ICLR 2026 Papers

Diffusion language models have recently emerged as a competitive alternative to autoregressive language models. Beyond next-token generation, they are more efficient and flexible by enabling parallel and any-order token generation. However, despite empirical successes, their computational power and fundamental limitations remain poorly understood. In this paper, we formally study whether non-autoregressive generation in Masked Diffusion Models (MDM) enables solving problems beyond the reach of Auto-Regressive Models (ARM). Our results show that MDM with sufficiently large context length is computationally universal with decoding steps matching the optimal parallel time complexity in PRAM. However, when controlling for other factors, MDM's flexibility to generate in any-order does not expand what ARM can already solve. To address this, we propose a new form of generation called any-process generation, which extends MDM with capabilities to remask, insert and delete tokens, allowing self-correction, length-variable editing, and adaptive parallelism. Theoretically and empirically, we demonstrate these capabilities enable scalability to significantly harder reasoning problems that are otherwise intractable for ARM and vanilla MDM. Additionally, they prove essential for generation tasks where objects naturally evolve through non-sequential processes, crucial for extending current LLMs beyond natural language to domains such as coding and science.

Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condition for nonnegativity is the Sum-of-Squares property, i.e., it can be written as a sum of squares of other polynomials. In practice, however, certifying the SOS criterion remains computationally expensive and often involves solving a Semidefinite Program (SDP), whose dimensionality grows quadratically in the size of the monomial basis of the SOS expression; hence, various methods to reduce the size of the monomial basis have been proposed. In this work, we introduce the first learning-augmented algorithm to certify the SOS criterion. To this end, we train a Transformer model that predicts an almost-minimal monomial basis for a given polynomial, thereby drastically reducing the size of the corresponding SDP. Our overall methodology comprises three key components: efficient training dataset generation of over 100 million SOS polynomials, design and training of the corresponding Transformer architecture, and a systematic fallback mechanism to ensure correct termination, which we analyze theoretically. We validate our approach on over 200 benchmark datasets, achieving speedups of over $100\times$ compared to state-of-the-art solvers and enabling the solution of instances where competing approaches fail. Our findings provide novel insights towards transforming the practical scalability of SOS programming.

Infographic charts are a powerful medium for communicating abstract data by combining visual elements (e.g., charts, images) with textual information. However, their visual and structural richness poses challenges for large vision-language models (LVLMs), which are typically trained on plain charts. To bridge this gap, we introduce ChartGalaxy, a million-scale dataset designed to advance the understanding and generation of infographic charts. The dataset is constructed through an inductive process that identifies 75 chart types, 440 chart variations, and 68 layout templates from real infographic charts and uses them to create synthetic ones programmatically. We showcase the utility of this dataset through: 1) improving infographic chart understanding via fine-tuning, 2) benchmarking code generation for infographic charts, and 3) enabling example-based infographic chart generation. By capturing the visual and structural complexity of real design, ChartGalaxy provides a useful resource for enhancing multimodal reasoning and generation in LVLMs.

Graph Neural Networks (GNNs) achieve strong empirical performance across domains, yet their fundamental statistical behavior remains poorly understood. This paper develops a minimax analysis of ReLU message-passing GNNs with explicit architectural assumptions, in both inductive (graph-level) and transductive (node-level) settings. For arbitrary graphs without structural constraints, we show that the worst-case generalization error scales as $\sqrt{\log d / n}$ with sample size $n$ and input dimension $d$, matching the $1/\sqrt{n}$ behavior of feed-forward networks. Under a spectral--homophily condition combining strong label homophily and bounded spectral expansion, we prove a stronger minimax lower bound of $d/\log n$ for transductive node prediction. We complement these results with a systematic empirical study on three large-scale benchmarks (ogbn\_arxiv, ogbn\_products\_50k, Reddit\_50k) and two controlled synthetic datasets representing the worst-case and structured regimes of our theory. All benchmark graphs we study fall in the slow-mixing, bottlenecked regime captured by our spectral-homophily condition, and ratio-based scaling tests show error decay consistent with the $d/\log n$ rate in real and structured settings, while the worst-case synthetic dataset follows the $\sqrt{\log d / n}$ curve. Together, these results indicate that practical GNN tasks often operate in the spectral-homophily regime, where our lower bound $d/\log n$ is tight and effective sample complexity is driven by graph topology rather than universal $1/\sqrt{n}$ behavior.

Safety evaluation of multimodal foundation models often treats vision and language inputs separately, missing risks from joint interpretation where benign content becomes harmful in combination. Existing approaches also fail to distinguish clearly unsafe content from borderline cases, leading to problematic over-blocking or under-refusal of genuinely harmful content. We present Vision Language Safety Understanding (VLSU), a comprehensive framework to systematically evaluate multimodal safety through fine-grained severity classification and combinatorial analysis across 17 distinct safety patterns. Using a multi-stage pipeline with real-world images and human annotation, we construct a large-scale benchmark of 8,187 samples spanning 15 harm categories. Our evaluation of eleven state-of-the-art models reveals systematic joint understanding failures: while models achieve 90\%+ accuracy on clear unimodal safety signals, performance degrades substantially to 20-55\% when joint image-text reasoning is required to determine the safety label. Most critically, 34\% of errors in joint image-text safety classification occur despite correct classification of the individual modalities, further demonstrating absent compositional reasoning capabilities. Additionally, we find that models struggle to balance refusing unsafe content while still responding to borderline cases that deserve engagement. For example, we find that instruction framing can reduce the over-blocking rate on borderline content from 62.4\% to 10.4\% in Gemini-1.5, but only at the cost of under-refusing on unsafe content with refusal rate dropping from 90.8\% to 53.9\%. Overall, our framework exposes weaknesses in joint image-text understanding and alignment gaps in current models, and provides a critical test bed to enable the next milestones in research on robust vision–language safety.

The pursuit of robot generalists—instructable agents capable of performing diverse tasks across diverse environments—demands rigorous and scalable evaluation. Yet real-world testing of robot policies remains fundamentally constrained: it is labor-intensive, slow, unsafe at scale, and difficult to reproduce. Existing simulation benchmarks are similarly limited, as they train and test policies within the same synthetic domains and cannot assess models trained primarily on real-world demonstrations, which is the dominant paradigm for today’s vision-language-action (VLA) models. As policies expand in scope and complexity, these barriers only intensify, since defining ``success" in robotics often hinges on nuanced human judgments of execution quality. In this paper, we introduce a new benchmarking framework that overcomes these challenges by shifting VLA evaluation into large-scale simulated environments augmented with online human feedback. Leveraging advances in vision-language models, 2D-to-3D generative modeling, and differentiable rendering, our approach automatically converts video demonstrations from widely used robot datasets into simulated counterparts. Within these digital twins, we assess VLA policies using both automated VLM-guided scoring and scalable human preference judgments collected from crowdworkers—transforming human involvement from tedious scene setup, resetting, and safety supervision into lightweight preference comparisons.

Urban development impacts over half of the global population, making human-centered understanding of its structural and perceptual changes essential for smart city planning. While Multimodal Large Language Models (MLLMs) have shown remarkable capabilities across various domains, existing benchmarks that explore their performance in urban environments remain limited, lacking systematic exploration of temporal evolution and subjective perception of urban environment that aligns with human perception. To address these limitations, we propose UrbanFeel, a comprehensive benchmark designed to evaluate the performance of MLLMs in urban development understanding and subjective environmental perception. UrbanFeel comprises 14.3K carefully constructed visual questions spanning three cognitively progressive dimensions: Static Scene Perception, Temporal Change Perception, and Subjective Environmental Perception. We collect multi-temporal single-view and panoramic street-view images from 11 representative cities worldwide, and generate high-quality question-answer pairs through a hybrid pipeline of spatial clustering, rule-based generation, model-assisted prompting, and manual annotation. Through extensive evaluation of 20 state-of-the-art MLLMs, we observe that Gemini-2.5 Pro achieves the best overall performance, with its accuracy approaching human expert levels and narrowing the average gap to just 1.5%. Most models perform well on tasks grounded in scene understanding. In particular, some models even surpass human annotators in pixel-level change detection. However, performance drops notably in tasks requiring temporal reasoning over urban development. Additionally, in the subjective perception dimension, several models reach human-level or even higher consistency in evaluating dimension such as beautiful and safety. Our results suggest that MLLMs are demonstrating rudimentary emotion understanding capabilities. Our UrbanFeel benchmark will be made publicly available.

Video generation models, as one form of world models, has emerged as one of the most exciting frontiers in AI, promising agents the ability to imagine the future by modeling the temporal evolution of complex scenes. In autonomous driving, this vision gives rise to driving world models—generative simulators that imagine ego and agent futures, enabling scalable simulation, safe testing of corner cases, and rich synthetic data generation. Yet, despite fast-growing research activity, the field lacks a rigorous benchmark to measure progress and guide priorities. Existing evaluations remain limited: generic video metrics overlook safety-critical imaging factors; trajectory plausibility is rarely quantified; temporal and agent-level consistency is neglected; and controllability with respect to ego conditioning is ignored. Moreover, current datasets fail to cover the diversity of conditions required for real-world deployment. To address these gaps, we present DrivingGen, the first comprehensive benchmark for generative driving world models. DrivingGen combines a diverse evaluation dataset—curated from both driving datasets and internet-scale video sources, spanning varied weather, time of day, geographic regions, and complex maneuvers—with a suite of new metrics that jointly assess visual realism, trajectory plausibility, temporal coherence, and controllability. Benchmarking 14 state-of-the-art models reveals clear trade-offs: general models look better but break physics, while driving-specific ones capture motion realistically but lag in visual quality. DrivingGen offers a unified evaluation framework to foster reliable, controllable, and deployable driving world models, enabling scalable simulation, planning, and data-driven decision-making.

Humans can imagine and manipulate visual images mentally, a capability known as \textit{spatial visualization}. While many multi-modal benchmarks assess reasoning on visible visual information, the ability to infer unseen relationships through spatial visualization remains insufficiently evaluated as a spatial skill. This reliance on publicly sourced problems from IQ tests or math competitions risks data contamination and compromises assessment reliability. To this end, we introduce \textbf{\textit{SpatialViz-Bench}}, a comprehensive multi-modal benchmark for \textit{spatial visualization} with \emph{12} tasks across \emph{4} sub-abilities, comprising \emph{1,180} programmatically generated problems, a scalable framework that allows for expansion to ensure fair and continuously reliable evaluations. Our evaluation of \emph{27} Multi-modal Large Language Models (MLLMs) reveals wide performance variations, demonstrates the benchmark's strong discriminative power, and uncovers counter-intuitive findings: Chain-of-Thought (CoT) prompting paradoxically degrades accuracy on open-source models. Through statistical and qualitative analysis of error types, SpatialViz-Bench demonstrates that state-of-the-art MLLMs exhibit deficiencies in \textit{spatial visualization} tasks, thereby addressing a significant lacuna in the field.

Recent progress in Large Language Models (LLMs) has transformed them from text generators into agentic systems capable of multi-step reasoning, structured planning, and tool use. However, existing benchmarks inadequately capture their ability to orchestrate complex workflows across multiple domains under realistic constraints. To address this, we propose OrchestrationBench, a multilingual (English/Korean) benchmark that systematically evaluates (1) workflow-based planning and (2) constraint-aware tool execution. OrchestrationBench spans 17 representative domains with nearly 100 realistic virtual tools, covering scenarios that require sequential/parallel planning and compliance with business constraints. Unlike previous work, it explicitly disentangles planning evaluation from tool execution evaluation, which assesses tool selection, argument extraction, validation, and rejection handling. Constructed entirely through manual annotation with cultural adaptation, the benchmark ensures authenticity, diversity, and freedom from model-specific biases. Extensive experiments across state-of-the-art models show that function calling performance is relatively consistent, whereas planning capabilities exhibit substantial variation across models, emphasizing the need for structured planning evaluation. As a living benchmark, OrchestrationBench is designed to expand toward new domains, tools, and integration enabling rigorous, cross-cultural, and service-ready evaluation of LLM orchestration capabilities. The benchmark is publicly available at GitHub.

Spiking neural networks (SNNs) are a promising paradigm for energy-efficient computation, yet their theoretical foundations—especially regarding stability and robustness—remain limited compared to artificial neural networks. In this work, we study discrete-time leaky integrate-and-fire (LIF) SNNs through the lens of Boolean function analysis. We focus on noise sensitivity and stability in classification tasks, quantifying how input perturbations affect outputs. Our main result shows that wide LIF-SNN classifiers are stable on average, a property explained by the concentration of their Fourier spectrum on low-frequency components. Motivated by this, we introduce the notion of *spectral simplicity*, which formalizes simplicity in terms of Fourier spectrum concentration and connects our analysis to the *simplicity bias* observed in deep networks. Within this framework, we show that random LIF-SNNs are biased toward simple functions. Experiments on trained networks confirm that these stability properties persist in practice. Together, these results provide new insights into the stability and robustness properties of SNNs.

Video understanding, including video captioning and retrieval, is still a great challenge for video-language models (VLMs). The existing video retrieval and caption benchmarks only include short descriptions, limits their ability of detailed video understanding evaluation. To address this problem, we present CaReBench, a testing benchmark for fine-grained video Captioning and Retrieval with 1,000 high-quality pairs of videos and human-annotated detailed captions. Uniquely, it provides manually separated spatial annotations and temporal annotations for each video. Based on this design, we introduce two evaluation metrics, ReBias and CapST, specifically tailored for video retrieval and video captioning tasks, respectively. These metrics enable a comprehensive investigation into the spatial and temporal biases inherent in VLMs. In addition, to handle both video retrieval and video captioning tasks in a unified framework, we develop a simple baseline based on a Multimodal Language Model (MLLM). By implementing a two-stage Supervised Fine-Tuning (SFT), we fully unlock the potential of MLLM, enabling it not only to generate detailed video descriptions but also to extract video features. Surprisingly, experimental results demonstrate that, compared to the CLIP-based models designed for retrieval and the popular MLLMs skilled in video captioning, our baseline shows competitive performance in both fine-grained video retrieval and video detailed captioning.

The evaluation of discourse-level translation in expert domains remains inadequate, despite its centrality to knowledge dissemination and cross-lingual scholarly communication. While these translations demand discourse-level coherence and strict terminological precision, current evaluation methods predominantly focus on segment-level accuracy and fluency. To address this limitation, we introduce DiscoX, a new benchmark for discourse-level and expert-level Chinese-English translation. It comprises 200 professionally-curated texts from 7 domains, with an average length exceeding 1700 tokens. To evaluate performance on DiscoX, we also develop Metric-S, a reference-free system that provides fine-grained automatic assessments across accuracy, fluency, and appropriateness. Metric-S demonstrates strong consistency with human judgments, significantly outperforming existing metrics. Our experiments reveal a remarkable performance gap: even the most advanced LLMs still trail human experts on these tasks. This finding validates the difficulty of DiscoX and underscores the challenges that remain in achieving professional-grade machine translation. The proposed benchmark and evaluation system provide a robust framework for more rigorous evaluation, facilitating future advancements in LLM-based translation. Our data and code are available at https://anonymous.4open.science/r/DiscoX-5F18.

Existing language model benchmarks provide contradictory model rankings, even for benchmarks that aim to capture similar skills. This dilemma of conflicting rankings hampers model selection, clouds model comparisons, and adds confusion to a growing ecosystem of competing models. In this paper, we take a different perspective on model comparison: instead of relying on out-of-the-box performance via direct evaluation, we compare model potential by providing each model with identical benchmark-specific fine-tuning before evaluation. We call this approach train-before-test. Our primary contribution is a comprehensive empirical evaluation of model potential across 24 benchmarks and 61 models. First, we demonstrate that model potential rankings obtained through train-before-test exhibit remarkable consistency across all benchmarks. Whereas traditional rankings demonstrate little external validity under direct evaluation, they enjoy a significant degree of external validity when applying train-before-test: model potential rankings transfer gracefully from one benchmark to another. Second, train-before-test restores the connection between perplexity and downstream task performance, lost under direct evaluation. Remarkably, even pre-finetuning perplexity of a base model predicts post-finetuning downstream performance, suggesting that ranking consistency reflects inherent model potential rather than fine-tuning artifacts. Finally, train-before-test reduces the model-score matrix to essentially rank one, indicating that model potential is dominated by one latent factor, uncovered by train-before-test. While direct evaluation remains useful for assessing deployment-ready performance, train-before-test provides a complementary lens for understanding achievable performance of models after adaptation.

The pre-training of large language models (LLMs) relies on massive text datasets sourced from diverse and difficult-to-curate origins. Although membership inference attacks and hidden canaries have been explored to trace data usage, such methods rely on *regurgitation* of training data, which LM providers try to limit. In this work, we demonstrate that *indirect data poisoning* (where the targeted behavior is absent from training data) is not only feasible against LLMs but also allows to effectively protect a dataset and trace its use. Using gradient-based optimization prompt-tuning, we craft poisons to make a model learn arbitrary *secret sequences*: secret responses to secret prompts that are **absent from the training corpus**.\ We validate our approach on language models pre-trained from scratch and show that less than 0.005\% of poisoned tokens are sufficient to covertly make a LM learn a *secret* and detect it with extremely high confidence ( $p < 10^{-55}$ ) with a theoretically certifiable scheme. Crucially, this occurs without performance degradation (on LM benchmarks) and despite secrets **never appearing in the training set**.

Weight-space models learn directly from the parameters of neural networks, enabling tasks such as predicting their accuracy on new datasets. Naive methods -- like applying MLPs to flattened parameters -- perform poorly, making the design of better weight-space architectures a central challenge. While prior work leveraged permutation symmetries in standard networks to guide such designs, no analogous analysis or tailored architecture yet exists for Kolmogorov–Arnold Networks (KANs). In this work, we show that KANs share the same permutation symmetries as MLPs, and propose the KAN-graph, a graph representation of their computation. Building on this, we develop WS-KAN, the first weight-space architecture that learns on KANs, which naturally accounts for their symmetry. We analyze WS-KAN’s expressive power, showing it can replicate an input KAN’s forward pass - a standard approach for assessing expressiveness in weight-space architectures. We construct a comprehensive ``zoo'' of trained KANs spanning diverse tasks, which we use as benchmarks to empirically evaluate WS-KAN. Across all tasks, WS-KAN consistently outperforms structure-agnostic baselines, often by a substantial margin.

This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best capture the modes of variation of the underlying dataset. We first address the case of a collection of Gaussian distributions, and show how to lift the computations in the space of invertible linear maps. For the more general setting of absolutely continuous probability measures, we leverage a novel approach to parameterizing geodesics in Wasserstein space with neural networks. Finally, we compare to classical tangent PCA through various examples and provide illustrations on real-world datasets.

Large Language Models have demonstrated strong performance across a wide range of tasks, but adapting them efficiently to new domains remains a key challenge. Parameter-Efficient Fine-Tuning (PEFT) methods address this by introducing lightweight, trainable modules while keeping most pre-trained weights fixed. The prevailing approach, LoRA, models updates using a low-rank decomposition, but its expressivity is inherently constrained by the rank. Recent methods like HiRA aim to increase expressivity by incorporating a Hadamard product with the frozen weights, but still rely on the structure of the pre-trained model. We introduce ABBA, a new PEFT architecture that reparameterizes the update as a Hadamard product of two independently learnable low-rank matrices. In contrast to prior work, ABBA fully decouples the update from the pre-trained weights, enabling both components to be optimized freely. This leads to significantly higher expressivity under the same parameter budget, a property we validate through matrix reconstruction experiments. Empirically, ABBA achieves state-of-the-art results on arithmetic and commonsense reasoning benchmarks, consistently outperforming existing PEFT methods by a significant margin across multiple models. Our code is publicly available at: https://github.com/CERT-Lab/abba.

Peptide therapeutics are widely regarded as the “third generation” of drugs, yet progress in peptide Machine Learning (ML) are hindered by the absence of standardized benchmarks. Here we present \textbf{PepBenchmark}, which standardizes datasets, preprocessing, and evaluation protocols for peptide drug discovery. PepBenchmark comprises three components: (1) \textbf{PepBenchData}, a well-curated collection comprising 29 canonical-peptide and 6 non-canonical-peptide datasets across 7 groups, systematically covering key aspects of peptide drug development—representing, to the best of our knowledge, the most comprehensive AI-ready dataset resource to date; (2) \textbf{PepBenchPipeline}, a standardized preprocessing pipeline that ensures consistent cleaning, representation conversion, and dataset splitting, addressing the quality issues that often arise from ad-hoc pipelines; and (3) \textbf{PepBenchLeaderboard}, a unified evaluation protocol and leaderboard with strong baselines across 4 major methodological families: fingerprint-based, GNN-based, PLM-based, and SMILES-based models. Together, PepBenchmark provides the first standardized and comparable foundation for peptide drug discovery, facilitating methodological advances and translation into real-world applications. Code is included in the supplementary material and will be made publicly available.