NeurIPS 2026 论文列表

Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present L$^2$EAP (LLM-in-Lean Environment Agentic Prover), an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. L$^2$EAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement. By decomposing complex problems into smaller units, the system bridges formal proof construction with informal blueprints through continuous interaction with the Lean compiler. To provide a rigorous evaluation beyond increasingly saturated benchmarks, we introduce Lean-IMO-Bench, a benchmark of IMO-style problems formalized in Lean, with short statements yet highly non-routine and multi-step proofs across a wide range of difficulty levels. Empirically, on the latest 2025 Putnam Competition, an annual mathematics competition for undergraduate students in North America, L$^2$EAP solves all 12 problems, matching recent breakthroughs by frontier formal mathematical models; on Lean-IMO-Bench, L$^2$EAP raises the one-shot formal solve rate of general-purpose LLMs from below 10\% to 70\%. It also compares favorably to the best baseline performance of 48\% attained by a specialized system with dedicated ATP components that achieved gold-medal-level performance at the 2025 IMO.

Probabilistic time-series forecasting requires models that simultaneously capture structured temporal dynamics, expressive uncertainty, and efficient inference, yet existing approaches fall short of this goal: latent dynamical models impose structure but rely on restrictive generation mechanisms, while modern generative methods such as diffusion and flow matching achieve flexibility at the cost of iterative and computationally expensive sampling. We introduce the Koopman Generative Operator (KGO), a probabilistic forecasting method that conceptualizes prediction as the evolution of structured uncertainty. KGO integrates three core components: (1) Koopman Patch Embedding (KoPE) for temporally consistent latent trajectory extrapolation; (2) Koopman Flow Matching (KoFM), which enables fast, single-step generation through a closed-form matrix exponential in a Koopman latent space, bypassing iterative sampling; and (3) an Adaptive Uncertainty Gate (AUG), which provides calibrated predictions by adapting uncertainty per-variable and per-horizon, corresponding to a learned decomposition of aleatoric uncertainty without manual tuning. By unifying these components, KGO achieves state-of-the-art accuracy across the majority of ProbTS datasets, outperforming existing methods on 12/17 benchmarks in CRPS and 11/17 in NMAE. Further, by eliminating iterative sampling, KGO delivers at least a 25$\times$ reduction in inference time compared to iterative generative models. These results establish KGO as a practical, principled, and highly scalable framework for next-generation probabilistic forecasting.

Modern LLMs continue to exhibit significant variance in behavior across languages, such as being able to recall factual information in some languages but not others. While typically studied as a problem to be mitigated, in this work, we propose leveraging this cross-lingual inconsistency as a tool for interpretability in mixture-of-experts (MoE) LLMs. Our knowledge localization framework contrasts routing for sets of languages where the model correctly recalls information from languages where it fails. This allows us to isolate model components that play a functional role in answering about a piece of knowledge. Our method proceeds in two stages: (1) querying the model with difficult factual questions across a diverse set of languages to generate "success" and "failure" activation buckets and then (2) applying a statistical contrastive analysis to the MoE router logits to identify experts important for knowledge. To validate the necessity of this small number of experts for answering a knowledge question, we deactivate them and re-ask the question. We find that despite only deactivating about 20 out of 6000 experts, the model no longer answers correctly in over 40% of cases. Generally, this method provides a realistic and scalable localization approach to increasingly complex LLMs, but also suggests redundant and highly dispersed knowledge parameterization in MoEs.

Large language models frequently ignore in-context evidence that contradicts their parametric priors, producing answers that reflect default beliefs rather than the supplied passage, a phenomenon termed *knowledge conflict*. This failure is commonly attributed to insufficient encoding of the contextual signal. We challenge this explanation. Through systematic, layer-by-layer analysis in a controlled multi-hop question-answering setting, we show that models faithfully encode the context-supported answer in their intermediate representations, yet suppress it in the final layers before generation. We term this *late-layer reversal*: the representational support for the evidence answer rises through the middle layers, then collapses in the final ~40\% of the network. To explain this phenomenon, we identify a *Dual-Track* computational structure within the transformer's hidden state. A *knowledge direction*, recovered by a learned linear probe, encodes the contextually supported answer; a nearly orthogonal *output direction*, aligned with the unembedding geometry, determines the model's prediction. These two directions are causally severed: interventions along the knowledge direction produce no change in output, whereas targeted suppression of prior-restoring computation along the output direction reliably causes the model to follow the contextual evidence. Our findings hold across nine model-dataset combinations and reveal that knowledge conflict failures arise not because models fail to represent contextual knowledge, but because their generation pathway declines to consult it.

At deployment, a multivariate forecaster may expose only a recent input window and a frozen point prediction, with no access to ground truth, calibration residuals, repeated inference, or model internals. We study deployment-constrained forecast risk localization: ranking future timesteps by likely error before they are observed. We introduce SubDx, a zero-parameter diagnostic that audits the forecast against the local cross-channel subspace of the input history. Each predicted channel vector receives an off-subspace residual score, computed with no labels, no learned parameters, and less than 1% runtime overhead on Traffic. Under a linear factor model, we derive closed-form score distributions and a two-population AUROC expression showing how heterogeneous off-subspace error visibility makes the ranking identifiable. On Traffic (N=862), SubDx reaches within-horizon AUROC 0.90 and reduces MSE by 62% at 50% coverage; on Solar (N=137), it reaches AUROC 0.85 with 67% MSE reduction. The same post-hoc score applies to frozen pretrained forecasters, with Chronos reaching AUROC 0.838 on Traffic without fine-tuning. Across trained backbones, pretrained models, and synthetic controls, the results show that local cross-channel consistency can provide a practical abstention signal for redundant multivariate systems.

Long-term conversational memory poses a fundamental system challenge for LLM agents: reasoning over all past interactions improves coverage but incurs prohibitive token costs and noise, while retrieval-based methods are efficient yet often fail on multi-hop and temporal questions. Existing multi-step retrievers partially address this gap, but typically operate over an ever-growing textual history, causing context expansion and noise accumulation across iterations. We propose MemR$^3$, a backend-agnostic closed-loop controller that reformulates conversational memory retrieval as explicit stateful decision-making. At each iteration, MemR$^3$ maintains an evidence-gap state consisting of grounded information (evidence) and unresolved information requirements (gaps), and uses this state to route among three actions: retrieve, reflect, and answer. Newly retrieved snippets are incorporated into the state and then masked from subsequent prompts, so the model conditions on a compact summary of progress rather than the full retrieval history. This design turns multi-step memory retrieval into a bounded, inspectable control process whose query-time context scales with the state instead of raw accumulated text. Experiments on LongMemEval$_s$ show that MemR$^3$ surpasses implicit multi-step retrieval baselines and often approaches or exceeds full-context prompting while using only 1%-5% of the full-context tokens on long conversations. On LoCoMo, MemR$^3$ consistently improves over its underlying RAG- and Zep-based memory backbones. These results suggest that explicit evidence-gap tracking is an effective abstraction for token-efficient conversational memory.

Large language models (LLMs) have shown promise in scientific discovery tasks such as protein optimization, but remain limited by the lack of a mechanism for persistent and reusable knowledge accumulation. Existing approaches adapt LLMs through parameter optimization or trajectory refinement, but in both cases, knowledge remains implicit, either encoded in opaque model weights or scattered across transient solution histories. As a result, knowledge cannot be systematically inspected, attributed, or reused. We propose \emph{KnowEvo}, a framework that treats externalized knowledge itself as the optimization target. Our key insight is that scientific knowledge is inherently modular: multiple interacting mechanisms jointly determine the design outcomes. This makes knowledge evolution fundamentally challenging, as improvements cannot be attributed to individual components in isolation. To address this, \emph{KnowEvo} represents knowledge as executable expertise blocks and organizes their refinements into strategy mutation trees, enabling structured exploration over a combinatorial knowledge space. The framework combines a forward exploration phase that adaptively allocates evaluation budget across strategy variants with a backward revision phase in which an agentic sandbox converts rollout evidence into localized program improvements. This design enables persistent accumulation, attribution, and refinement of mechanistic expertise across iterative experimentation. We evaluate \emph{KnowEvo} on protein optimization tasks including thermostability and solubility. Results show that knowledge evolution consistently improves over initial expert heuristics and outperforms monolithic program evolution and prior LLM-guided evolution baselines across ranking metrics such as pass@$k$, MRR, MAP, and NDCG@5. Codes are available at \url{https://anonymous.4open.science/r/KnowEvo-6E3B/}.

Cooperative multi-agent reinforcement learning under task variability requires both identifying which task an episode belongs to and adapting the learning algorithm to that identity. Recent class-aware methods address the first half of this problem by clustering trajectories into latent task classes and feeding the class label to the agent policy. They leave the second half largely untouched: the Bellman update and the credit assignment performed by the value mixer remain identical across all task classes. We show empirically that, even when task identity is recovered with high accuracy, the Bellman dynamics across classes diverge sharply, with simple classes saturating early and harder classes sustaining large temporal-difference residuals and large cross-agent value disagreement. Building on this observation, we propose Know Your Task, Learn It Right (KYT), a task-aware extension of value factorization that injects per-class learning signal into the Bellman update itself. KYT maintains a lightweight tracker that summarizes the per-class TD-error and cross-agent value spread without any extra network, and uses the tracker in two places: an optimistic target that adds a bounded per-class exploration bonus, and a class-conditioned mixer that modulates credit assignment through a softplus-gated affine layer preserving the IGM property. Across StarCraft II micromanagement benchmarks including SMACv2 and the unit-combination suite SurComb, KYT outperforms strong class-aware and exploration-aware baselines, with the largest gains concentrated on the hardest task classes that current methods underfit.

Memory enables long-context dialogue agents to maintain user state across many turns, but it also introduces a fundamental source-choice problem: grounding the response in the immediate context or retrieved prior memory? A wrong choice incurs two complementary costs: neglecting valid aged-out evidence, or overwriting sufficient context with stale memory. Existing systems and benchmarks largely conflate retrieval with source choice, relying on the model to resolve it implicitly and leaving this critical decision largely unexplored. In this paper, we introduce MSBench, a controlled benchmark that isolates source choice by pairing questions answerable exclusively from context with those requiring prior memory. Under this protocol, strategies that depend on the model's implicit judgment exhibit sharply degraded performance, exposing the limits of leaving source choice ungoverned. To this end, we propose the Memory-Source Reasoner (MSR), which frames source choice as an explicit metacognitive decision: it reasons about contextual sufficiency, answers directly when appropriate, and selectively retrieves missing evidence otherwise. Experimental results show that MSR achieves the best overall accuracy and selection accuracy across four answer backbones. On the primary GPT-5-mini run, it improves over the best non-MSR baselines by 12.6 points in overall accuracy and 6.3 points in selection accuracy. Our benchmark, code, prompts, and evaluation scripts are available at https://anonymous.4open.science/r/msbench-msr-0C72.

Post-LayerNorm Transformers have seen limited practical adoption due to enduring difficulties in scaling them to large depths. While prior research has focused on stabilising Post-LayerNorm by improving conditioning at initialisation, stability often deteriorates when models are trained with large learning rates, forcing additional compromises. In the decoder-only settings we study, existing Post-LayerNorm methods fail to outperform strong Pre-LayerNorm baselines. We propose KiteNorm, a novel normalisation method designed to break this trend. KiteNorm achieves stability through residual scaling and a regularisation technique based on hidden-state variance. Beyond stabilisation, KiteNorm learns separate scales for the skip and residual branches in each sublayer, improving performance. Across decoder-only Transformers up to 1B parameters, KiteNorm remains stable throughout training and consistently outperforms leading baselines, with scaling laws favouring KiteNorm across depth, width, batch size, and training budget. Ablations show that each component is necessary for the full stability and performance gains. We offer theoretical insights into KiteNorm through a new perspective on the gradient vanishing problem in Post-LayerNorm, linking the underlying hidden-state expansion to rank collapse.

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher–Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Demo and code are available in the supplementary materials.

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on Gaussian processes, kernel machines, linear models, or linearized neural approximations, leaving a gap between theory and the nonlinear models used in practice. We develop a kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data. Our approach uses kernels over the parameter space to induce reproducing-kernel Hilbert space structures over the corresponding model class, yielding confidence bounds for models trained with broad classes of regularized convex losses. We show how these bounds can support convergence guarantees for nonlinear acquisition and surrogate models, including randomized regularized policies that select points by maximizing a trained random model. These results provide a unified route to analyzing nonlinear parametric models in Bayesian optimization and related adaptive optimization settings.

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because it enables fast, high-quality generation without distilling a large pretrained diffusion model, but its theory is currently understood mainly for Gaussian kernels, where the drift coincides with smoothed score matching and is identifiable. Our gradient-based reformulation exposes this score-based structure for general kernels: the resulting drift is the score difference between kernel-smoothed data and model distributions, yielding identifiability for characteristic kernels and a smoothed-KL descent interpretation of the drifting dynamics. Since kernel gradients are intrinsic tangent vectors, the same construction extends naturally to Riemannian manifolds and to discrete data via the Fisher-Rao geometry of the probability simplex. Across spherical geospatial data, promoter DNA and molecule generation, kernel-gradient drifting enables state-of-the-art one-step generation beyond the Euclidean setting without distillation.

Value overestimation is a central challenge in offline reinforcement learning (RL), arising when Bellman backups propagate out-of-distribution (OOD) errors that lead to catastrophic inflation of $Q$-values. Prior approaches address this issue by encouraging the learned policy to stay close to the behavior policy, but they often result in suboptimal policies or require significant training complexity. More recent work attempts to tackle this issue through minimal modifications to the critic network, yet it remains limited in either theoretical grounding or practical implementation. In this work, we present Kernel Value Regression (KVR), a simple critic regularization method based on kernel regression. KVR builds on the vanishing extrapolation property of kernel ridge regression, which encourages value estimates to decay toward zero away from the data support. This inductive bias naturally suppresses $Q$-values for OOD actions without auxiliary regularizers, providing a structural mechanism for addressing value overestimation. Using random Fourier features, KVR can be incorporated into standard actor-critic algorithms with only minimal modifications. We empirically demonstrate that these properties persist in complex offline RL environments, leading to strong performance across diverse tasks in the D4RL and OGBench benchmarks.

The Maximum Mean Discrepancy (MMD) is a cornerstone statistic for nonparametric two-sample testing, but its test power is dictated entirely by the chosen kernel. Because any fixed kernel inherently fails to distinguish certain distributions, the kernel must be dynamically optimised. However, data-driven optimisation violates the foundational i.i.d. assumption, forcing a strict trade-off in existing frameworks. Ratio criteria ignore this dependence, inducing overfitting and variance collapse on rich kernel classes. Conversely, aggregation methods bypass the dependence using finite grids, but this strategy cannot scale to continuous search spaces like deep kernels. To break this dichotomy, we establish data-driven kernel selection as a model selection problem. We propose Complexity-Penalised MMD (CP-MMD), a criterion derived from a uniform concentration inequality (extending Maurer's framework to the two-sample setting) that bounds the post-optimisation distribution by penalising the empirical MMD with the complexity of the kernel search space. Because this penalty mathematically absorbs the cost of optimisation, CP-MMD enables direct, grid-free maximisation over continuous parametric classes, including scalar bandwidths, polynomial coefficients, and deep network parameters. By formally accounting for optimisation complexity, we theoretically guarantee that CP-MMD maximises true test power while ensuring unconditional Type-I validity. Consequently, CP-MMD enables grid-free kernel selection across linear, polynomial, and deep regimes, matching or exceeding state-of-the-art test power.

Operator learning has experienced a shift toward attention-based architectures. This trend has more recently extended to physics-informed operator learning, where stacked cross-attention blocks add considerable computational cost relative to the foundational PI-DeepONet. We ask whether this complexity is necessary. Starting from the DeepONet branch-trunk decomposition, we replace the bilinear readout with a single softmax-weighted readout in which the trunk emits a query vector and the branch emits a set of key-value pairs—a structure we show admits universal approximation via reduction to a simplex-bilinear form. The resulting architecture, KerONet, uses no iterated attention, layer normalization, or explicit learnable projection matrices. Under a unified hyperparameter optimization protocol with a strict $200{,}000$-parameter budget, we evaluate KerONet alongside iterated-attention architectures (PIT, PINTO) and PI-DeepONet on four canonical 1D PDEs whose solutions range from globally smooth to sharply localized. KerONet outperforms PIT and PINTO on every PDE, across all five seeds, in accuracy (approximately $2$–$4\times$ lower rel-$L^2$ error), reproducibility ($2$–$31\times$ lower standard deviation), and speed ($1.8$–$4.4\times$ faster training time). Against PI-DeepONet, KerONet shows substantial gains where input-dependent localized features dominate ($2.5$–$8\times$ lower error on Burgers and Allen-Cahn) while exhibiting comparable accuracy on smoother operators (advection and diffusion-reaction)–a balance the iterated-attention architectures do not achieve. Our findings demonstrate that iterated cross-attention is not necessary to realize the benefits of query-dependent feature mixing in physics-informed operator learning.

Training-free safeguards for text-to-image diffusion models often rely on a reusable safety signal, such as an unsafe direction or global toxic subspace, applied broadly across prompts. We provide a controlled geometric analysis of this global-unsafety assumption and reveal a consistent coverage-selectivity trade-off: compact unsafe subspaces fail to cover heterogeneous unsafe semantics, whereas broader aggregation increasingly distorts safety-adjacent benign prompts. Motivated by this finding, we propose CALM (Counterfactual Adaptive Local Modulation), a training-free safeguard that replaces uniform global removal with prompt-local counterfactual correction. Using matched unsafe-benign anchors, CALM routes each prompt to active unsafe categories, minimally edits only violating token representations toward the safe side, and suppresses positively aligned unsafe residual components. Across broad evaluation, CALM improves unsafe-content suppression while preserving benign utility, demonstrating that local counterfactual correction provides a more selective alternative to global unsafe-signal removal.

LLMs are increasingly applied to cybersecurity workflows, where they are expected to translate analysts' intent into tool invocations. However, existing evaluations focus on knowledge-based assessments or end-to-end agentic tasks, and do not directly measure LLMs’ ability to generate executable commands for real-world cybersecurity tools. This gap is critical because cybersecurity operations rely on strict command-line interfaces (CLIs), where minor syntax errors, incorrect flag-value bindings, or argument misordering can invalidate execution. We introduce KaliBench, a fine-grained benchmark and dataset for natural-language-to-CLI translation on Kali Linux, comprising 8,504 query-command pairs spanning 1,642 tools across 23 capability dimensions and 5 security phases. KaliBench is constructed via a manuscript-grounded pipeline with deterministic canonicalization and alias-aware evaluation, enabling precise and reproducible assessment of tool selection and argument construction. To ensure both semantic correctness and practical executability, we develop a multi-stage verification pipeline that combines LLM-based validation, sandboxed terminal execution, and human-in-the-loop refinement. Building on these fine-grained, deterministic signals, KaliBench further enables runtime-free verifiable rewards for training. Across three evaluation modes and over 20 general-purpose and security-focused LLMs, no model exceeds 35\% exact-command accuracy in the unrestricted setting, highlighting the difficulty of accurate CLI-based cybersecurity tool use without explicit tool hints. We further show that supervised fine-tuning and reinforcement learning with verifiable rewards derived from KaliBench significantly improve an 8B model and achieve performance comparable to a 685B MoE model. KaliBench will be publicly released.

Inherent temporal heterogeneity, such as varying sampling densities and periodic structures, has posed substantial challenges in zero-shot generalization for Time Series Foundation Models (TSFMs). Existing TSFMs predominantly rely on massive parameterization to absorb such heterogeneity, as their static tokenization and positional encoding schemes entangle diverse temporal patterns into a fixed representation space, encouraging memorization rather than adaptation. To address this limitation, we propose Kairos, a flexible and parameter-efficient TSFM dedicated to forecasting tasks, which decouples temporal heterogeneity from model capacity through a novel tokenization perspective. Kairos introduces a dynamic patching tokenizer and a mixture-of-size encoding that adapt observational granularity to local information density, enabling fine-grained temporal abstraction without increasing model width or depth. In addition, we design a multi-granularity positional embedding based on dynamic rotary encodings, which conditions on instance-level spectral features and temporal structure induced by dynamic patching tokenization, allowing robust modeling of diverse temporal dependencies. Trained on a novel Predictability-Stratified Time-Series (PreSTS) corpus, Kairos achieves superior zero-shot performance with substantially fewer parameters on two mainstream benchmarks, GIFT-Eval and Time-Series-Library.