm for power system dispatch (PSD), enabling operators to derive optimal dispatch strategies from multi-objective requirements and grid dynamics. However, isolated paradigms focusing on modeling or solving often yield decision bias or physical infeasibility. Meanwhile, end-to-end paradigms couple modeling-solving with reflection-feedback loops, obscuring whether failures stem from inaccurate modeling, invalid solutions, or insufficient feedback, thereby causing ineffective iterations. To address these challenges, we propose Agile Dispatch Agent (ADA), an agent based on two-time-scale evolution that decouples the optimization process into two asynchronous loops. On the fast time scale, the Planner actively acquires information to clarify complex requirements, while the Solver selects algorithms to adapt to the problem mathematical characteristics. On the slow time scale, the Summarizer module updates the modeling feasible region based on evaluations from the Judger. Under a finite-horizon Planner and standard two-time-scale stochastic approximation assumptions, our analysis provides local tracking guarantees for the fast decision process and the slow knowledge evolution. Experiments on L2RPN benchmarks with ambiguous requirements and renewable dynamics show that ADA outperforms state-of-the-art baselines.

Generative modeling continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

Flexible continuous-time survival modeling is critical for capturing complex temporal dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.

Virtual sensors replace expensive physical sensors in critical applications through machine learning by predicting target signals from available measurements. Existing virtual sensor approaches require application-specific models with hand-selected inputs for each sensor, cannot leverage task synergies, and lack consistent benchmarks. While emerging time series foundation models offer general-purpose, pretrained solutions in other domains, they are computationally expensive and limited to predicting their input signals, making them incompatible with virtual sensors. We introduce the first multi-task model for virtual sensors addressing both limitations. Our unified model can simultaneously predict diverse virtual sensors exploiting synergies while maintaining computational efficiency. It learns relevant input signals for each virtual sensor, eliminating expert knowledge requirements while adding explainability. In our large-scale evaluation on three standard benchmarks and an application-specific dataset with over 18 billion samples, our architecture reduces computation time by up to 415x and memory requirements by 951x, while maintaining or even improving predictive quality compared to unified baselines. Compared to existing isolated models for a single virtual sensor, our unified approach generates superior predictions at similar inference speed while scaling gracefully to hundreds of virtual sensors with nearly constant parameter count, enabling practical deployment in large-scale sensor networks.

Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the *mechanisms* that underlie their forecasts. Such an understanding could help to strip down overladen FM architectures to their bare essence and expose the minimal requirements for in-context learning in the DS domain. Toward this goal, here we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix (Hemmer & Durstewitz, 2025), to a minimal interpretable two-parameter form, which we call *DynaBase*. DynaBase produces forecasts through a linear blend of the current latent state and the nearest in-context neighbor and its temporal successor. Surprisingly, despite its extreme simplicity, DynaBase produces highly competitive zero-shot DS reconstructions across chaotic and cyclic systems, with a negligible parameter load, many orders of magnitude below that of other FMs. Even more, this extreme simplicity permits direct model optimization on DS reconstruction measures, as well as closed-form one-step analytical solutions on prediction MSE. Theoretical and empirical analysis of DynaBase further leads to a 1-parameter family of maps, with the context-parroting algorithm of (Zhang & Gilpin, 2026) recovered at one end, and chaotic (divergent but bounded) behavior at the other. We further show how different training strategies lead to models either optimal for short-term prediction or for DS reconstruction. Thus, DynaBase not only exposes the minimal mechanisms required for producing zero-shot DS reconstruction, but also reconciles within an accessible mathematical frame divergent observations in the literature.

Watermarking is a central tool for provenance in generative models, yet its application to multivariate time series remains hindered by reliability failures under post-editing attacks. We show that existing detectors, which rely on globally coupled re-encoding, suffer from bidirectional drift of the null distribution: post-editing attacks can shift the detection z-score of non-watermarked samples in either direction, invalidating clean-calibrated thresholds. We argue that this instability is a property of the re-encoding, and that reliable detection requires each recovered unit to depend only on a bounded temporal neighborhood. Guided by this principle, we propose L-VQVAE, a generative model in which each discrete token is produced from a short contiguous window, and LVQMark, a watermarking method over this token space that combines logit-bias injection with robust re-encoding for attack-time detection. Experiments on four benchmarks spanning finance, energy, and neuroimaging show that our approach preserves generation quality while stabilizing both detection power and false-positive behavior under post-editing attacks.

Hartigan's $k$-means algorithm has theoretical advantages over the standard Lloyd's variant, which has become synonymous with ``$k$-means''. Yet, Hartigan's algorithm is far slower in practice due to its inherently sequential calculations. We devise a Batched Hartigan's method that enables vectorized calculation by exploiting the triangle inequality to expose a set of parallel-safe updates and a smaller set of sequential updates. This makes Hartigan's method competitive with Lloyd's in execution speed for the first time.