ICLR 2026 Papers

We propose succinctness as a measure of expressive power of a transformer in describing a concept. To this end, we prove that transformers are highly expressive in that they can represent formal languages substantially more succinctly than standard representations of formal languages like finite automata and Linear Temporal Logic (LTL) formulas. As a by-product of this expressivity, verifying even simple properties of transformers is shown to be provably intractable (i.e. EXPSPACE-complete).

AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-specific datasets. A rich, largely untapped resource lies in non-Hermitian quantum physics, where the energy spectra of crystals form intricate geometries on the complex plane—termed as $\textit{Hamiltonian spectral graphs}$. Despite their significance as fingerprints for electronic behavior, their systematic study has been intractable due to the reliance on manual extraction. To unlock this potential, we introduce $\textbf{Poly2Graph}$ (https://github.com/sarinstein-yan/Poly2Graph): a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present $\textbf{HSG-12M}$ (https://github.com/sarinstein-yan/HSG-12M): a dataset containing 11.6 million static and 5.1 million dynamic Hamiltonian spectral graphs across 1401 characteristic-polynomial classes, distilled from 177 TB of spectral potential data. Crucially, HSG-12M is the first large-scale dataset of $\textit{spatial multigraphs}$—graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. This simultaneously addresses a critical gap, as existing graph benchmarks overwhelmingly assume simple, non-spatial edges, discarding vital geometric information. Benchmarks with popular GNNs expose new challenges in learning spatial multi-edges at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for data-driven scientific discovery in condensed matter physics, new opportunities in geometry-aware graph learning and beyond.

We introduce WorldSense, the first benchmark to assess the multi-modal video understanding, that simultaneously encompasses visual, audio, and text inputs. In contrast to existing benchmarks, our WorldSense has several features: (i) collaboration of omni-modality, we design the evaluation tasks to feature a strong coupling of audio and video, requiring models to effectively utilize the synergistic perception of omni-modality; (ii) diversity of videos and tasks, WorldSense encompasses a diverse collection of 1,662 audio-visual synchronised videos, systematically categorized into 8 primary domains and 67 fine-grained subcategories to cover the broad scenarios, and 3,172 multi-choice QA pairs across 26 distinct tasks to enable the comprehensive evaluation; (iii) high-quality annotations, all the QA pairs are manually labeled by 80 expert annotators with multiple rounds of correction to ensure quality. Based on our WorldSense, we extensively evaluate various state-of-the-art models. The experimental results indicate that existing models face significant challenges in understanding real-world scenarios (65.1% best accuracy). By analyzing the limitations of current models, we aim to provide valuable insight to guide development of real-world understanding. We hope our WorldSense can provide a platform for evaluating the ability in constructing and understanding coherent contexts from omni-modality.

General SVG modeling remains challenging due to fragmented datasets, limited transferability of methods across tasks, and the difficulty of handling structural complexity. In response, we leverage the strong transfer and generalization capabilities of multimodal large language models (MLLMs) to achieve unified modeling for SVG understanding, editing, and generation. We present the InternSVG family, an integrated data–benchmark–model suite. At its core is SAgoge, the largest and most comprehensive multimodal dataset for SVG tasks, encompassing both static graphics and dynamic animations. It covers icons, long-sequence illustrations, scientific diagrams, and dynamic animations, supporting tasks of varied difficulty levels and providing deeper hierarchies with richer attributes compared to previous datasets. Based on this resource, we introduce SArena, a companion benchmark with comprehensive task definitions and standardized evaluation that aligns with the domains and difficulty spectrum covered by SAgoge. Building on these foundations, we propose InternSVG, a unified MLLM for SVG understanding, editing, and generation with SVG-specific special tokens, subword-based embedding initialization, and a two-stage training strategy that progresses from short static SVGs to long-sequence illustrations and complex animations. This unified formulation induces positive transfer and improves overall performance. Experiments on \benchset and prior benchmark confirm that InternSVG achieves substantial gains and consistently outperforms leading open and proprietary counterparts.

We introduce **EA3D**, an Event-Augmented 3D Diffusion framework for generalizable novel view synthesis from event streams and sparse RGB inputs. Existing approaches either rely solely on RGB frames for generalizable synthesis, which limits their robustness under rapid camera motion, or require per-scene optimization to exploit event data, undermining scalability. EA3D addresses these limitations by jointly leveraging the complementary strengths of asynchronous events and RGB imagery. At its core lies a learnable EA-Renderer, which constructs view-dependent 3D features within target camera frustums by fusing appearance cues from RGB frames with geometric structure extracted from adaptively sliced event voxels. These features condition a 3D-informed diffusion model, enabling high-fidelity and temporally consistent novel view generation along arbitrary camera trajectories. To further enhance scalability and generalization, we develop the Event-DL3DV dataset, a large-scale 3D benchmark pairing diverse synthetic event streams with photorealistic multi-view RGB images and depth maps. Extensive experiments on both real-world and synthetic event data demonstrate that EA3D consistently outperforms optimization-based and generalizable baselines, achieving superior fidelity and cross-scene generalization.

Deep learning methods for electronic-structure Hamiltonian prediction have offered significant computational efficiency advantages over traditional density functional theory (DFT), yet the diversity of atomic types, structural patterns, and the high-dimensional complexity of Hamiltonians pose substantial challenges to the generalization performance. In this work, we contribute on both the methodology and dataset sides to advance universal deep learning paradigm for Hamiltonian prediction. On the method side, we propose NextHAM, a neural E(3)-symmetry and expressive correction method for efficient and generalizable materials electronic-structure Hamiltonian prediction. First, we introduce the zeroth-step Hamiltonians, which can be efficiently constructed by the initial charge density of DFT, as informative input descriptors that enable the model to effectively capture prior knowledge of electronic structures. Second, we present a neural Transformer architecture with strict E(3)-symmetry and high non-linear expressiveness for Hamiltonian prediction. Third, we propose a novel training objective to ensure the accuracy performance of Hamiltonians in both real space and reciprocal space, preventing error amplification and the occurrence of ``ghost states'' caused by the large condition number of the overlap matrix. On the dataset side, we curate a broad-coverage large benchmark, namely Materials-HAM-SOC, comprising $17,000$ material structures spanning more than $60$ elements from six rows of the periodic table and explicitly incorporating spin–orbit coupling (SOC) effects, providing high-quality data resources for training and evaluation. Comprehensive experimental results demonstrate that NextHAM achieves excellent accuracy in predicting Hamiltonians and band structures, with spin-off-diagonal blocks reaching the accuracy of sub-$\mu$eV scale. These results establish NextHAM as a universal and highly accurate deep learning model for electronic-structure prediction, delivering DFT-level precision with dramatically improved computational efficiency.

Offline reinforcement learning (RL) aims to learn the optimal policy from a fixed dataset generated by behavior policies without additional environment interactions. One common challenge that arises in this setting is the out-of-distribution (OOD) error, which occurs when the policy leaves the training distribution. Prior methods penalize a statistical distance term to keep the policy close to the behavior policy, but this constrains policy improvement and may not completely prevent OOD actions. Another challenge is that the optimal policy distribution can be multimodal and difficult to represent. Recent works apply diffusion or flow policies to address this problem, but it is unclear how to avoid OOD errors while retaining policy expressiveness. We propose ReFORM, an offline RL method based on flow policies that enforces the less restrictive support constraint by construction. ReFORM learns a behavior cloning (BC) flow policy with a bounded source distribution to capture the support of the action distribution, then optimizes a reflected flow that generates bounded noise for the BC flow while keeping the support, to maximize the performance. Across 40 challenging tasks from the OGBench benchmark with datasets of varying quality and using a constant set of hyperparameters for all tasks, ReFORM dominates all baselines with hand-tuned hyperparameters on the performance profile curves.

Reasoning models improve their problem-solving ability through inference-time scaling, allocating more compute via longer token budgets. Identifying which reasoning traces are likely to succeed remains a key opportunity: reliably predicting productive paths can substantially reduce wasted computation and improve overall efficiency. We introduce Latent-Trajectory signals that characterize the temporal evolution of a model's internal representations during the generation of intermediate reasoning tokens. By analyzing both the extent and temporal course of latent representational change, as well as its alignment with the final state, we show that these signals are strong predictors of solution accuracy, outperforming conventional output-based confidence measures. We use latent-trajectory signals to guide answer selection across multiple sampled generations, demonstrating that they make test-time scaling more effective and efficient, reducing token usage by up to 70% while preserving and even improving accuracy by 2.6% on average in comparison with majority voting. Finally, we show that these signals often emerge early in the reasoning trace, which enables early selection and allocation of compute to the most promising candidates during generation. Our findings contribute not only practical strategies for inference-time efficiency, but also a deeper interpretability perspective on how reasoning processes are represented and differentiated in latent space.

Large Vision-Language Models (LVLMs) exhibit outstanding performance on vision-language tasks but struggle with hallucination problems. Through in-depth analysis of LVLM activation patterns, we reveal two key findings: 1) truthfulness and visual perception capabilities predominantly engage different subsets of attention heads within the model architecture; and 2) truthfulness steering vectors vary significantly across different semantic contexts. Based on these observations, we propose Dynamic Multimodal Activation Steering, a training-free approach for hallucination mitigation. Our method constructs a semantic-based truthfulness steering vector database and computes visual perception steering vectors, enabling context-aware interventions during inference by dynamically selecting the most relevant steering vectors based on input semantic similarity and applying them to the most influential attention heads. We conduct comprehensive experiments across multiple models and datasets, demonstrating that our approach significantly enhances model performance, outperforming existing state-of-the-art methods.

Copulas are a fundamental tool for modelling multivariate dependencies in data, forming the method of choice in diverse fields and applications. However, the adoption of existing models for multimodal and high-dimensional dependencies is hindered by restrictive assumptions and poor scaling. In this work, we present methods for modelling copulas based on the principles of diffusions and flows. We design two processes that progressively forget inter-variable dependencies while leaving dimension-wise distributions unaffected, provably defining valid copulas at all times. We show how to obtain copula models by learning to remember the forgotten dependencies from each process, theoretically recovering the true copula at optimality. The first instantiation of our framework focuses on direct density estimation, while the second specialises in expedient sampling. Empirically, we demonstrate the superior performance of our proposed methods over state-of-the-art copula approaches in modelling complex and high-dimensional dependencies from scientific datasets and images. Our work enhances the representational power of copula models, empowering applications and paving the way for their adoption on larger scales and more challenging domains.

Video recognition models are typically trained on fixed taxonomies which are often too coarse, collapsing distinctions in object, manner or outcome under a single label. As tasks and definitions evolve, such models cannot accommodate emerging distinctions and collecting new annotations and retraining to accommodate such changes is costly. To address these challenges, we introduce category splitting, a new task where an existing classifier is edited to refine a coarse category into finer subcategories, while preserving accuracy elsewhere. We propose a zero-shot editing method that leverages the latent compositional structure of video classifiers to expose fine-grained distinctions without additional data. We further show that low-shot fine-tuning, while simple, is highly effective and benefits from our zero-shot initialization. Experiments on our new video benchmarks for category splitting demonstrate that our method substantially outperforms vision-language baselines, improving accuracy on the newly split categories without sacrificing performance on the rest. Project page: https://kaitingliu.github.io/Category-Splitting/.

Large Language Models (LLMs) increasingly use persistent memory from past interactions to enhance personalization and task performance. However, this memory creates critical risks when sensitive information is revealed in inappropriate contexts. We present CIMemories, a benchmark for evaluating whether LLMs appropriately control information flow from memory based on task context. CIMemories uses synthetic user profiles with 100+ attributes per user, paired with various task contexts where each attribute may be essential for some tasks but inappropriate for others. For example, mental health details are necessary for booking therapy but inappropriate when requesting time off from work. This design enables two forms of compositionality: (1) flexible memory composition by varying which attributes are necessary versus inappropriate across different settings, and (2) multi-task composition per user, measuring cumulative information disclosure across sessions. Our evaluation reveals frontier models exhibit between 14%-69% attribute-level violations (leaking inappropriate information), and that higher task completeness (sharing necessary information) is accompanied by increased violations, highlighting critical gaps in integrity-aware memory systems.

While scaling laws for Large Language Models (LLMs) traditionally focus on proxy metrics like pretraining loss, predicting downstream task performance has been considered unreliable. This paper challenges that view by proposing a direct framework to model the scaling of downstream accuracy from the training budget. We demonstrate that for a fixed token-to-parameter ratio, a simple two-parameter scaling law accurately describes this relationship. Our findings are validated by experiments on models with up to 17B parameters trained on up to 350B tokens, showing that downstream capabilities scaling can be described using a scaling law. Furthermore, we extend this framework to extrapolate and predict accuracy of target model with up to 6.7x larger training budget based on a set of smaller experiments. We will release a complete list of model losses and downstream evaluation results at various different scales to support reproducibility and encourage future research.

Neural scaling laws have driven the field's ever-expanding exponential growth in parameters, data and compute. While scaling behaviors for pretraining losses and discriminative benchmarks are well established, generative benchmarks such as mathematical problem-solving or software engineering remain under-explored. We propose and evaluate three different pretraining scaling laws for fitting pass-at-$k$ on generative evaluations and for predicting pass-at-$k$ of the most expensive model using cheaper models. Our three scaling laws differ in the covariates used: (1) pretraining compute, (2) model parameters and pretraining tokens, (3) log likelihoods of gold reference solutions. First, we demonstrate that generative evaluations introduce new hyperparameters (in our setting, $k$) that act as a control lever for scaling behavior, modulating both the scaling law parameters and the predictability of performance. Second, we identify a stark difference in parameter stability: while the compute and parameters+tokens laws stabilize for only the last $\mathord{\sim}1.5\mathord{-}2.5$ orders of magnitude, the gold reference likelihood law is uniquely stable, converging across $\mathord{\sim}5$ orders. Third, in terms of predictive performance, we find all three scaling laws perform comparably, although the compute law predicts slightly worse for small $k$ and the gold reference law predicts slightly worse for large $k$. Finally, we establish a theoretical connection, proving that the compute scaling law emerges as the compute-optimal envelope of the parameters-and-tokens law. Our framework provides researchers and practitioners with insights and methodologies to forecast generative performance, accelerating progress toward models that can reason, solve, and create.

We present Contamination Detection via Context (CoDeC), a practical and accurate method to detect and quantify training data contamination in large language models. CoDeC distinguishes between data memorized during training and data outside the training distribution by measuring how in-context learning affects model performance. We find that in‑context examples typically boost confidence for unseen datasets but may reduce it when the dataset was part of training, due to disrupted memorization patterns. Experiments show that CoDeC produces interpretable contamination scores that clearly separate seen and unseen datasets, and reveals strong evidence of memorization in open-weight models with undisclosed training corpora. The method is simple, automated, and both model- and dataset-agnostic, making it easy to integrate with benchmark evaluations.

Instruction-based image editing has advanced rapidly, yet reliable and interpretable evaluation remains a bottleneck. Current protocols either (i) depend on paired reference images—resulting in limited coverage and inheriting biases from prior generative models—or (ii) rely *solely* on zero-shot vision–language models (VLMs), whose prompt-based assessments of instruction following, content consistency, and visual quality are often imprecise. To address this, we introduce **EdiVal-Agent**, an automated and fine-grained evaluation framework grounded in an object-centric perspective, designed to assess not only standard single-turn but also multi-turn instruction-based editing with precision. Given an input image, **EdiVal-Agent** first decomposes it into semantically meaningful objects, then synthesizes diverse, context-aware editing instructions while dynamically updating object pools across turns. These two stages enable two novel object-centric metrics tailored for multi-turn evaluation and one global metric of visual quality: 1) EdiVal-IF, which measures instruction following by combining open-vocabulary object detectors for symbolic checks with VLMs for semantic verification on detector-guided crops; 2) EdiVal-CC, which evaluates content consistency by calculating semantic similarity of unchanged objects and background using the evolving object pools; and 3) EdiVal-VQ, which quantifies changes in overall visual quality with human preference models. Instantiating this pipeline, we build **EdiVal-Bench**, a multi-turn editing benchmark covering 9 instruction types and 13 state-of-the-art editing models spanning In-Context, flow-matching, and diffusion paradigms. We further conduct experiments comparing multi-turn editing with single-shot complex editing, highlighting the distinctive characteristics of different model paradigms. We demonstrate that EdiVal can be used to identify existing failure modes, thereby informing the development of the next generation of editing models.

Inversion-based watermarking is a promising approach to authenticate diffusion-generated images, yet practical use is bottlenecked by inversion that is both slow and error-prone. While the primary challenge in the watermarking setting is robustness against external distortions, existing approaches over-optimize internal truncation error, and because that error scales with the sampler step size, they are inherently confined to high-NFE (number of function evaluations) regimes that cannot meet the dual demands of speed and robustness. In this work, we have two key observations: (i) the inversion trajectory has markedly lower curvature than the forward generation path does, making it highly compressible and amenable to low-NFE approximation; and (ii) in inversion for watermark verification, the trade-off between speed and truncation error is less critical, since external distortions dominate the error. A faster inverter provides a dual benefit: it is not only more efficient, but it also enables end-to-end adversarial training to directly target robustness, a task that is computationally prohibitive for the original, lengthy inversion trajectories. Building on this, we propose **FARI** (**F**ast **A**symmetric **R**obust **I**nversion), a one-step inversion framework paired with lightweight adversarial LoRA fine-tuning of the denoiser for watermark extraction. While consolidation slightly increases internal error, FARI delivers large gains in both speed and robustness: with ~20 minutes of fine-tuning on a single NVIDIA RTX A6000 GPU, it surpasses 50-step DDIM inversion on watermark-verification robustness while dramatically reducing inference time.

Despite their impressive performance on computer vision benchmarks, Deep Neural Networks (DNNs) still fall short of adequately modeling human visual behavior, as measured by error consistency and shape bias. Recent work hypothesized that behavioral alignment can be drastically improved through generative - rather than discriminative - classifiers, with far-reaching implications for models of human vision. Here, we instead show that the increased alignment of generative models can be largely explained by a seemingly innocuous resizing operation in the generative model which effectively acts as a low-pass filter. In a series of controlled experiments, we show that removing high-frequency spatial information from discriminative models like CLIP drastically increases their behavioral alignment. Simply blurring images at test-time - rather than training on blurred images - achieves a new state-of-the-art score on the model-vs-human benchmark, halving the current alignment gap between DNNs and human observers. Furthermore, low-pass filters are likely optimal, which we demonstrate by directly optimizing filters for alignment. To contextualize the performance of optimal filters, we compute the frontier of all possible pareto-optimal solutions to the benchmark, which was formerly unknown. We explain our findings by observing that the frequency spectrum of optimal Gaussian filters roughly matches the spectrum of band-pass filters implemented by the human visual system. We show that the contrast sensitivity function, describing the inverse of the contrast threshold required for humans to detect a sinusoidal grating as a function of spatiotemporal frequency, is approximated well by Gaussian filters of a specific width.

How does the choice of optimization algorithm shape a model’s ability to learn features? To address this question for steepest descent methods—including sign descent, which is closely related to Adam—we introduce steepest mirror flows as a unifying theoretical framework. This framework reveals how optimization geometry governs learning dynamics, implicit bias, and sparsity and it provides two explanations for why Adam and AdamW often outperform SGD in fine-tuning. Focusing on diagonal linear networks and deep diagonal linear reparameterizations (a simplified proxy for attention), we show that steeper descent facilitates both saddle-point escape and feature learning. In contrast, gradient descent requires unrealistically large learning rates to escape saddles, an uncommon regime in fine-tuning. Empirically, we confirm that saddle-point escape is a central challenge in fine-tuning. Furthermore, we demonstrate that decoupled weight decay, as in AdamW, stabilizes feature learning by enforcing novel balance equations. Together, these results highlight two mechanisms how steepest descent can aid modern optimization.