NeurIPS 2026 论文列表

Low-rank factorization is a standard way to scale optimization in machine learning by replacing large matrix variables with compact factors. For positive semidefinite (PSD) variables, the symmetric Burer--Monteiro factorization (sBMF) writes $Z=XX^\top$ with a single low-rank factor $X$. A recent asymmetric alternative (aBMF) writes $Z=XY^\top$ and adds a quadratic penalty $(\gamma/2)\|X-Y\|_F^2$ to encourage symmetry. This split is attractive because it yields a biconvex objective with alternating convex subproblems, but its practical value depends strongly on how the penalty parameter $\gamma$ is chosen. We study a unified regularized aBMF framework and derive an explicit lower bound on $\gamma$ that guarantees exactness: under mild assumptions, any $\gamma$ above this threshold makes aBMF and sBMF share the same critical points. This gives a principled way to use the asymmetric formulation without altering the critical-point structure of the symmetric problem. In particular, it answers the open question of whether an exact penalty exists for asymmetric relaxation.

We study a stochastic bandit problem in which learning is split between two agents. In each round, a human observes rewards but can choose only between a pair of arms selected by an assistant, while the assistant observes the human's behavior but not realized rewards. We call this model the **assistive dueling bandit**. The human is modeled as a learning agent whose regret on any subset of arms is bounded by a function $g(T)$ unknown to the assistant. This is a natural model for recommender systems or AI assistants that must present a slate of options to a user who may be still learning about their own preferences. We provide a general reduction from assistive dueling bandits to the problem of **max-finding with imprecise feedback.** With it, we design assistant algorithms that cooperate with any $g(T)$-regret human to achieve a joint regret of $\tilde{\mathcal{O}}(K \cdot g(T/K))$, even without knowledge of $g(T)$. Crucially, when $g(T) \in \mathcal{O}(\sqrt{T})$, our method recovers the nearly optimal minimax rate of $\tilde{\mathcal{O}}(\sqrt{KT})$, implying that splitting up the responsibilities of learning in this way can be done without suffering any excess regret asymptotically. We complement our theoretical analysis with experimental evidence that this algorithm outperforms an assistant implemented via standard dueling bandit algorithms.

Recent advances in machine learning and large-scale biological data collections have revived the prospect of building a virtual cell, a computational model of cellular behavior that could accelerate biological discovery. One of the most compelling promises of this vision is the ability to perform in silico phenotypic screens, in which a model predicts the effects of cellular perturbations in unseen biological contexts. This task combines heterogeneous textual inputs with diverse phenotypic outputs, making it particularly well-suited to LLMs and agentic systems. Yet, no standard benchmark currently exists for this task, as existing efforts focus on narrower molecular readouts that are only indirectly aligned with the phenotypic endpoints driving many real-world drug discovery workflows. In this work, we present AssayBench, a benchmark for phenotypic screen prediction, built from 1,920 publicly available CRISPR screens spanning five broad classes of cellular phenotypes. We formulate the screen prediction task as a gene rank prediction for each screen and introduce the adjusted nDCG, a continuous metric for comparing performance across heterogeneous assays. Our extensive evaluation shows that existing methods remain far from empirically estimated performance ceilings and zero-shot generalist LLMs outperform biology-specific LLMs and trainable baselines. Optimization techniques such as fine-tuning, ensembling, and prompt optimization can further improve LLM performance on this task. Overall, AssayBench offers a practical testbed for measuring progress toward in-silico phenotypic screening and, more broadly, virtual cell models. Our benchmark is available at https://github.com/Genentech/AssayBench.

Long-horizon AI agents execute complex workflows spanning hundreds of sequential actions, yet a single wrong assumption early on can cascade into irreversible errors. When instructions are incomplete, the agent must decide not only whether to ask for clarification but when, and no prior work measures how clarification value changes over the course of execution. We introduce a forced-injection framework that provides ground-truth clarifications at controlled points in the agent's trajectory across four information dimensions (goal, input, constraint, context), three agent benchmarks, and four frontier models (three per benchmark; one on a single benchmark only; 84 task variants; 6,000+ runs). Counter to the common intuition that ``earlier is always better,'' we find that the value of clarification depends sharply on what information is missing: goal clarification loses nearly all value after 10% of execution (pass@3 drops from 0.78 to baseline), while input clarification retains value through roughly 50%. Deferring any clarification type past mid-trajectory degrades performance below never asking at all. Cross-model Kendall τ correlations (0.78-0.87 among models sharing identical task coverage; 0.34-0.67 across the full 4-model panel) confirm these timing profiles are substantially task-intrinsic. A complementary study of 300 unscripted sessions reveals that no current frontier model asks within the empirically optimal window, with strategies ranging from over-asking (52% of sessions) to never asking at all. These empirical demand curves provide the quantitative foundation that existing theoretical frameworks require but have lacked, and establish concrete design targets for timing-aware clarification policies. Code and data will be publicly released.

Computer-use agents turn visual predictions into executable GUI clicks, so uncertainty estimates must support rejection, calibration, miss-severity ranking, and spatial safety regions. Existing post-hoc uncertainty quantification (UQ) evidence is fragmented across isolated model and dataset pairs, leaving unclear whether UQ rankings remain stable when the agent, benchmark, or observable interface changes. We present a cross-regime benchmark for post-hoc UQ in single-step executable GUI grounding, covering a 27-method, seven-family open-weight matrix over 4 GUI-grounding VLM agents and 4 datasets, plus an 8-method API-compatible closed-source matrix across 3 frontier vendors where logits, hidden states, and attention maps are unavailable. The main finding is selective transfer: UQ rankings are stable across datasets for a fixed model, but degrade across model classes and observable interfaces. Hidden-state and density methods form the most stable open-weight family, while CoCoA-1MCA, Focus, sampling-based scores, and verbalised self-assessment win in specific regimes. Ranking transfer is strongest within a fixed model across datasets, reaching Spearman $\rho=0.969$ and averaging $\rho=0.705$ over 120 open-weight pairs. In contrast, open-weight to closed-source transfer is the strongest break: cross-tier Spearman $\rho$ averages only $+0.08$ over 12 vendor x dataset pairs on the shared 8-method intersection, indicating that UQ recommendations do not survive removal of internal model signals. Model-class transitions further reshape UQ preferences: attention, verbalised, and VLM-native families lose AUROC on every dataset, while density methods remain stable; a scale-only baseline shows that logit-family degradation on ScreenSpot-Pro is partly confounded by scale rather than grounding fine-tuning alone. Finally, conformal click regions show that score-level discrimination is not enough for deployment: locally weighted disks can shrink radii by 40-60% when the plug-in UQ is calibrated, but coverage can degrade under calibration-test or interface mismatch. We release per-item records, calibration/test splits, UQ scores, and analysis scripts as a reproducible basis for regime-aware UQ selection in GUI agents.

Events in spatiotemporal systems are ubiquitous, yet modeling their complex distributions remains challenging. Existing point process models often rely on strong structural assumptions and are typically limited to autoregressive, event-by-event prediction. As a result, they struggle to support broader inference tasks such as inverse inference, trajectory reconstruction, and recovery of missing event locations. We introduce Arbitrarily Conditioned Hierarchical Flows (ARCH), a hierarchical flow matching framework for spatiotemporal event modeling. ARCH is expressive enough to capture complex event distributions while enabling tractable and accurate computation of conditional intensities, which quantify instantaneous event risk. Built on a history-encoder-generative-decoder architecture, ARCH introduces a hybrid masking strategy for flexible conditioning on arbitrary observed events. This enables a unified treatment of forecasting, inverse inference, and partial trajectory recovery within a single framework. Experiments on synthetic and real-world datasets show that ARCH consistently outperforms existing baselines across both prediction and conditional inference tasks.

Aptamers are programmable DNA and RNA receptors with broad potential in diagnostics, therapeutics, biosensing, and molecular monitoring. Although they offer chemically synthesizable alternatives to protein-based binders in several applications, computational aptamer discovery remains much less mature, especially for small-molecule targets. This gap reflects three persistent evaluation failures: fragmented and inconsistent affinity annotations, unreliable negatives derived from untested rather than experimentally validated pairs, and random splits that leak related aptamers or recurring ligand identities across train and test sets. As a result, current benchmarks make it difficult to distinguish transferable aptamer-ligand recognition from dataset-specific shortcuts. We present AptaBench, the first curated, standardized, and leakage-aware benchmark for aptamer-small-molecule binding prediction with experimentally reported active and inactive measurements and paired classification and affinity-regression tasks. AptaBench integrates eight curated sources into 6,289 interaction pairs covering 1,610 DNA/RNA aptamers and 942 ligands. We standardize sequences, resolve ligands to canonical molecular representations, harmonize duplicate and conflicting records, and convert dissociation constants to p$K_d$. More than 30% of entries contain quantitative affinity values, while inactive labels are taken only from explicitly reported non-binding or low-affinity measurements rather than synthetic cross-pairing. AptaBench provides fixed in-distribution, molecule-disjoint, and aptamer-disjoint protocols reflecting practical discovery scenarios: prediction for unseen targets and evaluation of new candidate sequences. Across descriptor-based models, pretrained sequence and molecular encoders, and sequence-ligand fusion architectures, in-distribution evaluation substantially overestimates generalization. The best classifier reaches ROC-AUC 0.95 in-distribution, but drops to 0.87 for unseen molecules and 0.86 for unseen aptamers. Affinity prediction is more sensitive, with $R^2$ decreasing from 0.65 to approximately 0.30 under disjoint protocols. These results show that reliable progress in computational aptamer discovery requires broader chemical coverage, experimentally grounded inactive labels, and standardized quantitative annotations. By releasing curated data, fixed leakage-aware splits, reproducible baselines, and preprocessing code, AptaBench is poised to expose the generalization limits of existing models, challenge future sequence-molecule recognition methods, and provide a rigorous foundation for practice-oriented aptamer evaluation.

We study revenue-optimal posted-price design for GPU markets under a finite capacity $B$. We focus on two settings: \emph{sales}, where each purchase permanently consumes a vendor's GPU inventory, and \emph{rentals}, where each job occupies GPUs for a finite duration and then releases them. In both settings, the vendor must commit to an anonymous price menu before observing customers' valuation, GPU demand, and job duration. First, in the sales setting, we show that computing the optimal anonymous static menu is NP-hard, and that the common practice of linear pricing (per-GPU price) can be highly suboptimal. We develop three methods with varying approximation guarantees, all of which outperform linear pricing. Our main method is a convex program (CP) obtained via an ex-ante relaxation of the problem, which obtains a $\tfrac{1-\epsilon}{2}$ approximation to the optimum when the maximum GPU demand $\overline{N}$ satisfies $\overline{N}\leq \epsilon B$. Building on these results, we analyze the \emph{rental} model. We again show that linear pricing (per-GPU-hour price) is highly suboptimal, and design duration-aware posted-price policies based on slot-coupled ex-ante CP. Our \emph{Throttled CP-Menu Posted Pricing} (TCMPP) policy posts the CP-induced menu randomly and achieves a $\frac{1-\epsilon}{4}$ approximation. We further introduce a slackened version of the same convex program, which reserves capacity in each time slot and achieves stronger guarantees in the small job regime. We corroborate our theoretical results with simulations.

Sequence models in machine learning compress long input histories into finite-dimensional states, from recurrent networks and reservoir computing to recent state space models for long-context data. This raises a basic expressivity question: how simple can the recurrent memory be before it can no longer approximate stable causal sequence-to-sequence maps? We answer this question for fading-memory operators, where the distant past has uniformly diminishing influence. We show that every continuous causal time-equivariant fading-memory operator on a compact input set can be uniformly approximated by a state space model whose recurrence is a fixed diagonal linear contraction. The dynamics are time-invariant, input-independent, and contain no nonlinear hidden-state update or delay-line structure. The construction uses a bank of short exponential traces; although such traces do not exactly store a recent input window, a singular Vandermonde extraction approximately reconstructs the window while the remaining tail becomes negligible as delta decreases. We also prove that exact delay recovery is impossible for any fixed finite trace bank, showing that the accuracy-dependent extraction is essential. Technically, the result separates recurrent expressivity from exact memory storage, while exposing a conditioning cost in the readout. More broadly, it clarifies why highly stable, structurally simple SSM cores can still be universal approximators for stable sequence behavior.

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

Complex Instruction Following (CIF) is a foundational capability for deploying Large Language Models (LLMs) in production-grade applications. It demands stable, precise outputs under increasing horizon length, deeply nested rules, and multi-turn interactions. Yet existing benchmarks are predominantly atomic and short-horizon, failing to capture the logical depth and distractor pressure of real-world settings. We introduce **AppCIF**, the first application-level CIF benchmark. AppCIF stratifies difficulty along two orthogonal axes: *Horizon Length* ($H$), the span over which distractors accumulate and critical signals must be tracked; and *Logical Depth* ($L$), the nesting depth of rules to be unfolded. Together, $\langle H, L\rangle$ defines four hierarchical complexity levels, scaling from clean few-step execution (L1) to extreme pressure deduction (L4). AppCIF comprises 466 curated samples across five application scenarios. It adopts a "**Prompt-as-Environment**" paradigm, pairing Complex System Prompts (averaging ~14k words) with executable Code Simulation Engines (averaging ~3.5k lines of Python) to sustain rigorous state-machine deduction. The benchmark is constructed via a **Labor-Divided Human-AI pipeline** with scenario-specific collaboration strategies, and evaluated on 12 representative LLMs. Results reveal sharp performance stratification: Hard Satisfaction Rate ranges from 1.1% to 45.9%, exposing severe bottlenecks in long-horizon, distractor-laden instruction execution.

We present AnyHand, a large-scale synthetic dataset designed to advance the state of the art in 3D hand pose estimation. While recent works with foundation approaches have shown that scaling training data markedly improves hand pose estimation, existing real-world datasets are limited in coverage, and prior synthetic datasets rarely provide occlusions, arm details, and aligned depth together at scale. To address this bottleneck, our proposed AnyHand contains 2.5M single-hand and 4.1M hand-object interaction RGB-D images, with rich geometric annotations. We show that extending the original training data recipes of existing RGB baselines with AnyHand yields significant gains on multiple benchmarks (FreiHAND and HO-3D), even when keeping the architectures and training schemes fixed. Together with extensive ablations on the scale and composition of the training data setups, these results suggest that training data diversity and quality are as critical as scale for advancing hand pose estimation. We further examine the utility of AnyHand's aligned depth maps in the appendix, showing that scaling RGB-D supervision with AnyHand allows a lightweight depth-fusion variant of existing RGB baselines to outperform prior RGB-D methods.

Despite being a pivotal frontier, interactive world modeling remains underexplored in terms of the versatile controllability required by practical scenarios. To bridge this gap, we present AnchorWorld, a framework that advances egocentric simulation through enhanced interaction integrity and a flexible mechanism for world customization. First, we utilize 3D human motion as the primary interaction modality. To complement the out-of-view or truncated body parts in egocentric views, we introduce an auxiliary training supervision that incorporates exogenous viewpoints decoupled from the agent’s first-person sensorium. It allows the model to observe the agent's full-body positioning relative to the environment, facilitating a more robust spatial grounding of human-world interactions. Furthermore, we propose a simple yet effective mechanism for customizing self-evolving worlds. This is achieved by defining anchor views within a unified world coordinate system, coupled with textual descriptions dictating the dynamic evolution of local scenes. Experimental results show that AnchorWorld significantly outperforms state-of-the-art baselines, while ablation studies validate the effectiveness of our key designs. Notably, our customization scheme exhibits promising spatio-temporal geometric consistency and adheres strictly to the prescribed evolutionary dynamics.

3D brain MRI generation has made significant advances for medical imaging, simulation, and controllable anatomical analysis. However, existing generative models typically synthesize 3D volumes monolithically, often overlooking regional anatomical structures and limiting local controllability. To address these limitations, we introduce AnaDiffusion, an anatomically compositional latent diffusion framework that factorizes the generation process into distinct, anatomically meaningful regions followed by part-to-whole assembly and global refinement. Our approach trains part diffusion models first to capture local structural priors. Then, we inject assembled anatomical composite of parts into whole-brain latent and continue denoising. This mechanism enables the model to resolve global context while preserving the injected anatomy. As a result, AnaDiffusion outputs both explicit part assets and a globally coherent volume, enabling controllable part editing without requiring additional dense segmentation masks at inference time while maintaining coherent part-to-whole brain structure. On ADNI, AnaDiffusion achieves the lowest FID across the whole brain, left/right hemispheres, cerebellar-brainstem complex, and seam regions, while also reducing Cohen's d for ventricles, cerebellum, and brainstem. In localized editing experiments, paired MS-SSIM shows high target transfer and off-target preservation, supporting controllable part replacement with limited non-target anatomical drift.

Quantifying bias in training data---independently of any downstream model---is critical for fair machine learning, especially when data collection and model design occur in silos. Yet most fairness research focuses on model-level mitigation, leaving the data side underexplored. We address this gap by deriving multiple information-theoretic measures for auditing unfairness bias in data without requiring access to model predictions. We define our measures over feature sets and use Shapley values to deduce feature-level contributions to global unfairness bias. For some of these measures, we prove that Shapley values moderate redundancy across feature coalitions, matching empirical evidence in prior work. We develop our measures within an axiomatic framework that embeds a fairness notion, such as statistical parity (SP) or equalized odds (EO), into desired and undesired independence properties. We characterize baseline measures that guide those we develop, for example, by showing that a baseline upper bounds the bias of any downstream restricted predictor. Finally, we show that SP- and EO-aligned independence properties can conflict, paralleling Kleinberg et al.'s result on incompatible fairness notions. We validate our measures through an empirical study on real and synthetic datasets, assessing how well they predict the true bias of an extensively tuned neural network trained on the same data, and via a simple feature selection experiment. For synthetic data, we propose a parametric linear structural causal model that enables controlled generation of diverse correlation structures and bias types. Overall, our analysis provides a theoretically and empirically validated guideline for selecting an unfairness measure given a group fairness notion and testable data conditions.

We introduce the Thresholding Monte Carlo Tree Search problem, in which, given a tree $\mathcal{T}$ and a threshold $\theta$, a player must answer whether the root node value of $\mathcal{T}$ is at least $\theta$ or not. In the given tree, 'MAX' or 'MIN' is labeled on each internal node, and the value of a 'MAX'-labeled ('MIN'-labeled) internal node is the maximum (minimum) of its child values. The value of a leaf node is the mean reward of an unknown distribution, from which the player can sample rewards. For this problem, we develop a $\delta$-correct sequential sampling algorithm based on the Track-and-Stop strategy that has asymptotically optimal sample complexity. We show that a ratio-based modification of the D-Tracking arm-pulling strategy leads to a substantial improvement in empirical sample complexity, as well as reducing the per-round computational cost from linear to logarithmic in the number of arms.

We study image inpainting with generative diffusion models. Existing methods typically either train dedicated task-specific models, or adapt a pretrained diffusion model separately for each masked image at deployment. We introduce a middle-ground model, termed Amortized Inpainting with Diffusion (AID), which keeps a pretrained diffusion backbone fixed, trains a small reusable guidance module offline, and then reuses it across masked images without per-instance optimization. We formulate it as a deterministic guidance problem with a supervised terminal objective. To make this problem learnable in high dimensions, we derive an auxiliary Gaussian formulation and prove that solving this randomized problem recovers the optimal deterministic guidance field. This bridge yields a principled continuous-time actor--critic algorithm for learning the guidance module in a fully data-driven manner. Empirically, on AFHQv2 and FFHQ under the pixel EDM pipeline and on ImageNet under the latent EDM2 pipeline, AID consistently improves the quality--speed trade-off over strong fixed-backbone and amortized inpainting baselines across multiple mask types, while adding less than one percent trainable overhead.

Mixture-of-Experts (MoE) architectures scale model capacity through sparse expert activation, but their deployment remains memory-bound because all expert weights must reside in memory. Mixed-precision quantization can substantially reduce this footprint by assigning different bit-widths to different experts. Existing approaches, however, typically rely on calibration data to estimate expert importance and determine bit allocation. For frontier MoE LLMs, the original training data, and hence the true training distribution, is proprietary and inaccessible. As a result, calibration sets are inevitably imperfect surrogates, which can misestimate expert utilization and lead to suboptimal bit allocation. Motivated by the substantial cross-expert quality variability observed in modern MoE models, we propose AlphaQ, a calibration-free bit-allocation method for MoE quantization. AlphaQ draws on Heavy-Tailed Self-Regularization (HT-SR) theory and follows a simple principle: experts with more heavy-tailed weight spectra are typically better trained and should receive higher bit-widths, while experts with weaker heavy-tailed structure can be quantized more aggressively. AlphaQ operationalizes this principle by measuring expert-wise spectral heavy-tailedness and solving a budget-constrained optimization problem that minimizes total quantization error under a global bit-budget constraint. Across several MoE models, AlphaQ consistently outperforms calibration-based baselines under matched bit budgets. Notably, on Qwen1.5-MoE, AlphaQ achieves near full-precision accuracy with an average expert precision of only 3.5 bits, while delivering more than 4$\times$ memory compression.

To advance the development of embodied intelligence, Open-Environment Active 3D Mapping has attracted increasing attention, aiming to perform a long-horizon and shortest trajectory exploration for reconstructing unseen scenarios. Since only limited information about unseen environments is available, methods built on the closed-set assumption, i.e., assuming that the test environments are similar to those seen during training, cannot generalize satisfactorily. In existing active mapping methods, long-horizon exploration is often guided by predicting a coarse long-range goal and then converting it into an executable path. However, this stage is usually formulated as single-point prediction. Under partial observability, the same local observation may correspond to multiple plausible exploration directions, making such deterministic prediction prone to brittle decisions and degraded performance in unseen scenarios. Our experiments further verify that this is a key factor underlying their weak generalization. To address this issue, we reformulate long-horizon target prediction as conditional multimodal anchor generation using Conditional Flow Matching. Instead of predicting a single goal, our method learns a conditional distribution over coarse exploration anchors from the current mapping state. These anchors are first converted into executable candidate paths through obstacle-aware planning. We then apply exploration-mode clustering to compress geometrically similar trajectories and reduce candidate redundancy. Finally, a hierarchical selection module selects the most promising mode and reranks paths within it to produce the final executable trajectory. Experiments show that our method improves generalization and reconstruction efficiency in open environments.