NeurIPS 2026 Papers

Training quality is the primary determinant of reasoning efficiency in large language models, yielding greater returns than proportional increases in inference computation. Evaluating 44 language models (0.5B--685B parameters) across six reasoning benchmarks totalling over 67000 assessments, this study establishes when additional inference tokens are beneficial, redundant or actively harmful. Standard models exhibit near-universal accuracy convergence at approximately 1000 tokens regardless of architecture or parameter count. Causal intervention experiments demonstrate that constraining generation length improves reasoning accuracy by 15.4 percentage points, identifying over-generation rather than capacity exhaustion as the primary efficiency bottleneck. Among 13 reasoning-specialised models, training methodology yields 18.8-fold efficiency improvement at matched parameter scales, exceeding gains from ten-fold parameter increases. Graduate-level evaluation reveals that arithmetic benchmark performance does not predict reasoning capability on complex tasks ($r = -0.03$, $P = 0.91$), exposing fundamental limitations invisible to standard evaluation practice. Mechanistic profiling reveals two orthogonal dimensions of training quality---quality control and decomposition efficiency---that independently predict efficiency profiles, providing a measurable framework linking training decisions to inference-time behaviour.

Inference-time scaling provides a promising path for improving agentic reasoning performance, and one widely adopted form is sample-then-select: first sample a pool of candidate reasoning trajectories, then select from the resulting candidates. While this keeps scaling lightweight without updating the policy, it exposes a training-deployment mismatch. Standard trajectory-wise Reinforcement Learning (RL) objectives optimize normalized signals for individual trajectories, whereas choosing from a large candidate pool with the policy's own selection signal is inherently set-conditional: it requires calibrated ranking and confidence aggregation across correlated trajectories. To address this challenge, we propose AutoPortfolio, a set-conditional policy alignment framework for efficient and effective sample-then-select scaling. AutoPortfolio builds a tractable environment-informed target on the sampled candidates, and uses its induced Plackett-Luce (PL) ranking to calibrate the policy which trajectories to prioritize within that set. It trains the policy with a balanced PL-motivated objective that reallocates probability mass among competing trajectories, preserving reward-aligned alternatives while sharpening away from low-quality distractors. Aligned with our policy training, our lightweight inference-time Mass Aggregation scaling adaptively perceives confidence from candidate trajectories and selects the most promising answer(s). Theoretically, we show that reducing our set-conditional loss narrows the discrepancy between policy-induced and environment-informed PL rankings on the sampled set. Empirically, across 12 challenging reasoning benchmarks, AutoPortfolio improves over strong agentic RL baselines, with the clearest gains in larger candidate pools where the set-level selection is crucial.

Human mobility differs from text and from generic time series in three structural ways: visits are tuple-valued events whose meaning depends on the joint distribution over location, time, and activity; users carry persistent signatures across trajectories; and visits are not independent across users, since co-location at shared places is a primary signal. Existing pre-training recipes for mobility import objectives from language modeling, treating trajectories as sentences and visits as tokens, an analogy that fails against each of the three properties above. These properties define a broader class, multi-entity spatiotemporal event streams (MESES), spanning enterprise authentication logs, electronic health records, and other event-stream domains where entities share infrastructure, schedules, or contexts. We make the properties precise as three axioms that any pre-training framework for MESES should satisfy, and introduce TraXion, whose objectives and architecture are jointly designed to meet them. A single TraXion checkpoint per dataset beats task-specific baselines on every task across six public mobility datasets covering anomaly detection, next-POI recommendation, next-visit prediction, and social-link prediction. The same recipe, applied unchanged to enterprise authentication logs and ICU mortality prediction, matches or exceeds prior work on both, showing that event streams from domains as different as mobility, security, and healthcare can be modeled under a single framework.

Test-time training and test-time policy optimization have emerged as effective tools for improving the robustness of LLMs under distribution shift. A common approach constructs label-free reward signals from multiple sampled rollouts using majority voting, but existing methods typically rely on a fixed, large rollout budget for every query. This fixed allocation is inefficient because many queries reach consensus well before the rollout budget is exhausted. In this work, we introduce \textbf{AdaPO}, which replaces fixed-budget majority voting with an adaptive two-stage voting procedure that moves from electing to confirming when a leader is statistically dominant, and stops once the posterior error of accepting that leader is sufficiently low. AdaPO is plug-and-play with standard policy optimization algorithms such as PPO and GRPO, and it is also compatible with supervised fine-tuning at test time. Our rigorous theoretical results show that, under the symmetric categorical noise model with known likelihood parameters, AdaPO's electing-stage trigger coincides with the classical sequential probability ratio test (SPRT), while the confirming-stage rule yields a principled posterior-threshold stopping mechanism. Across representative reasoning benchmarks, AdaPO substantially reduces compute, achieving over 40\% token savings on GPQA while maintaining competitive accuracy. The source code will be open upon acceptance at \url{https://open-upon-acceptance}.

Graph-level anomaly detection (GLAD) aims to identify graphs that deviate significantly from the majority and plays a crucial role in applications such as molecular analysis and fraud detection. While recent advances have achieved competitive performance, existing approaches mainly follow a dataset-specific paradigm, requiring substantial in-domain data and training cost when applied to new application scenarios. This limits their scalability and practicality in real-world applications where labeled data is scarce and diverse domains are continuously emerging. In this paper, we investigate the problem of generalist GLAD, which seeks to learn a single unified model capable of detecting anomalous graphs across multiple domains with minimal supervision on the target data. This problem introduces key challenges, including learning transferable patterns from heterogeneous graph datasets and effective adaptation under limited supervision. To address these challenges, we propose GenGLAD, a generalist GLAD approach that leverages discriminative subgraph extraction as the core mechanism to learn transferable anomaly knowledge and enable efficient adaptation to new domains. Specifically, GenGLAD employs a graph neural network-based discriminative subgraph extraction model to learn the anomaly-discriminative substructures that distinguish anomalous and normal graphs across diverse domains. During the test-time adaptation phase, multi-dimensional discrepancies between the extracted subgraph and multi-level contextual information are calculated to characterize anomalies from multiple perspectives. For efficient adaptation, a lightweight scoring module is introduced to automatically decide the most informative signals, improving robustness against misleading patterns. Extensive experiments on diverse benchmark datasets demonstrate that the proposed approach achieves strong performance, superior generalization ability, and improved data efficiency compared to existing methods.

We design the first regret guarantees for robust dynamic pricing which decouples the dependence on the corruption $C$ and the time horizon $T$. In dynamic pricing, a seller with unlimited supply of a good interacts with a stream of buyers over $T$ rounds, with the goal of maximizing revenue. At each round $t$, the seller posts a price $p_t$, and the buyer purchases the good only if their unknown valuation $v^\star$ exceeds this price. The seller observes only the binary feedback $\mathbb{I}[p_t \leq v^\star]$, indicating whether a sale occurred. In the robust pricing setting, a malicious adversary is allowed to corrupt this feedback in at most $C$ rounds. Even if the learner knows the corruption $C$, the best known regret bound is $\mathcal{O}(C\log\log T)$ by Gupta et al. [2025]. They left as an open problem to "decouple'' the dependence on $C$ and $T$. In this work, we resolve this open problem. In particular, we develop a robust variant of binary search that achieves regret $\mathcal{O}(C+\log T)$ when the corruption $C$ is known and $\mathcal{O}(C+\log^2 T)$ when the corruption is unknown.

Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike threshold-based binarisation, which produces brittle masks under test-time distribution shift (TTDS), TDA allows anomalies to be characterised as disruptions to global structure rather than local fluctuations. We introduce TopoOT, a topology-aware optimal transport (OT) framework for source-free test-time adaptation in AS. Our key innovation is Optimal Transport Chaining, which sequentially aligns persistence diagrams (PDs) across thresholds and filtrations, yielding geodesic stability scores that identify features consistently preserved across scales. These stability-aware pseudo-labels supervise a lightweight head updated online using only unlabelled target samples, without access to source data or target labels, with OT-consistency and contrastive objectives, ensuring robust adaptation under TTDS. Across standard 2D and 3D anomaly detection benchmarks, TopoOT achieves state-of-the-art performance, outperforming second-best methods by up to +24.1\% mean F1 on 2D datasets and +10.2\% on 3D AS benchmarks.

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing phase-space dynamics of time-series data, where persistent homology can reveal loops associated with periodicity. However, rigorous statistical uncertainty quantification for these features remains underdeveloped. First, we analyze the topology of time-delay embeddings, showing that the embedded trajectory is homotopy equivalent to a circle ($S^1$) for periodic signals and contractible for non-periodic ones. We also prove a positive lower bound on the embedding reach, ensuring stable topological features. Second, we develop a subsampling approach to construct confidence bounds for persistence diagrams. Under standard manifold regularity conditions, we derive data-dependent bounds with asymptotic guarantees. Finally, we propose Topological Periodicity Test (TopPT), a hypothesis testing framework for periodicity with asymptotically controlled type I and type II error rates. Experiments on bounded-error synthetic data show that raw TDA detects periodic alternatives while avoiding false rejections on structured non-periodic signals, and that the robust rule is conservative after interpolation-error correction. On PhysioNet Fantasia and BIDMC respiratory waveforms, TDA detects most records but only a subset of local windows, unlike scalar periodogram baselines.

Test-time reinforcement learning (TTRL) has emerged as a promising paradigm for adapting large reasoning models (LRMs) on unlabeled test inputs, using self-consensus rewards derived from majority voting over sampled rollouts. However, majority voting can mistake popularity for correctness: a spurious yet high-frequency unverified consensus may become a biased reward signal, causing test-time RL to reinforce frequent but wrong answers and collapse into an incorrect mode. We address this false-popular failure mode with T^3RL (Tool-Verification for Test-Time Reinforcement Learning), a verification-aware test-time RL framework. T^3RL grounds pseudo-label construction in external tool evidence. Concretely, a verifier uses external tool evidence, such as code execution, to upweight verified rollouts during verification-aware voting, producing more reliable pseudo-labels for training. Across mathematical reasoning benchmarks of varying difficulty, including MATH-500, AMC, and AIME 2024, and diverse backbone families, T^3RL significantly improves over TTRL, with stronger performance on harder problems. More broadly, T^3RL is positioned as a verified online data synthesizer, highlighting the role of test-time tool verification in reliable online adaptation.

Time series transformers have achieved strong forecasting performance, yet fundamental questions about their internal mechanisms remain unanswered: among self-attention and feed-forward networks (FFN), which component constructs temporal features? Why does a simple linear model outperform transformers? Why does patching help? We propose a temporal probing framework consisting of 15 token-level diagnostic tasks to trace information flow across transformer components. Applied to 5 architectures across 8 benchmarks, we find that temporal feature construction is not inherently tied to any single component—it emerges from the interaction between tokenization strategy and architectural design. In PatchTST, FFN dominates feature construction across all 8 datasets, with a $3.2\times$ mean ratio over attention. Even when attention is completely removed, FFN's feature construction capability is preserved or enhanced, indicating that attention is not essential for temporal feature construction. Conversely, iTransformer's variate-level attention dominates over FFN, and CATS's cross-attention is responsible for nearly all feature transfer. Point-wise tokenization ($P=1$) structurally deactivates FFN, explaining why early transformers lagged behind linear models. These findings unify contradictory results across DLinear, PatchTST, attention-free models (TSMixer, PatchMLP), and CATS within a single framework.

Adapting CLIP for anomaly detection on unseen objects has shown strong potential in a zero-shot manner. Existing methods typically rely on a single textual space to align with visual semantics across diverse objects and domains. The indiscriminate alignment hinders the model from accurately capturing anomaly semantics. We propose TokenCLIP, a token-wise dynamic framework that aligns each visual token with learnt textual subspaces corresponding to its visual characteristics. However, explicitly assigning a unique learnable textual space to each token is computationally intractable and prone to insufficient optimization. We instead expand the token-agnostic textual space into a set of orthogonal subspaces, and then dynamically assign each token to a subspace combination guided by semantic affinity, which jointly supports customized and efficient token-wise adaptation. To this end, we formulate dynamic alignment as an optimal transport problem, where all visual tokens in an image are transported to textual subspaces under the cross-modal cost matrix. \textbf{The marginal constraint and minimal cost objective of OT ensure sufficient optimization across subspaces and encourage them to focus on different semantics.} Solving the problem yields a transport plan that adaptively assigns each token to semantically relevant subspaces. Extensive experiments show that the textual subspaces naturally specialize in different semantics, such as foreground and background, to promote fine-grained anomaly learning. The comparison between baselines shows the superiority of TokenCLIP.

Probabilistic long-term time series forecasting requires estimating a distribution over future trajectories under practical deployment constraints, where inference latency and stability can be as critical as forecast quality. Existing diffusion-based forecasters provide expressive uncertainty modeling, yet their iterative denoising incurs substantial horizon insensitive runtime overhead, which limits real time long-term use. In contrast, one-shot generative models such as VAEs and flows are computationally efficient but often struggle to capture complex multi-modal structure and heavy tailed uncertainty. We propose \textbf{ToLD}, an efficient time‑series forecasting framework built upon \textbf{to}kenized truncated \textbf{l}atent \textbf{d}iffusion to enable fast and reliable long term generation. ToLD adopts a tokenized conditional latent modeling and performs compact token-wise refinement via a few-step truncated latent diffusion process, where the diffusion noise is injected in a context-dependent manner to model non-stationary uncertainty. To reduce train test mismatch in multi-sample forecasting, we further introduce a score distillation scheme that learns a target-free scoring function for test-time candidate ranking. Experiments on eight real-world datasets show that ToLD improves both point accuracy and probabilistic quality over state-of-the-art, achieving up to \textbf{4.3\%} MSE improvement and \textbf{19.3\%} CRPS reduction on long-term tasks with minimal additional inference overhead.

The prevailing Direct Forecasting (DF) paradigm dominates Long-term Time Series Forecasting (LTSF) by forcing models to predict the entire future horizon in a single forward pass. While efficient, this rigid coupling of output and evaluation horizons necessitates computationally prohibitive re-training for every target horizon. In this work, we uncover a counter-intuitive optimization anomaly: models trained on short horizons—when coupled with our proposed Evolutionary Forecasting (EF) paradigm—significantly outperform those trained directly on long horizons. We attribute this success to the mitigation of a fundamental optimization pathology inherent in DF, where conflicting gradients from distant futures cripple the learning of local dynamics. We establish EF as a unified generative framework, proving that DF is merely a degenerate special case of EF. Extensive experiments demonstrate that a singular EF model surpasses task-specific DF ensembles across standard benchmarks and exhibits robust asymptotic stability in extreme extrapolation. This work propels a paradigm shift in LTSF: moving from passive Static Mapping' to autonomous Evolutionary Reasoning.

Recent advances in Vision-Language Models (VLMs) have achieved impressive performance across many tasks, yet prior studies report unsatisfactory performance when applying large language or multimodal models to finding abnormal patterns in sequential data. Public anomaly detection benchmarks typically provide interval annotations but not natural-language rationales, making it difficult to fine-tune VLMs to produce grounded, interpretable decisions. To address this gap, we construct VisAnomBench, an explanation-augmented curated benchmark built from public time-series datasets and augmented with high-quality anomaly explanations selected from multiple large VLMs using fine-grained, task-specific rewards. Building on this benchmark, we present VisAnomReasoner, a parameter-efficient VLM for time-series anomaly detection. Experimental results on VisAnomBench show that VisAnomReasoner achieves more accurate anomaly localization and consistently outperforms all baselines, with improvements of at least 21.23 and 23.87 percentage points in precision and F1, respectively. Additional experiments on the TSB-AD-U benchmark demonstrate strong cross-benchmark generalization, with VisAnomReasoner improving precision and F1 by 9.57 and 13.39 percentage points, respectively. Dataset, code, and model weights will be open-sourced.

Multivariate time series forecasting is important in real-world applications, but practical data often show both temporal and spectral non-stationarity. Existing methods may treat severe spectral drift as informative evolution, allow unreliable spectral components to contaminate temporal representations through credibility-agnostic time--frequency interaction, and infer cross-variable dependencies from noisy local correlations, which may lead to spurious long-term dependencies. To address these issues, we propose TFNS, a dual-stream time--frequency framework for suppressing unreliable spectral evidence under non-stationarity. Specifically, we introduce a Spectral Credibility Estimator to quantify patch-level spectral stability and softly suppress low-credibility frequency components for more reliable frequency modeling; a Credibility-Gated Cross-Interaction module to enable bidirectional time--frequency enhancement while adaptively constraining cross-domain information injection according to spectral reliability; and a Spectral Cointegration Graph to capture stable long-term cross-variable structure in the spectral domain while mitigating spurious dependencies under non-stationary drift. Together, these modules form a progressive pipeline from local spectral purification to reliability-aware cross-domain interaction and robust long-term structure modeling. Experiments on 11 benchmarks show that TFNS achieves state-of-the-art performance, ranking first in 44/55 MSE and 43/55 MAE comparisons.

Time-series data are inherently multiscale, spanning diverse temporal granularities from coarse trends to fine-scale dynamics. However, existing time-series generative models provide limited control over the temporal granularity of both inputs and outputs, restricting their ability to condition on user-provided coarse sketches and generate samples at a desired target granularity. To address this, we introduce TimeTok, a unified framework for Granularity-Controllable Time-Series Generation (GC-TSG), which generates time series at $any$ target granularity from $any$ coarser input (e.g., rough sketches) or without conditioning. At the core of TimeTok is a hierarchical tokenization strategy that maps time series into an ordered sequence of tokens, from coarse to fine temporal granularity. Our autoregressive generation process operates across these granularity levels, producing token blocks that are decoded back into continuous time series. This design naturally enables GC-TSG within a single framework, where controlling the number of token blocks provides explicit control over output detail. Experiments show that TimeTok excels at GC-TSG tasks while achieving state-of-the-art performance in standard generation. Furthermore, we showcase TimeTok's potential as a foundational tokenizer by training on multiple datasets with heterogeneous temporal granularities, verifying strong transferability that consistently outperforms models trained on individual datasets. To our knowledge, this is the first unified framework that covers the full generative spectrum for time series, offering a valuable foundation for models that benefit from diverse temporal granularities.

Most time-series foundation models operate on fixed temporal grids, representing signals as vectors, tokens, or patches and learning maps between discretized observations. This grid-to-grid view is convenient for standard forecasting, but it is not the natural object for reusable time-series modeling, where temporal resolution, forecast horizon, and query locations may change across tasks and deployments. We argue that time-series foundation models should instead learn sample-conditioned function-to-function operators. Given finite observations of an underlying signal, such an operator maps the observed context to an output function that can be evaluated at user-specified times. We propose \textbf{TimeOperator}, a compact branch-trunk backbone that realizes this view with a shared context encoder, spectrally informed query features, context-adaptive trunk parameters, and multi-basis temporal responses. Forecasting and imputation are handled by evaluating the same operator on different query sets, while classification reuses the shared context representation. Across deterministic and probabilistic forecasting, imputation, and classification benchmarks, TimeOperator is competitive with existing time-series foundation models. Further analyses show that cross-frequency and cross-horizon prediction can be handled by changing only the query set, rather than changing the decoder or relying on post-hoc resampling.

Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their ability to accurately predict both the expected trajectory and its uncertainty in non-stationary time series. Motivated by Evolutionary Spectra (ES) theory, we propose \textbf{TimeES}, a general framework that enables probabilistic and deterministic forecasting via the evolutionary spectra theory. Specifically, we derive a parameterizable evolutionary spectra formulation, recasting non-stationary random process modeling as learning an evolving representation modulated by random variables. Furthermore, we reduce the complexity of the estimated spectra from $\mathcal{O}(NM)$ to $\mathcal{O}(NK)$, where $K \ll M/2$, by exploiting Hermitian symmetry and energy-guided frequency selection. Based on a simple linear backbone, our proposed TimeES achieves consistent state-of-the-art performance across both deterministic and probabilistic forecasting tasks, with high efficiency and interpretability. Code is available at: \url{https://anonymous.4open.science/r/TimeES}.

Time series analysis underpins forecasting, monitoring, and decision making in domains such as finance and weather, where solving a task often requires both numerical accuracy and contextual reasoning. Recent progress has moved from specialized neural predictors to approaches built on LLMs and foundation models that can reason over time series inputs and use external tools. However, most such systems remain execution-centric: they focus on solving the current instance but learn little from exploratory execution. This is especially limiting in verifiable numeric settings, where multiple candidate executions and tool-use procedures may all be task-valid yet differ sharply in quantitative quality, and where early success can trigger tool-prior collapse that suppresses further exploration. To address this limitation, we present TimeClaw, an exploratory execution learning framework that turns exploratory execution into reusable hierarchical distilled experience through a four-stage loop: Explore, Compare, Distill, and Reinject. TimeClaw combines metric-supervised exploratory execution learning, task-aware tool dropout, and hierarchical distilled experience for inference-time reinjection, while keeping the base model frozen and avoiding online test-time adaptation. In an MTBench-aligned evaluation with 17 tasks that span finance and weather prediction and reasoning tasks, TimeClaw delivers consistent gains over the baselines. These results suggest that, for scientific systems, the bottleneck is not only execution-time capability, but how exploratory experience is compared, distilled, and reused.