NeurIPS 2026 Papers

Text-to-image (T2I) generation models have achieved remarkable progress in producing visually realistic images from natural language prompts. Yet it remains unclear whether their success reflects genuine causal understanding or sophisticated pattern matching over visual-textual correlations. Inspired by Russell’s inductivist turkey, we introduce Counterfactual-World (CF-World), a counterfactual benchmark designed to probe whether text-to-image models can generate images under rules that systematically contradict real-world priors. CF-World organizes each scenario into three progressive levels: factual generation under ordinary world knowledge, explicit counterfactual generation with direct visual instructions, and implicit counterfactual generation requiring causal deduction from altered rules. We evaluate both open-source and closed-source T2I models using a Vision Language Model(VLM)-based evaluator (CF-Eval), and introduce two metrics: Prior Resistance Rate (PRR), which measures a model’s ability to overcome entrenched real-world priors, and Reasoning Retention Rate (RRR), which assesses whether models can maintain reasoning-dependent counterfactual generation without explicit visual cues. Experiments show that all models exhibit sharp degradation from factual to counterfactual settings. Further analyses suggest that these failures arise because current T2I models encode world knowledge and visual appearances as tightly coupled patterns. They rely heavily on frequent visual co-occurrences in their training data, causing them to default to familiar commonsense priors when tasked with generating counterfactual worlds.

Multimodal benchmarks are central to evaluating whether models can reason over information from multiple modalities. However, existing literature has revealed that some benchmarks may contain shortcut items that can be answered from a single modality or from answer-option regularities alone, thus failing to reflecting models' true cross-modal inference ability. Existing methods for assessing benchmarks typically rely either on intrinsic item structure or extrinsic model response behavior, which are not adequate for a comprehensive diagnosis. To fill in this gap, we propose SRCoD, a structure-response co-calibrated diagnosis framework for item-level diagnosis of modality dependence in multimodal benchmarks. SRCoD estimates sample-wise multimodal information structure from benchmark content and target answers, and uses this signal as a soft structural anchor for modality-conditioned item response modeling. The learned model produces a calibrated item-level diagnostic profile that reflects how strongly an item depends on different forms of modality evidence, enabling fine-grained benchmark analysis beyond aggregate accuracy. SRCoD also provides interpretable attribution of the diagnosis results. Extensive experiments on two complementary protocols, i.e., benchmark-refinement oriented validation and human-labeled item validation, demonstrate that SRCoD outperforms state-of-the-art benchmark diagnosis methods. Our code and data are available at https://anonymous.4open.science/r/SRCoD-61B0.

Language agents are increasingly deployed in complex professional workflows, with tutoring emerging as a particularly high-stakes capability that remains largely unmeasured in existing benchmarks. Effective tutor agents require more than producing correct answers or executing accurate tool calls: a robust tutor must diagnose learner state, adapt support over time, make pedagogically justified decisions grounded in educational evidence, and execute interventions within realistic learning-management systems. We introduce EduAgentBench, a source-grounded benchmark for holistically evaluating tutor agents across the full scope of teaching work. It contains 150 quality-controlled tasks across three capability surfaces: situated multi-turn tutoring, professional pedagogical judgment, and Canvas-style teaching workflow completion. Tasks are constructed through a pedagogical-insight-driven pipeline and evaluated with complementary verification signals and human review. Across a comprehensive evaluation of frontier models, our findings reveal that current models are generally capable of bounded pedagogical judgment, but still fall short of professional teaching standards in situated tutoring and autonomous teaching-workflow execution. To our knowledge, EduAgentBench is the first theory-grounded and realistic benchmark for evaluating the holistic teaching capability of tutor agents, providing a measurement foundation for developing future tutor agents that can support realistic teaching work.

Physics-Informed Neural Networks (PINNs) struggle to capture high-frequency components of PDE solutions, a failure mode known as spectral bias. Most existing fixes adjust the loss, the sampling, or the input encoding, but the network itself remains agnostic to the equation it is supposed to solve. We take a different route and embed physics priors into the architecture. The network's internal spectrum is shaped to match the spectrum of the target PDE through three components that are trained end-to-end: a bounded coordinate warping that contracts regions where the solution varies sharply, a spectral attention layer driven by the PDE residual that emphasizes physically active Fourier modes, and an inter-harmonic gate that lets low-frequency channels modulate high-frequency ones. We test the design on four forward PDEs (Helmholtz, Wave, Klein--Gordon, Burgers), the Burgers inverse problem, and seismic reconstruction, including Gulf of Mexico field data. Across these tasks, the architecture clearly outperforms seven PINN baselines on accuracy and produces noticeably fewer artifacts. Code will be made publicly available upon acceptance.

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 $d=8,000$.

Watermarking is an important tool for promoting the responsible use of large language models (LLMs). Existing watermarks insert a signal into generated tokens that either flags LLM-generated text (zero-bit watermarking) or encodes more complex messages (multi-bit watermarking). Though a number of recent approaches insert multiple bits into text without perturbing average next-token predictions, they largely extend design principles from the zero-bit setting, such as encoding a single bit per token. In contrast, a watermarker capable of embedding multiple bytes into the text would dramatically increase the potential applications, by embedding information such as the ID of the user who submitted the prompt, the precise model version that was used, or even the prompt itself. We address this problem by introducing ArcMark: a new watermark construction based on coding and information-theoretic principles that is capable of reliably embedding multiple bytes of information into just a few hundred tokens, without any distortion of the underlying LLM next-token distribution. We derive ArcMark by formulating the distortion-free watermarking problem as a channel coding problem, and deriving an information-theoretic channel capacity that establishes the fundamental limit of embedding information in LLM output in a distortion-free manner. This capacity formulation informs the design of ArcMark. In practice, ArcMark outperforms competing multi-bit distortion-free watermarks in terms of reconstruction accuracy, including in the face of attacks that alter a subset of the LLM text. ArcMark output is also shown to be indistinguishable from unwatermarked text in terms of perplexity, and in downstream task quality.

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.

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest—including differential operators—are discontinuous or set-valued, and lie outside classical approximation frameworks. We propose a paradigm shift by formulating approximation via graph convergence (Painlevé–Kuratowski convergence), which is well-suited for closed operators. We show that uniform and $L^p$ approximation are fundamentally inadequate in this setting. Focusing on maximally monotone operators, we prove that any such operator can be approximated in the sense of local graph convergence by continuous encoder–decoder architectures, and further construct structure-preserving approximations that retain maximal monotonicity via resolvent-based parameterizations.

Contrastive representation learning (CRL) is a fundamental paradigm for learning transferable representations. Recent work identifies its population target as the pointwise mutual information (PMI) $ \log\frac{p(\mathbf{x},\mathbf{y})}{p_\mathcal{X}(\mathbf{x})p_\mathcal{Y}(\mathbf{y})} $ between two modalities $\mathcal{X},\mathcal{Y}$, where $p$ is the joint density function and $p_\mathcal{X},p_\mathcal{Y}$ are the marginals. However, it remains unclear why standard inner-product scores $f(\mathbf{x})^\top g(\mathbf{y})$ can effectively approximate a generally nonseparable population target PMI. In this paper, we address this question from the aspect of approximation for CRL. By linking PMI to a compact operator, we show that $D$-dimensional inner-product models perform rank-$D$ spectral approximation, with error controlled by the spectral tail. We then study neural network realizations: in general settings, we show that deep neural network scoring functions are universally consistent, and the approximation error rates depend on the smoothness of the PMI function; under structured low-rank data models we obtain improved rates attained by moderate-width encoders. Finally, we establish a fast calibration rate from contrastive excess risk to downstream retrieval error under a density-ratio Tsybakov noise condition.

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.

Matrix-vector products (MVPs) are a key primitive in numerical linear algebra and machine learning. However, the naive quadratic running time for exact computation is prohibitive for large matrices, motivating approximate methods. In this paper, we study approximate MVPs under a natural ``lightness'' assumption, which bounds the total $\ell_1$-mass of a $n \times n$ input matrix $A$ by $\gamma n$. For general matrices, we give an algorithm for approximating $Ax$ up to additive $\epsilon \|x\|_2$ error in $O(\gamma n^{1.5}/\epsilon)$ query time and polynomial preprocessing. We extend this algorithm to kernel matrices by establishing a black-box reduction to Kernel Density Estimation data structures and analyzing a noisy entry sampling scheme. For kernel matrices, our algorithm does not require any preprocessing and improves the best-known running times for Gaussian kernel matrices of [Indyk, Kapralov, Sheth, Wagner; ICLR `25] by polynomial factors in $n$ and $1/\epsilon$, and also provides the first algorithms leveraging the lightness assumption for other kernel functions as well.

We study the problem of finding approximate envy-free allocations up to any $k$ goods ($\alpha$-EFkX), when agents have additive values over goods in a bundle. As our main result, we show that for any $k>2$, $\frac{k+1}{k+2}$-EFkX allocations exist for any number of agents, and can be computed in polynomial time, via an appropriate generalization of the 3PA algorithm of (Amanatidis et al., 2024). An immediate corollary of this result is that $3/4$-EF2X allocations exist for any number of agents; in contrast, $2/3$-EFX allocations are only known to exist for up to 7 agents. We improve this latter result by devising an algorithm that achieves $2/3$-EFX for 8 agents. We also consider EFkX graph orientations; we prove that such orientations do not always exist, and that deciding their existence is NP-complete, thereby generalizing the corresponding result of (Christodoulou et al., 2023) for $k=1$.

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.

With the growing number of fine-tuned variants derived from pre-trained models, model merging emerges as a key challenge: effectively integrating task-specific adaptations while preserving performance. However, naive weight averaging often fails when parameter updates are misaligned, revealing the need for a structured space in which merging becomes principled. In this work, we hypothesize that pre-trained models possess an intrinsic low-rank structure. Specifically, we posit that the transformation from input to output is mediated by a latent bottleneck of low intrinsic dimensionality; we leverage this low-dimensional space to construct a model embedding space. This space ensures that fine-tuned updates, i.e., model embeddings, of all adaptations remain confined within the intrinsic structure of the pre-trained model. As model embeddings lie in the same low-dimensional space, model merging via direct averaging becomes more effective. Moreover, we further introduce an aligned subspace of these model embeddings to improve the efficacy of model merging. Experiments across vision and multimodal tasks, including ViT and multimodal LLMs, demonstrate that our approach enables effective model merging and provides a unified geometric view of adaptation and combination in pre-trained models.

Modern video generation models are increasingly hailed as emerging world models with an internalized grasp of physical law. Yet existing benchmarks largely evaluate physical plausibility only at the output level, without verifying whether the model arrives there through a faithful, law-grounded reasoning process. We introduce **Apple-$\pi$**, the first benchmark that anchors video-model evaluation explicitly in physical laws. Apple-$\pi$ comprises three components. **1) Orchard**: a dataset of 400 videos covering ten canonical tasks in classical mechanics. It separates single-law tasks for confounder-free diagnosis from multi-law tasks for probing generalization. **2) Benchmark Protocol**: a three-stage protocol based on scientific reasoning, including Perception, Formulation, and Deduction. It uses *chain-of-frames* prompting on infographic-annotated first frames, treating the generated video as the model's visible reasoning trace. **3) Evaluation Suite**: a hybrid evaluation suite that combines MLLM-based subjective scoring with physics-law-grounded objective measures. This enables stage-resolved diagnosis of not only whether a model fails, but where it fails. Benchmarking 11 models shows that current video models remain far from reliable law-grounded world simulators, with the best video model scoring only 0.473. Our stage-, pillar-, and source-resolved analyses further expose a Perception-to-Formulation-to-Deduction bottleneck, weak multi-law state transfer, and a persistent Sim-to-Real gap. These findings position Apple-$\pi$ as a diagnostic foundation for guiding future video models toward world models with law-grounded physical intelligence.

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.

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.