NeurIPS 2026 Papers

Conference on Neural Information Processing Systems

Decision breakdown

6,437papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    991.5%
  • Spotlight
    2403.7%
  • Poster
    6,09894.7%

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Topic: Datasets and Benchmarks · 623 papers · Reset filters

DualWorldBench: Can Agents Plan Deliveries across Symbolic and Grounded Worlds?

Yang Chen, Bin Wen, Danyang Peng, Hong-Jie You, Ziqiao Shang, Lan-Zhe Guo

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Recent multimodal agents have shown promising progress in embodied planning and web interaction. However, existing evaluations often rely on simplified tasks with limited combinatorial structure, leaving it unclear whether current agents can robustly integrate perception and reasoning for multi-goal planning under temporal, physical, and multimodal constraints. We introduce DualWorldBench, a unified benchmark for evaluating agent planning under controlled symbolic--temporal and grounded--topological complexity. Built around a shared pickup--delivery interface, DualWorldBench consists of three complementary components: TextWorld, which isolates symbolic planning under varying task compositions and release dynamics; SimWorld, which evaluates grounded path planning under controlled topological variation with text, image, or multimodal inputs; and DualWorld-VQA, a diagnostic suite spanning perception, scene understanding, and planning. Experiments show that current state-of-the-art agents remain brittle under increasing combinatorial complexity. Multimodal input does not consistently improve planning and can even degrade performance, revealing difficulties in aligning symbolic task specifications with grounded topology. Diagnostics further show that models handle perception or understanding in isolation, but fail when decision-making requires integrating both. These findings establish DualWorldBench as a challenging testbed for agents with tighter perception--reasoning--planning integration. All datasets and code are publicly available at our project website https://dualworld.netlify.app/.

Poster
Dual-Rate Diffusion: Accelerating diffusion models with an interleaved heavy-light network

Grigory Bartosh, David Ruhe, Emiel Hoogeboom, Jonathan Heek, Thomas Mensink, Tim Salimans

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Diffusion models achieve state-of-the-art generative performance but suffer from high computational costs during inference due to the repeated evaluation of a heavy neural network. In this work, we propose Dual-Rate Diffusion, a method to accelerate sampling by interleaving the execution of a heavy high-capacity context encoder and a light efficient denoising model. The context encoder is evaluated sparsely to extract high-dimensional features, which are effectively reused by the light denoising model at every step to refine the sample efficiently. This approach significantly accelerates inference without compromising sample quality. On ImageNet benchmarks, Dual-Rate Diffusion matches the performance of standard baselines while reducing computational cost by a factor of $2$--$4$. Furthermore, we demonstrate that our method is compatible with distillation techniques, such as Moment Matching Distillation, enabling further efficiency gains in few-step generation.

Poster
Dual Dimensionality for Local and Global Attention

Zhiyuan Wang, Xuan Luo, Sirui Zeng, Xifeng Yan

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Decoder-only Transformers compute attention over the KV cache of preceding tokens. Keys (and Values) are typically represented with the same dimensionality, regardless of its distance from the prediction target. In natural language, however, the next word is most strongly influenced by the immediately preceding tokens. We hypothesize that local and distant tokens impose asymmetric demands on representational capacity: local tokens are more critical for predicting immediate outputs and thus require richer representations, whereas distant tokens primarily serve as long-range memory, for which lower-dimensional representations may suffice. We formalize this idea as Distance-Adaptive Representation (DAR), implemented in a controlled setting that preserves full-dimensional representations within a local context window while assigning reduced-dimensional representations (e.g. 1/4 of the original dimensionality) to tokens beyond that window. Across multiple pretraining scales (70M to 410M parameters), as well as continued supervised fine-tuning on a 1B-scale model, this approach closely matches the performance of full-dimensional baselines. In contrast, uniformly reducing dimensionality across all token positions leads to worse performance. These results challenge the common assumption that key and value dimensionality should be uniform across token positions. Our findings suggest a new direction for designing attention architectures that adaptively allocate representational capacity across the sequence, enabling further reductions in KV cache during inference.

Poster
Drive vs. Decay: On the Training Dynamics of Joint-Embedding Predictive Architectures

José Lucas De Melo Costa, Seong Woo Ahn, Fabrice Popineau, Arpad Rimmel, Bich-Liên DOAN

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Joint-Embedding Predictive Architectures (JEPAs) are prone to representation collapse, typically mitigated through empirical heuristics. We develop an early-training stability theory that unifies these heuristics. Linearising the coupled JEPA gradient flow around the trivial fixed point reveals two competing effects: a driving force ($\gamma$) and a decay effect ($\sigma$). Under approximate spectral decoupling, a per-mode stability ratio $\mu_i = \gamma_i / \sigma_i$ factorises into independent data-side and predictor-side terms and the count of unstable modes tracks the rank of representations that can emerge. The framework predicts a phase boundary, which we confirm empirically across more than 800 Tabular-JEPA configurations. It also unifies predictor scaling, masking ratio, and EMA as distinct mechanisms for shifting $\mu$. Guided by this analysis, we introduce ResidualPred, a transformer predictor whose attention is biased toward the identity at initialisation; it improves both effective rank and downstream accuracy on tabular benchmarks and on I-JEPA pretraining over CIFAR-10, CIFAR-100, and STL-10. Our framework connects empirical collapse-avoidance heuristics to an explicit dynamical picture, yielding theory-driven stabilizers. Code is available as supplementary material.

Poster
DopplerWild: A Doppler Dataset and Benchmark for Human Kinematic Understanding in the Wild

Shubo Yang, Aaron Wang, Narayan Schuetz, Jida Zhang, Edison R Altamirano, Kaitlyn Leitherer, Ehsan Adeli, Amin Arbabian

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Understanding human kinematics in outdoor, real-world environments is critical for assistive robots and intelligent infrastructure. Many perception systems rely on cameras and LiDAR, which infer motion indirectly from spatial observations, making estimates sensitive to discontinuities and ambiguity under low lighting or at distance. In contrast, mmWave radar is robust to lighting and weather, operates at long range, and directly measures motion through Doppler signatures. However, Doppler-based kinematic understanding remains largely unexplored in the wild because existing datasets are primarily controlled and scripted. We introduce DopplerWild, a dataset and benchmark for evaluating Doppler-based kinematic understanding in the wild. DopplerWild comprises 447k radar frames across four outdoor locations, including an unlabeled subset for self-supervised representation learning and a labeled subset of 539 subjects with nearby-person interference (56\%) and occlusion (16\%). The benchmark spans coarse and fine-grained motion classification, as well as velocity estimation. Beyond aggregate metrics on controlled datasets, DopplerWild evaluation isolates real-world factors: subject variation, location shift, multi-person interference, occlusion, sensing geometry, and low-label regimes. DopplerWild reveals three findings. First, self-supervised pretraining matches supervised performance with less than half the labeled data and improves performance under interference, occlusion, and lateral motion. Second, we identify key challenges for single-view Doppler sensing, including physical limits in lateral motion, subtle asymmetric limb motion, and location distribution shifts. Third, we observe bidirectional transfer asymmetry between DopplerWild and an external controlled Doppler dataset, suggesting that real-world coverage is important for transferable Doppler representations. DopplerWild provides an evaluation framework for characterizing the generalization, limits, and transferability of Doppler-based kinematic representations in the wild.

Poster
Doomed to Re-Annotate, Forever: The ImageNet Story

Illia Volkov, Nikita Kisel, Tetiana Mishkina, Klara Janouskova, Jiri Matas

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Top-1 accuracy on ImageNet-1k remains the most universally reported metric in visual recognition, despite its well-documented label quality issues. In the paper, we describe the effort to obtain accurate and complete ImageNet-1k validation set annotations. The result -- ReImageNet -- is a from-scratch reannotation, which includes multilabel correction, object localisation, revised class definitions, and semantic attributes---text-recognition, rendition, reflection, crowd, and dominant. The reannotation reveals that $\approx13$\% of the original ImageNet-1k labels are incorrect, $32.7$\% of images are multilabel and $4.7$\% contain no object from an ImageNet-1k class. With the new labels, top-1 accuracy increases by $0.7$--$1.4$\% for supervised models and by $6$--$8$\% for MLLMs. We show that annotation errors in ImageNet-1k propagate into its derivative test sets, indicating that the problem is structural rather than specific to any single benchmark. We observed that LLMs outperform unaided crowd annotators, and that human and LLM collaboration with appropriate tooling represents the current quality ceiling for annotation at this scale. All [annotations](https://huggingface.co/datasets/c1rcuslegend/ReImageNet), [class definitions](https://gonikisgo.github.io/imagenet-annotation-preview/), [guidelines](https://gonikisgo.github.io/imagenet-annotation-preview/), and [analysis code](https://github.com/klarajanouskova/ImageNet) have been publicly released.

Spotlight
Domain-Conditioned Class Imbalance: Why Global Class Balance Fails Across Domains

Yongkun Deng, Nan Yang, Xiatong Guo, Zhiyong Wang, Dong Yuan

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Modern visual recognition systems increasingly rely on unlabeled images collected from diverse visual domains. A common goal in dataset construction is to avoid obvious marginal imbalance, such as skewed class totals or uneven domain sizes. However, marginal balance can be misleading in multi-domain data: even when per-class totals and per-domain sample sizes are balanced, sample allocations can be highly skewed across domain-class pairs. We call this hidden conditional skew Domain-Conditioned Class Imbalance (DCI), where class imbalance is revealed only after conditioning on domain context. For controlled evaluation, we fix class and domain marginals and vary only the joint domain--class allocation, making the effect of domain-conditioned imbalance directly measurable. To address this challenge, we propose HyperIDAC, a hypernetwork-based classifier for multi-domain imbalance. HyperIDAC infers domain priors from visual features and lightweight zero-shot predictions, then dynamically generates instance-specific classifier parameters and domain-conditioned class embeddings. This design yields domain-sensitive decision boundaries while leveraging CLIP semantics to support underrepresented domain--class pairs. Furthermore, a multi-level pseudo-labeling module combines teacher–student training with historical label tracking and a fallback for low-confidence samples, mitigating bias reinforcement in unlabeled settings. Extensive experiments on four multi-domain benchmarks under three regimes show that HyperIDAC substantially outperforms state-of-the-art methods, highlighting the value of domain-aware hypernetwork-based adaptation under DCI.

Poster
DocPTBench: Benchmarking End-to-End Photographed Document Parsing and Translation

Yongkun Du, Pinxuan Chen, Xuye Ying, Zhineng Chen

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The advent of Multimodal Large Language Models (MLLMs) has unlocked the potential for end-to-end document parsing and translation. However, prevailing benchmarks such as OmniDocBench and DITrans are dominated by pristine scanned or digital-born documents. They do not adequately represent the intricate challenges of real-world capture conditions, such as geometric distortions and photometric variations. To fill this gap, we introduce DocPTBench, a comprehensive benchmark specifically designed for Photographed Document Parsing and Translation. DocPTBench comprises over 1,300 high-resolution photographed documents from multiple domains, includes eight translation scenarios, and provides meticulously human-verified annotations for both parsing and translation. Our experiments demonstrate that transitioning from digital-born to photographed documents results in a substantial performance decline: popular MLLMs exhibit an average accuracy drop of 18\% in end-to-end parsing and 12\% in translation, while specialized document parsing models show a more prominent average decrease of 22\%. This substantial performance gap highlights the unique challenges posed by documents captured in real-world conditions and reveals the limited robustness of existing models. The benchmark and related code will be made publicly available for further research.

Poster
Do You CARE to Generalize? Extracting Robust Concept Directions from LLMs

Sweta Karlekar, Claudia Shi, Aahlad Manas Puli, Carolina Zheng, Maggie Makar, John Bowlan, Michal Kucer, David Blei

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Transformer-based large language models (LLMs) encode many high-level concepts as linear directions in the latent activation space. Once identified, these directions support both measurement, the quantification of a concept's presence, and intervention, the steering of the model's behavior. In practice, however, a direction learned from one context often fails when applied to prompts from a new context. This poor transfer can have two distinct sources: spurious correlation between the concept label and dataset-specific features, and genuine heterogeneity in how the concept is encoded across contexts. Methods from out-of-distribution (OOD) literature can address the first, but worsen the second by discarding context-specific structure that may carry concept signal. We introduce Context-Aided Representation Extraction (CARE), which bridges OOD generalization and mechanistic interpretability. Given activations labeled with a concept and an environment, CARE jointly learns a shared direction, optimized to be invariant across environments, and orthogonal environment-specific residuals that capture how the concept varies by context. We evaluate CARE on subject--verb agreement, refusal of harmful prompts, and toxicity. CARE produces directions that measure concepts more reliably under distribution shift and in unseen environments and datasets than existing methods while remaining effective for intervention. Its decomposition also supports a swap-cost diagnostic that identifies when context-specific structure carries concept-relevant signal.

Poster
Do LLMs Feel Social Pressure? Locating and Steering Social Desirability Bias in LLMs

Yi Feng, Jiaqi Wang, Wenxuan Zhang

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Humans often say what sounds acceptable rather than what they truly think when facing social pressure, a well-documented phenomenon called \textbf{Social Desirability Bias (SDB)}. Trained on human-generated text, LLMs are steeped in the same social fabric that produces these pressures, yet whether and how SDB shapes their responses remains unknown. We present \textbf{PRESS} (\textbf{P}sychologically-grounded \textbf{R}epresentation \textbf{E}xtraction for \textbf{S}ocial-desirability \textbf{S}teering), the first framework to identify, localise, and steer SDB inside open-weight LLMs. We decompose SDB into four observable and relatively orthogonal mechanisms: \emph{Audience}, \emph{Accountability}, \emph{Self-Monitoring}, and \emph{Social Norms}, and operationalise each as paired High/Low pressure conditions across 9 cultures in cultural values where social pressure bites hardest. Our experiments show that SDB forms a decodable and low-dimensional direction inside LLMs, organised by specific psychological mechanism rather than cultural origin. Steering along it improves all 58 downstream cultural content moderation tasks across three model families (Qwen $+5.7\%$,Gemma $+7.9\%$, Llama $+16.3\%$ mean F1 across cultures), and a direction extracted from one culture can transfer to others without re-extraction. Ablation confirms the direction is causally necessary, and evaluation on capability benchmarks further shows PRESS shifts cultural stance without disrupting factual knowledge.We hope this work makes social pressure in LLMs more transparent and opens new directions toward more honest and socially aware language models.

Poster
Do Composed Image Retrieval Benchmarks Require Multimodal Composition?

Matteo Attimonelli, Alessandro De Bellis, Aryo Gema, Rohit Saxena, Monica Sekoyan, Wai-Chung Kwan, Claudio Pomo, Alessandro Suglia, Dietmar Jannach, Tommaso Di Noia, Pasquale Minervini

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Composed Image Retrieval (CIR) is a multimodal retrieval task where a query consists of a reference image and a textual modification, and the goal is to retrieve a target image satisfying both. In principle, strong performance on CIR benchmarks is assumed to require multimodal composition, i.e., combining complementary information from reference image and textual modification. In this work, we show that this assumption does not always hold. Across four widely used CIR benchmarks and eleven Generalist Multimodal Embedding models, a large fraction of queries can be solved using a single modality (from 32.2% to 83.6%), revealing pervasive unimodal shortcuts. Thus, high CIR performance can arise from unimodal signals rather than true multimodal composition. To better understand this issue, we perform a two-stage audit. First, we identify shortcut-solvable queries through cross-model analysis. Second, we conduct human validation on 4,741 shortcut-free queries, of which only 1,689 are well-formed, with common issues including ambiguous edits and mismatched targets. Re-evaluating models on this validated subset reveals qualitatively different behaviour: queries can no longer be solved with a single modality, and successful retrieval requires combining both inputs. While accuracy decreases, reliance on multimodal information increases. Overall, current CIR benchmarks conflate shortcut-solvable, noisy, and genuinely compositional queries, leading to an overestimation of model capability in multimodal composition. Datasets and annotations are available here.

Poster
Do Coding Agents Deceive Us? Detecting and Preventing Cheating via Capped Evaluation with Randomized Tests

Thanawat Lodkaew, Johannes Ackermann, Soichiro Nishimori, Nontawat Charoenphakdee, Masashi Sugiyama, Takashi Ishida

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A growing failure mode in agent evaluation and training is that models can achieve high evaluation scores by exploiting shortcuts instead of solving the intended task, producing \emph{deceptive} performance. This makes evaluation scores unreliable as measures of true task-solving ability. We propose CapCode, a framework for constructing coding datasets with randomized tests whose best achievable non-cheating performance is deliberately capped below one. This capped-performance design gives evaluation scores a clearer interpretation: scores substantially above the cap are implausible and therefore provide evidence of cheating. To prevent cheating, we propose CapReward, a reward design based on the CapCode principle to discourage optimization beyond the cap. Experiments across multiple datasets show that CapCode detects cheating while preserving performance ranking, and CapReward reduces cheating behavior, yielding models that better follow the intended task specification.

Poster
Distribution Corrected Decision Transformer for Offline Reinforcement Learning with Imbalanced Datasets

Chufan Chen, Bohao Tang, Dejiang Chen, zhang chao, Ruiqi Li, Hanbin Zhao, Hui Qian

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Decision Transformer (DT) has emerged as a powerful paradigm for offline reinforcement learning. For complex tasks with imbalanced datasets, where high-quality samples constitute only a small fraction of the data while the majority is suboptimal, the performance of DT methods usually degrade significantly due to the the offline data distribution deviates substantially from the stationary distribution of the optimal policy. In this paper, we construct a dual-based correction mechanism to mitigate the distribution shift problem and propose a Distribution Corrected Decision Transformer method. Specifically, we investigate the Lagrangian duality of the reward maximizing objective in the standard Markov decision problem and recover the optimal correction weights between the static offline data and optimal stationary distribution. Note that a double-KL regularizer is integrated in the objective to prioritize high-return state-action pairs while remaining anchored to valid data support. Subsequently, we use the learned weights to correct distributional bias in two critical components of DT: stabilizing policy evaluation through weighted temporal-difference learning, and improving policy extraction by prioritizing DT training on weighted dataset aligned with the corrected target distribution. We theoretically analyze the performance guarantee, proving our method improves upon standard baselines, and empirically demonstrate strong performance on D4RL benchmarks, particularly on highly imbalanced datasets where prior methods fail.

Poster
Disentangled Representation Learning via Flow Matching

Jinjin Chi, Taoping Liu, Mengtao Yin, Ximing Li, Yongcheng Jing, Jialie Shen, Leszek Rutkowski, Dacheng Tao

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Disentangled representation learning aims to capture the underlying explanatory factors of observed data, enabling a principled understanding of the data-generating process. Recent advances in generative modeling have introduced new paradigms for learning such representations. However, existing diffusion-based methods encourage factor independence via inductive biases, yet frequently lack strong semantic alignment. In this work, we propose a flow-matching–based framework for disentangled representation learning, which casts disentanglement as learning factor-conditioned flows in a compact latent space. To enforce explicit semantic alignment, we introduce a non-overlap (orthogonality) regularizer that suppresses cross-factor interference and reduces information leakage between factors. Extensive experiments across multiple datasets demonstrate consistent improvements over representative baselines, yielding higher disentanglement scores as well as improved controllability and sample fidelity.

Poster
Differentially Private Model Merging

Qichuan Yin, Manzil Zaheer, Tian Li

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In machine learning applications, privacy requirements during inference or deployment time could change constantly due to varying policies, regulations, or user experience. In this work, we aim to generate a magnitude of models to satisfy any target differential privacy (DP) requirement without additional training steps, given a set of existing models trained on the same dataset with different privacy/utility tradeoffs. We propose two post processing techniques, namely random selection and linear combination, to output final private models satisfying any target privacy parameter. We provide privacy accounting of these approaches from the lens of R\'enyi DP and privacy loss distributions for general problems. In a case study on private mean estimation, we precisely characterize the privacy/utility results and theoretically establish the superiority of linear combination over random selection. Empirically, we validate our approaches and analyses on several models and both synthetic and real-world datasets.

Poster
Differential Item Functioning as an Item-Level Diagnostic for LLM Benchmarks

Hansol Lee, Jason B Cho, Nick Haber, Benjamin Domingue, Sanmi Koyejo

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Comparative claims about large language model (LLM) performance are typically based on aggregate benchmark scores. This treats models with similar scores as comparable on the items the benchmark contains, an assumption that can fail if models from different populations succeed on systematically different items. We test this assumption using Differential Item Functioning (DIF), a psychometric diagnostic that flags items whose relative difficulty differs across groups after conditioning on overall performance. Applying Mantel--Haenszel DIF analyses to six widely-used LLM benchmarks across two widely-used open-source model families (Llama and Qwen), we find that many items behave differently across families even among models with the same total benchmark score, with some items favoring Llama-family models and others favoring Qwen-family models. The flagged items concentrate in benchmark-provided categorical content (subjects, subtasks, problem types), and choosing items based on which family they favor can substantially amplify, attenuate, or reverse aggregate family-level comparisons. Our results show that aggregate benchmark scores can summarize different item-level performance patterns across model populations, and that DIF offers a useful diagnostic for surfacing this variation.

Poster
Differentiable Exact Learning of Algorithms

Hristo Papazov, Francesco D&#x27, Angelo, Nicolas Flammarion

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We introduce a framework for differentiable exact learning of algorithms. The framework couples a state-tracking neural controller to an unbounded external environment and trains on policy-trajectory observations (PTOs) -- traces that record the environment's evolution under an expert's actions without exposing the expert's internal state. This supervision regime sidesteps Gold's impossibility barrier for input-output recursive learning while avoiding the unrealistic internal-state access required by prior provably correct approaches. As controllers, we propose Differentiable Finite-State Transducers (DFSTs), a minimalist multilinear model family that contains no nonlinearities and admits log-parallel training via prefix scans. Trained on tiny datasets, DFST and RNN controllers achieve error-free generalization on binary and decimal addition and multiplication to operands thousands of times longer than the training examples. Moreover, we provide strong empirical proof for exact learning of universal computation. Finally, we develop an extraction procedure that recovers compact finite-state transducers from trained controllers. We prove under a geometric clustering assumption that for binary addition the extracted transducer exactly replicates the expert policy on all valid inputs -- certifying differentiable exact learning of the algorithm.

Poster
DiffScore: Text Evaluation Beyond Autoregressive Likelihood

Wen Lai, Yingli Shen, Dingnan Jin, Qing Cui, JUN ZHOU, Maosong Sun, Alexander Fraser

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Autoregressive language models are widely used for text evaluation, however, their left-to-right factorization introduces positional bias, i.e., early tokens are scored with only leftward context, conflating architectural asymmetry with true text quality. We propose masked reconstruction as an alternative paradigm, where every token is scored using full bidirectional context. We introduce DiffScore, an evaluation framework built on Masked Large Diffusion Language Models. By measuring text recoverability across continuous masking rates, DiffScore eliminates positional bias and naturally establishes an evaluation hierarchy from local fluency to global coherence. We further provide diagnostic tools unavailable to autoregressive frameworks: multi-timestep quality profiles that decompose scores across masking rates, and bidirectional Pointwise Mutual Information (PMI) decomposition that disentangles fluency from faithfulness. Experiments across ten benchmarks show that DiffScore consistently outperforms autoregressive baselines in both zero-shot and fine-tuned settings.

Poster
Detection and Classification in Latent Spaces: High-Dimensional Analysis and Validation

Enis Chenchene, Anil S. Baslamisli, Paolo Braca

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Foundation models produce high-dimensional latent representations in which suitably designed statistical decision rules can be effective yet analytically tractable. We study such detectors in the high-dimensional regime, where latent dimension and training sample size grow proportionally. For linear and quadratic statistics, we derive explicit large-deviation characterizations of false-alarm and miss-detection performance under the Neyman--Pearson paradigm, and show how the binary analysis extends to multi-class classification. The resulting error probabilities and corresponding decay rates exhibit non-monotonic dependence on the shape parameter, including double-descent and, in some regimes, multiple-descent. Experiments on vision, text, and audio datasets using modern foundation models show close agreement between theoretical predictions and empirical performance. In particular, the proposed framework allows us to set a prescribed false-alarm level and accurately predict the corresponding miss-detection probability. Overall, our results provide a theoretically grounded and interpretable framework with competitive empirical performance across different modalities.

Poster
Derivative-Informed Training of Neural Operators On-the-Fly via Sketched Tangent Consistency

Shancong (Sean) Mou, Xinhan Yang, Lu Lu

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Derivative-informed training improves neural operators by directly supervising their input--output sensitivities, but existing methods rely on offline tangent solves and stored derivative labels. We propose sketched tangent consistency loss (sTCL), an on-the-fly drop-in derivative regularizer for neural-operator training that improves learned Jacobians without changing the architecture or generating offline sensitivity data. At each training step, sTCL samples a small number of perturbation directions in the input function space, computes the corresponding surrogate Jacobian--vector products using forward-mode automatic differentiation, and penalizes the residual of the forward sensitivity equation. This equation is obtained by differentiating the governing PDE with respect to the input perturbation direction, so derivative supervision is obtained directly from the physics rather than from stored tangent labels. We further show that sketching makes online derivative-informed training computationally feasible, while conditioning is the key to making it effective. Random directional sketching keeps the derivative penalty at the same order of cost as the standard data-fitting loss, making sTCL compatible with stochastic neural-network training as a lightweight loss term. However, raw forward-sensitivity residual penalties can fail for stiff, ill-conditioned, or indefinite tangent operators. To address this, we introduce lightweight operator-aware preconditioners selected by a simple tangent-operator decision rule. Across four PDE benchmarks---Helmholtz, nonlinear diffusion--reaction, Burgers, and two-dimensional Navier--Stokes---operator-conditioned sTCL achieves accuracy comparable to offline DIFNO while eliminating the offline derivative-data generation stage. These results show that on-the-fly derivative-informed training need not merely amortize offline tangent-solve cost into training; with appropriate sketching and conditioning, sTCL provides an attractive drop-in path to derivative-informed neural operators.

Poster