NeurIPS 2026 Papers

The ability to reliably distinguish human-written text from that generated by large language models is of profound societal importance. The dominant approach to this problem exploits the likelihood hypothesis: that machine-generated text should appear more probable to a detector language model than human-written text. However, we demonstrate that the token-level signal distinguishing human and machine text is non-uniform across the hidden space of the detector model, and naively averaging likelihood-based token scores across regions with fundamentally different statistical structure, as most detectors do, causes a form of Simpson's paradox: a strong local signal is destroyed by inappropriate aggregation. To correct for this, we introduce a learned local calibration step grounded in Bayesian decision theory. Rather than aggregating raw token scores, we first learn lightweight predictors of the score distributions conditioned on position in hidden space, and aggregate calibrated log-likelihood ratios instead. This single intervention dramatically and consistently improves detection performance across all baseline detectors and all datasets we consider. For example, our calibrated variant of Fast-DetectGPT improves AUROC from $0.63$ to $0.85$ on GPT-5.4 text, and a locally-calibrated DMAP detector we introduce achieves state-of-the-art performance across the board. That said, our central contribution is not a new detector, but a precise diagnosis of a significant cause of under-performance of existing detectors and a principled, modular remedy compatible with any token-averaging pipeline. This will serve as a foundation for the community to build upon, with natural avenues including richer distributional models, improved calibration strategies, and principled ensembling with hidden-space geometry signals via the full Bayes-optimal decision rule.

Modern language models are trained on heterogeneous web-scale text corpora. Consequently, studying knowledge and skill acquisition is difficult, as prior exposure to related content is hard to characterize. To address this challenge, we introduce **LittleCurriculum**, a meticulously curated 88B-token pretraining corpus tailored to U.S. elementary school material, explicitly excluding concepts, facts, and vocabulary taught above Grade 5. Training a 2B-parameter LLM from scratch on **LittleCurriculum** yields **LittleLearner**, a model with sufficient language competence for open-ended evaluation, yet with clear knowledge and capability boundaries mapped to interpretable curriculum guidelines. We release **LittleCurriculum** and **LittleLearner** as a developmentally restricted sandbox to study how models acquire, represent, and use data under a well-defined training scope. We illustrate the sandbox's utility in a first suite of experiments on injecting new knowledge through post-training and in-context learning. These methods let **LittleLearner** better utilize existing knowledge, but do not raise out-of-scope capabilities. Our findings underscore the value of this controlled environment for future investigations.

Remote sensing lithology interpretation is fundamental to geological surveys, mineral exploration, and regional geological mapping. Unlike general land-cover recognition, lithology interpretation is a knowledge-intensive task that requires experts to infer rock types from various features, e.g., subtle visual, making reliable automated interpretation highly challenging. Geological knowledge-guided large multimodal models offer new opportunities, yet their evaluation remains constrained by the lack of benchmarks that capture lithological annotations, multi-level geological semantics, and expert-informed assessment. Here, we propose LithoBench, a multi-level benchmark for evaluating geological semantic understanding in remote sensing lithology interpretation. LithoBench contains 10,000 expert-annotated interpretation instances across 12 representative lithological categories, including 4,000 multiple-choice and 6,000 open-ended tasks organized into five cognitive levels: Identification and Description, Comparative Analysis, Mechanism Explanation, Practical Application, and Comprehensive Reasoning. We further develop an expert-in-the-loop, knowledge-grounded semi-automated construction pipeline, coupling multi sub-processes, e.g., structured geological image descriptions, to enhance geological validity and evaluation reliability. Experiments with multiple large vision-language models reveal substantial limitations in geological semantic understanding, particularly on higher-order explanation, application, and reasoning tasks. Taken together, LithoBench establishes a dedicated testbed for advancing geological knowledge-guided multimodal models, supporting systematic model evaluation, domain-specific training and adaptation, and knowledge-enhanced reasoning toward expert-level lithology interpretation from remote sensing imagery.

We study for the first time, stochastic dueling bandits over continuous action spaces with Lipschitz structure, where feedback is purely comparative. While dueling bandits and Lipschitz bandits have been studied separately, their combination has remained unexplored. We propose the first algorithm for Lipschitz dueling bandits, using round-based exploration and recursive region elimination guided by an adaptive reference arm. We develop new analytical tools for relative feedback and prove a regret bound of $\tilde O\!\left(T^{\frac{d_z+1}{d_z+2}}\right)$, where $d_z$ is the zooming dimension of the near-optimal region. Further, our algorithm takes only logarithmic space in terms of the total time horizon, best achievable by any bandit algorithm over continuous action space.

Modern language models use a single matrix for input embedding and output projection. This couples two distinct objectives: token representation and discrimination over a vocabulary. This work introduces *Leviathan*, a Transformer architecture that replaces the input embedding matrix with *learned embedding vectorization (LEV)*, a compact continuous mapping from token indices to embeddings. Leviathan's output head remains untied for a parameter increase of as low as 0.2\%. Under controlled comparisons with identical Transformer backbones, Leviathan consistently improves language modeling performance over standard tied-embedding baselines across a 200M-1.2B parameter regime on The Pile with gains that grow during training. At 1.2B scale, Leviathan reduces validation perplexity by 9\%, requires $2.1\times$ fewer training tokens to reach the tied baseline's final loss, and improves on all six downstream benchmarks evaluated, including a 30\% reduction in LAMBADA perplexity. Frequency-stratified analysis reveals gains to be concentrated in rare tokens, where continuous parameterization reduces perplexity by 81\%, falling to near zero for the most frequent.

The performance of machine learning models often relies on large labeled datasets; however, data collected from diverse sources can contain label noise. Recent work has shown that, in noisy settings, there may exist a subset of the training data on which models can achieve performance comparable to training on a noise-free dataset. A widely used method for identifying such subsets is \textit{cutstats}, which employs $k$-nearest neighbors ($k$-NN) to detect low-noise samples. However, its performance on high-dimensional data remains largely unexplored. In this work, we formally establish that the performance of a classifier trained on a subset of a noisy dataset selected via \textit{cutstats} is influenced by the accuracy of $k$-NN. We further demonstrate that, in noisy environments, exploiting data invariance and knowledge of underlying symmetries can significantly enhance the performance of $k$-NN, bringing it closer to the Bayes optimal classifier even in high-dimensional regimes. Finally, we show that for real-world scenarios, where information about the underlying invariance is only partially known, learnt invariant representations can still facilitate the identification of near-optimal subsets.

AI-Generated Image (AIGI) Detection is becoming critical as generative models proliferate, yet existing detectors often generalize poorly by relying on narrow, dataset-specific artifacts. Many prior works improve generalization through additions, such as introducing extra artifact cues, pretraining models, training constraints, or test-time operations, which may increase inference cost and model complexity. In this paper, we take the opposite route and study generalization through subtractions and propose AID--, a plug-and-play framework that improves transformer-based AIGI detectors from both feature and parameter perspectives. At the feature level, we introduce high-order dependency ranking to identify and prune redundant or potentially misleading tokens for progressive token reduction; and at the parameter level, we design relative-advantage head supervision and a class-asymmetric exit rule to train depth-specific early-exit heads. AID-- can be seamlessly integrated into transformer-based AIGI detectors to improve both efficiency and out-of-distribution generalizability, which is experimentally validated on six public datasets. For example, AID-- helps the detector Effort achieve up to a 2.2× speedup while improving generalization accuracy by 3.6% on GenImages.

Web agents promise to automate consequential operations on enterprise web systems, yet the benchmarks used to evaluate them score correctness on surface-level proxies: DOM/URL predicates, action-trace matchers, or vision-language verdicts on a closing screen. These proxies are inadequate for enterprise resource planning (ERP) systems, where every action commits to a transactional ledger and the criterion of correctness is what the ledger now records, not what the page now renders. We argue that ERP web operations should be evaluated against what a run actually wrote to the relational backend, with the server-side operation trace recorded alongside the outcome to provide the audit provenance that enterprise governance requires. We introduce Ledger, a path-validated, database-grounded benchmark for browser agents on a production-grade open-source ERP: 424 oracle-certified task instances across 53 functional modules, scored by an Atomic Edit Set validator (field-level $F_1$ against a PostgreSQL oracle, under a typed normalization function) paired with a Canonical Operation Tracer (server-side instrumentation of the ERP’s JSON-RPC dispatch). Each episode runs under pg_restore snapshot isolation; no language-model judge is invoked; three formal guarantees (score determinism, episode isolation, tracer completeness) make scores auditable and exactly replayable. A cross-paradigm evaluation of seven contemporary browser agents shows Ledger discriminates architectures sharply, with task-success rate spanning 81.6% down to 13.7% across the roster while long-horizon enterprise workflows remain far from saturated.

Boolean satisfiability (SAT) provides a foundation tool for cryptographic key recovery by encoding ciphers into CNF or ANF representations. However, heuristic solvers and their neural-enhanced variants often degrade significantly on cryptographic instances due to pronounced structural symmetry, a large number of intermediate variables, and complex algebraic dependencies. Existing neural approaches—ranging from end-to-end prediction to solver-integrated heuristics—face challenges in scalability, assignment accuracy, or computational efficiency. In this paper, we propose a unified neural-guided enumerative SAT framework for cryptographic key recovery. It performs a single forward neural guidance to identify a subset of $k$ critical variables, followed by enumeration over their assignments before invoking a heuristic SAT solver. This design effectively reduces the combinatorial search space while keeping neural overhead minimal. We further introduce a taxonomy of neural guidance across data and model capability regimes, including supervised selection with cryptographic priors, uncertainty-driven selection with assignment prediction, and robust fallback strategies using the model trained on general SAT datasets. Experiments on 10 SAT solvers and 2 cube-and-conquer strategies over SAT4CryptoBench and SAT Competition benchmarks demonstrate up to $5\times$ speedup and approximately 2× average improvement on cryptographic instances, while maintaining better performance on general SAT datasets. These results highlight the effectiveness and generalization of this framework, illustrating its potential to bridge machine learning and SAT solving in cryptanalysis tasks.

Self-supervised monocular depth estimation is appealing for its potential to scale with unlabeled data, yet existing methods often degrade when trained on diverse scenes. This study finds that, under self-supervision, models tend to encode dataset-specific structural biases rather than transferable scene geometry, leading to cross-domain optimization conflicts. To address this issue, this study proposes the MaSS framework, aiming to make self-supervised depth learning scalable to diverse data. MaSS introduces a dedicated structural representation pathway explicitly decoupled from contextual features, which is guided by a novel scene-structure discrimination objective to learn generalized, layout-aware structural representations for depth decoding. Trained and evaluated on four diverse datasets, both individually and jointly, MaSS substantially outperforms prior self-supervised methods and is the first to consistently benefit from mixed-domain training. Zero-shot evaluation on eight additional datasets further demonstrates its remarkable generalizability, particularly on those entirely out-of-distribution scenes. The source code will be publicly available upon publication.

Deep neural networks are highly vulnerable to bit corruption in stored weights, whether from naturally occurring memory faults or deliberate fault-injection attacks. Existing defenses remain fundamentally limited: fault-tolerance methods degrade under cumulative corruption and remain vulnerable to strong white-box attacks, while ECC-based recovery methods are often tied to specific precisions or architectures and expose concentrated vulnerable surfaces. We propose a simple training-based recovery framework that endows model weights with recoverable structure through block-wise zero-sum constraints enforced by differentiable projection. The resulting method incurs no parameter-space overhead and generalizes naturally across architectures and numerical precisions. We further develop adaptive adversarial bit-flip attacks tailored to recovery-based defenses, covering both our method and prior ECC-based approaches. Across diverse architectures, precisions, datasets, and threat models, our method consistently delivers strong robustness and recoverability while preserving clean performance.

Learning parity functions, more general modular addition, is a challenging machine learning task due to its input sensitivity. A recent study substantially scaled modular addition learning in both the number of summands and the modulus. Its key idea is to increase zeros in training sequences, reducing the effective number of summands and thus controlling training difficulty; however, this induces covariate shift between training and test input distributions. This study theoretically and empirically analyzes this side effect and proposes a covariate-shift-free method for modular addition. Specifically, we introduce an auxiliary modulus $Kq$ during training, which reduces wrap-around frequency and problem difficulty while preserving the same input distribution across training and testing. Experiments show strong scalability and sample efficiency: even for large input length $N$, large modulus $q$, and small datasets---where the sparse method fails to learn---our method achieves equal or better match accuracy and relaxed $\tau$-accuracy. For example, at $N=64$ and $q=974269$, our method trained on 100K samples achieves $97.0\%$ $\tau$-accuracy at $\tau=0.05$, while the sparse method achieves only $9.5\%$ with the same data size and $93.9\%$ even when extended to 1M samples.

Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability (SAT) problems, no prior work has shown that transformer-based models can learn effective cubing heuristics. We introduce a neuro-symbolic post-training framework for this task. We design an MCTS-based data curation pipeline that uses symbolic heuristics to explore splitting decisions over SAT competition formulas, producing preference data grounded in solver statistics and augmented with reasoning traces from a teacher model. Our two-stage post-training, supervised fine-tuning (SFT) followed by direct preference optimization (DPO), enables a 4B-parameter model to achieve a pass@5 score of 53 on 100 SAT competition benchmarks, surpassing frontier LLMs such as Claude-Sonnet-4 (50) and matching the best symbolic heuristic (53). Ablations show that SFT alone improves pass@5 from 46 to 51, with DPO adding 2 additional benchmarks; an entropy/agreement ablation on realized first-cube decisions further shows that SFT, not DPO, accounts for the root-level decision diversity that produces complementary per-run coverage over deterministic symbolic methods. This demonstrates that transformers can be trained to make effective cubing decisions in a domain traditionally dominated by symbolic methods.

A point source in a PDE does not occupy an entire grid. A weather station reports one value at one site; it does not observe the temperature between stations. A pickup event in a city occurs at a coordinate and a time; it is not born as an image. Yet many neural-operator pipelines begin by turning such sparse observations into dense surrogate fields before learning. This interpolation step is often treated as harmless preprocessing, but in sparse regimes it changes the object on which the operator is asked to act. We introduce the Dirac Neural Operator (DIRAC-NO), a measure-native neural operator for sparse event-to-field learning without interpolation. DIRAC-NO keeps observations as atomic event measures until query time and constructs the output field through adaptive Dirac-kernel aggregation. Because this aggregation is implemented by direct summation, the front end preserves source additivity at the aggregation stage and admits a learned Green-kernel view of source-to-field response. Across controlled point-source PDE benchmarks and real sparse reconstruction tasks, DIRAC-NO exposes the cost of interpolation-first learning. On MeasureBench-1D, it achieves relative $L^2$ error 0.015 at $n=128$, compared with 0.49 for FNO, and it better preserves superposition structure in trained models. In 2D, it is strongest under parameter and density shift, while ERA5 reconstruction shows that the representation advantage persists beyond analytic PDEs at high observation budgets. Boundary cases and negative-control event streams further show that the benefit appears where the representation argument predicts: sparse, event-native tasks with source-response structure. These results suggest that sparse operator learning should be organized not only by the neural backbone, but by the native space in which the input is represented.

Learning an energy-based model from data samples is a central problem in machine learning. Many recent and popular methods, such as denoising score matching for training energy-based diffusion models, use stochastic interpolants to corrupt data samples at different noise levels indexed by a time variable. This defines a joint density over both the data space and time, and most methods learn its energy through either spatial or temporal differences. We identify distinct failure modes for both of these approaches. To solve them, we propose Spatiotemporal Noise-Contrastive Estimation (stNCE), a framework for learning the energy through joint spatiotemporal differences. stNCE unifies many existing methods and leads to new training objectives. Experiments on images and molecules demonstrate performance competitive with state-of-the-art density estimation methods.

We present Leak-CURBER, the largest multimodal, leakage-controlled benchmark for evaluating machine learning and deep learning models for enzymatic reactions. Leak-CURBER standardizes data from 10 biochemical databases and curates datasets with multimodal inputs, metrics, and leakage-controlled splits for 4 tasks. The benchmark comprises 10 subtasks: prediction of reaction outcomes (2), enzyme function (2), kinetic parameters (3), and protein–ligand binding (3). Leak-CURBER establishes new evaluation protocols that control for train/validation/test overlap across protein sequence and structure, molecule string and structure, and reaction similarity, thereby exposing generalization failures of learning methods. Evaluating the state-of-the-art (SOTA) models on Leak-CURBER shows that their strong performance degrades sharply under these splits, often approaching random classification or retrieval performance, and near-zero regression performance. Leak-CURBER includes precomputed embeddings, continual benchmark releases, reproducible curation scripts, and a public leaderboard to support reliable comparison of enzymatic-reaction models.

Forward-Forward (FF) training allows each layer to learn from a local goodness criterion. In cumulative-goodness variants, however, later layers can inherit a task that earlier layers have already partially separated. We formalize this phenomenon as layer free-riding: under the softplus FF criterion, the class-discrimination gradient reaching block $d$ decays exponentially with the positive margin accumulated by preceding blocks. We then study three local remedies---per-block, hardness-gated, and depth-scaled---that recover current-layer separation measures without relying on backpropagated gradients. On CIFAR-10 and CIFAR-100, these remedies dramatically improve layer-separation statistics, with $4\times$--$45\times$ gains in deeper layers, while changing accuracy by less than one percentage point for non-degenerate training procedures. Tiny ImageNet provides a tougher cross-dataset check for our selected block-wise configuration and reveals the same qualitative gap between layer-health diagnostics and final accuracy. Calibration experiments further show that architecture and augmentation choices have a larger effect on final accuracy than the training-rule modifications studied here. Cumulative free-riding is therefore a real and repairable optimization pathology. Nonetheless, for the FF training rules, architectures, and datasets we study, it is not the dominant factor limiting achievable accuracy.

We introduce the Lattice Deduction Transformer (LDT), a recurrent transformer that approximates logically sound deduction by projecting its latent state through a lattice between forward passes. We train on-policy in a process that mirrors deduction in a search-based constraint solver and supervise training via a domain-agnostic, abstract-interpretation-based approximation of the set of solution candidates. An $800$K-parameter LDT achieves $100\%$ accuracy on Sudoku-Extreme and Snowflake Sudoku, at a fraction of the training cost of prior small recurrent reasoners, while remaining empirically sound: the model returns a correct answer or abstains. A $1.8$M-parameter variant reaches $99.9\%$ accuracy on Maze-Hard. Frontier LLMs score $0\%$ on all three benchmarks.

Self-supervised video models are increasingly framed as world models, yet their evaluation remains largely confined to a single top-1 accuracy score on clean benchmarks. This leaves a major gap in comprehending their potential as world models. We present the first systematic study addressing this gap, analyzing four matched-capacity frontier video foundation models, V-JEPA 2.1, V-JEPA 2, VideoPrism, and VideoMAEv2, across five robustness axes relevant to their deployment as video world models: feature discriminability, corruption robustness, fine-grained discrimination, occlusion robustness, and sensitivity to temporal direction. Our evaluations establish that across all five axes, latent-prediction models form a distinct and consistent profile. They degrade more gracefully under pixel corruption, preserve usable class structure rather than mere geometric stability under occlusion, capture fine-grained physical contact cues without reconstructing pixels, and uniquely encode the arrow of time. These advantages can even survive task adaptation: a frozen V-JEPA 2 backbone with a lightweight attentive probe outperforms a fully fine-tuned VideoMAE and a supervised TimeSformer on corruption and occlusion robustness. Our extensive results offer concrete new evidence in favor of latent prediction for robust world modeling.