ICLR 2026 Papers

Assessing the privacy of large language models (LLMs) presents significant challenges. In particular, most existing methods for auditing *differential privacy* require the insertion of specially crafted canary data *during training*, making them impractical for auditing already-trained models without costly retraining. Additionally, *dataset inference*, which audits whether a suspect dataset was used to train a model, is *infeasible* without access to a private non-member held-out dataset. Yet, such held-out datasets are often unavailable or difficult to construct for real-world cases since they have to be from the same distribution (IID) as the suspect data. These limitations severely hinder the ability to conduct scalable, *post-hoc* audits. To enable such audits, this work introduces **natural identifiers (NIDs)** as a novel solution to the above-mentioned challenges. NIDs are structured random strings, such as cryptographic hashes and shortened URLs, naturally occurring in common LLM training datasets. Their format enables the generation of unlimited additional random strings from the same distribution, which can act as alternative canaries for audits and as same-distribution held-out data for dataset inference. Our evaluation highlights that indeed, using NIDs, we can facilitate post-hoc differential privacy auditing *without any retraining* and enable dataset inference for any suspect dataset containing NIDs without the need for a private non-member held-out dataset.

The progress of AI is bottlenecked by the quality of evaluation, making powerful LLM-as-a-Judge models a core solution. The efficacy of these judges depends on their chain-of-thought reasoning, creating a critical need for methods that can effectively optimize this reasoning process. In this work, we introduce J1, a reinforcement learning framework for teaching LLM judges to think before making decisions. Our core contribution lies in converting all judgment tasks for nonverifiable and verifiable prompts into a unified format with verifiable rewards, enabling direct optimization of evaluation quality while mitigating positional bias. We then use RL to train thinking-judges at scales of 8B, 32B, and 70B and show that they obtain state-of-the-art performance across multiple benchmarks. In particular, J1-Qwen-32B, our multitasked pointwise and pairwise judge also outperforms o1-mini, o3, and a much larger 671B DeepSeek-R1 on some benchmarks, while only training on synthetic data. Through comprehensive ablations of pairwise, pointwise, and multitask J1 variants, we demonstrate the effectiveness of our approach across seed prompts, reward strategies, and training recipes. Qualitative analysis reveals that J1 develops systematic evaluation strategies, including dynamic criteria generation, reference answer creation, iterative self-correction of initial assessments, and feedback generation for low-quality responses.

Realistic talking-head video generation is critical for virtual avatars, film production, and interactive systems. Current methods struggle with nuanced emotional expressions due to the lack of fine-grained emotion control. To address this issue, we introduce a novel two-stage method (AUHead) to disentangle fine-grained emotion control, i.e. , Action Units (AUs), from audio and achieve controllable generation. In the first stage, we explore the AU generation abilities of large audio-language models (ALMs), by spatial-temporal AU tokenization and an "emotion-then-AU" chain-of-thought mechanism. It aims to disentangle AUs from raw speech, effectively capturing subtle emotional cues. In the second stage, we propose an AU-driven controllable diffusion model that synthesizes realistic talking-head videos conditioned on AU sequences. Specifically, we first map the AU sequences into the structured 2D facial representation to enhance spatial fidelity, and then model the AU-vision interaction within cross-attention modules. To achieve flexible AU-quality trade-off control, we introduce an AU disentanglement guidance strategy during inference, further refining the emotional expressiveness and identity consistency of the generated videos. Results on benchmark datasets demonstrate that our approach achieves competitive performance in emotional realism, accurate lip synchronization, and visual coherence, significantly surpassing existing techniques. Our implementation is available at https://github.com/laura990501/AUHead_ICLR

Lightweight neural networks, essential for on-device applications, often suffer from a low-frequency bias due to their constrained capacity and depth. This limits their ability to capture the fine-grained, high-frequency details (e.g., textures, edges) that are crucial for complex computer vision tasks. To address this fundamental limitation, we perform the first systematic analysis of gating mechanisms from a frequency perspective. Inspired by the convolution theorem, we show how the interplay between element-wise multiplication and non-linear activation functions within Gated Linear Units (GLUs) provides a powerful mechanism to selectively amplify high-frequency signals, thereby enriching the model's feature representations. Based on these findings, we introduce the Gating Mechanism Network (GmNet), a simple yet highly effective architecture that incorporates our frequency-aware gating principles into a standard lightweight backbone. The efficacy of our approach is remarkable: without relying on complex training strategies or architectural search, GmNet achieves a new state-of-the-art for efficient models.

Earth observation (EO) is essential for understanding the evolving states of the Earth system. Although recent MLLMs have advanced EO research, they still lack the capability to tackle complex tasks that require multi-step reasoning and the use of domain-specific tools. Agent-based methods offer a promising direction, but current attempts remain in their infancy, confined to RGB perception, shallow reasoning, and lacking systematic evaluation protocols. To overcome these limitations, we introduce Earth-Agent, the first agentic framework that unifies RGB and spectral EO data within an MCP-based tool ecosystem, enabling cross-modal, multi-step, and quantitative spatiotemporal reasoning beyond pretrained MLLMs. Earth-Agent supports complex scientific tasks such as geophysical parameter retrieval and quantitative spatiotemporal analysis by dynamically invoking expert tools and models across modalities. To support comprehensive evaluation, we further propose Earth-Bench, a benchmark of 248 expert-curated tasks with 13,729 images, spanning spectrum, products and RGB modalities, and equipped with a dual-level evaluation protocol that assesses both reasoning trajectories and final outcomes. We conduct comprehensive experiments varying different LLM backbones, comparisons with general agent frameworks, and comparisons with MLLMs on remote sensing benchmarks, demonstrating both the effectiveness and potential of Earth-Agent. Earth-Agent establishes a new paradigm for EO analysis, moving the field toward scientifically grounded, next-generation applications of LLMs in Earth observation. Our code and dataset will be publicly released.

Local loss geometry in machine learning is fundamentally a two-operator concept. When only a single loss is considered, geometry is fully summarized by the Hessian spectrum; in practice, however, both training and test losses are relevant, and the resulting geometry depends on their spectra together with the alignment of their eigenspaces. We first establish general foundations for two-loss geometry by formulating a universal local fluctuation law, showing that the expected test-loss increment under small training perturbations is a trace that combines train and test spectral data with a critical additional factor quantifying eigenspace overlap, and by proving a novel transfer law that describes how overlaps transform in response to noise. As a solvable analytical model, we next apply these laws to ridge regression with arbitrary covariate shift, where operator-valued free probability yields asymptotically exact overlap decompositions that reveal overlaps as the natural quantities specifying shift and that resolve the puzzle of multiple descent: peaks are controlled by eigenspace (mis-)alignment rather than by Hessian ill-conditioning alone. Finally, for empirical validation and scalability, we confirm the fluctuation law in multilayer perceptrons, develop novel algorithms based on subspace iteration and kernel polynomial methods to estimate overlap functionals, and apply them to a ResNet-20 trained on CIFAR10, showing that class imbalance reshapes train–test loss geometry via induced misalignment. Together, these results establish overlaps as the critical missing ingredient for understanding local loss geometry, providing both theoretical foundations and scalable estimators for analyzing generalization in modern neural networks.

Large Language Models (LLMs) have demonstrated outstanding capabilities in various code-related tasks, including code completion, translation, or summarization. However, these pretrained models are static, posing a challenge to incorporate new knowledge into an LLM to correct erroneous behavior. Approaches such as retraining or fine-tuning demand extensive labeled datasets and might be computationally expensive, while prompt engineering fails to change models permanently. Knowledge Editing (KE) techniques offer a more efficient alternative, enabling model updates with minimal data, even just a single example. Nevertheless, existing KE methods often manipulate parameters within the Transformer's multi-layer perceptrons (MLPs), where neuronal polysemanticity hinders both the precision and interpretability of the edits. To address these limitations, we exploit TransCoder, an MLP-like model component with a wide and sparsely activated hidden feature vector. Specifically, we introduce **TransCoder-based Precise Editing** (**TCPE**), a novel method that leverages the sparsity and monosemanticity of the TransCoder’s neurons for highly localized knowledge editing. TCPE exhibits neuron-level mechanistic interpretability characteristics, revealing the correspondence between the edited neurons and the specific code-related knowledge. Furthermore, we present KECode, a new evaluation benchmark for code-to-code translation based on functional equivalence. Using KECode, we conduct a systematic evaluation of representative KE methods in the context of code-to-code translation. Our experimental results demonstrate that TCPE outperforms existing KE methods, achieving a substantial improvement of translation accuracy of CodeLlama-7b-Instruct from 57.5% to 64.0% in a low-resource scenario of Java-to-D translation.

Modern optimization faces a fundamental challenge: local gradient-based methods provide no global information about the objective function $L$ landscape, often leading to suboptimal convergence and sensitivity to initialization. We introduce a novel optimization framework that leverages resurgence theory from complex analysis to extract global structural information from divergent asymptotic series. Our key insight is that the factorially divergent perturbative expansions of parameter space partition functions encode precise information about all critical objective function value in the landscape through their Borel transform singularities. The algorithm works by computing the statistical mechanical partition function $Z(g) = \int e^{-L(\theta)/g} d\theta$ for small coupling $g\ll 1$, extracting its asymptotic series coefficients, and identifying Borel plane singularities that correspond one-to-one with critical objective function values. These target values provide global guidance to local optimizers, enabling principled learning rate adaptation and escape from suboptimal regions. Unlike heuristic adaptive methods, targets are theoretically grounded in the geometry of the optimization landscape.

The Lipschitz bandit problem extends stochastic bandits to a continuous action set defined over a metric space, where the expected reward function satisfies a Lipschitz condition. In this work, we introduce a new problem of Lipschitz bandit in the presence of stochastic delayed feedback, where the rewards are not observed immediately but after a random delay. We consider both bounded and unbounded stochastic delays, and design algorithms that attain sublinear regret guarantees in each setting. For bounded delays, we propose a delay-aware zooming algorithm that retains the optimal performance of the delay-free setting up to an additional term that scales with the maximum delay $\tau_{\max}$. For unbounded delays, we propose a novel phased learning strategy that accumulates reliable feedback over carefully scheduled intervals, and establish a regret lower bound showing that our method is nearly optimal up to logarithmic factors. Finally, we present experimental results to demonstrate the efficiency of our algorithms under various delay scenarios.

Attention is foundational to large language models (LLMs), enabling different heads to have diverse focus on relevant input tokens. However, learned behaviors like attention sinks, where the first token receives the most attention despite limited semantic importance, suggest some heads may be inactive, and point to a significant source of computational redundancy. To analyze this phenomenon, we propose a taxonomy of 12 score functions that measure different ways a head can be inactive. Thresholding these scores allows us to analyze different sets of potentially inactive attention heads. We evaluate whether identified heads are inactive through model interventions, finding that more than 12% of attention heads are inactive on average, and can be ablated in specific contexts while maintaining MMLU accuracy to within 1% of the pretrained LLM. Across 3 model families, our score functions that measure the average norm of a head's output consistently identify inactive heads that would not have been found by score functions that rely solely on attention weights. We establish that relying on a score function that measures a first token attention sink would underestimate the prevalence of inactive heads, failing to identify more than 7% of inactive heads on average. We also show how measuring score distributions can provide insights into attention behavior. For instance, we find evidence that finetuning causes little to no change in attention behavior, and that even within the same model family, large model scales present markedly different attention behaviors.

We investigate the challenge of applying Large Language Models (LLMs) to long texts. We propose a theoretical framework that distinguishes the failure modes of long context tasks into three categories: cross-chunk dependence (task noise), confusion that grows with context size (model noise), and the imperfect integration of partial results (aggregator noise). Under this view, we analyze when it is effective to use multi-agent chunking, i.e., dividing a length sequence into smaller chunks and aggregating the processed results of each chunk. Our experiments on tasks such as retrieval, question answering, and summarization confirm both the theoretical analysis and the conditions that favor multi-agent chunking. By exploring superlinear model noise growth with input length, we also explain why, for large inputs, a weaker model configured with chunk-based processing can surpass a more advanced model like GPT4o applied in a single shot. Overall, we present a principled understanding framework and our results highlight a direct pathway to handling long contexts in LLMs with carefully managed chunking and aggregator strategies.

Text-to-image (T2I) models have achieved remarkable success in generating high-fidelity images, but they often fail in handling complex spatial relationships, e.g., spatial perception, reasoning, or interaction. These critical aspects are largely overlooked by current benchmarks due to their short or information-sparse prompt design. In this paper, we introduce SpatialGenEval, a new benchmark designed to systematically evaluate the spatial intelligence of T2I models, covering two key aspects: (1) SpatialGenEval involves 1,230 long, information-dense prompts across 25 real-world scenes. Each prompt integrates 10 spatial sub-domains and corresponding 10 multi-choice question-answer pairs, ranging from object position and layout to occlusion and causality. Our extensive evaluation of 21 state-of-the-art models reveals that higher-order spatial reasoning remains a primary bottleneck. (2) To demonstrate that the utility of our information-dense design goes beyond simple evaluation, we also construct the SpatialT2I dataset. It contains 15,400 text-image pairs with rewritten prompts to ensure image consistency while preserving information density. Fine-tuned results on current foundation models (\ie, Stable Diffusion-XL, Uniworld-V1, OmniGen2) yield consistent performance gains (+4.2%, +5.7%, +4.4%) and more realistic effects in spatial relations, highlighting a data-centric paradigm to achieve spatial intelligence in T2I models.

Embodied intelligence requires high-fidelity simulation environments to support perception and decision-making, yet existing platforms often suffer from data contamination and limited flexibility. To mitigate this, we propose World2Minecraft to convert real-world scenes into structured Minecraft environments based on 3D semantic occupancy prediction. In the reconstructed scenes, we can effortlessly perform downstream tasks such as Vision-Language Navigation(VLN). However, we observe that reconstruction quality heavily depends on accurate occupancy prediction, which remains limited by data scarcity and poor generalization in existing models. We introduce a low-cost, automated, and scalable data acquisition pipeline for creating customized occupancy datasets, and demonstrate its effectiveness through MinecraftOcc, a large-scale dataset featuring 100,165 images from 156 richly detailed indoor scenes. Extensive experiments show that our dataset provides a critical complement to existing datasets and poses a significant challenge to current SOTA methods. These findings contribute to improving occupancy prediction and highlight the value of World2Minecraft in providing a customizable and editable platform for personalized embodied AI research. We will publicly release the dataset and the complete generation framework to ensure reproducibility and encourage future work.

This paper introduces GraphOmni, a comprehensive benchmark designed to evaluate the reasoning capabilities of LLMs on graph-theoretic tasks articulated in natural language. GraphOmni spans diverse graph types, serialization formats, and prompting schemes, substantially extending upon prior efforts in both scope and depth. Through systematic evaluation, we uncover critical interactions among these dimensions, revealing their decisive impact on model performance. Our experiments show that state-of-the-art closed-source models such as Claude-3.5 and o4-mini consistently lead overall, yet still leave considerable headroom, while open-source models display pronounced sensitivity to various design choices. Beyond the standard scope, larger graphs, real-world graphs, and additional NP-hard tasks are further discussed. We further analyze efficiency via output token usage, highlighting cost–accuracy trade-offs, and introduce a reinforcement learning-based optimizer that adaptively selects factor combinations, reducing evaluation cost by 75\% while retaining strong accuracy. This flexible and extensible benchmark not only deepens understanding of LLM performance on structured graph reasoning but also establishes a robust foundation for advancing model design and evaluation.

Drug target interaction (DTI) prediction is a cornerstone of computational drug discovery, enabling rational design, repurposing, and mechanistic insights. While deep learning has advanced DTI modeling, existing approaches primarily rely on SMILES–protein pairs and fail to exploit the rich multimodal information available for small molecules and proteins. Inspired by recent successes in multimodal molecular property prediction, we introduce GRAM-DTI, a pre-training framework that integrates multimodal small molecule and protein inputs into a unified representation. GRAM-DTI extends volume-based contrastive learning to four modalities, capturing higher-order semantic alignment beyond conventional pairwise approaches. To handle modality informativeness, we propose adaptive modality dropout, dynamically regulating each modality’s contribution during pretraining. Additionally, IC50 activity measurements, when available, are incorporated as weak supervision to ground representations in biologically meaningful interaction strengths. Experiments on four publicly available datasets demonstrate that GRAM-DTI consistently outperforms state-of-the-art baselines. Our results highlight the benefits of higher-order multimodal alignment, adaptive modality utilization, and auxiliary supervision for robust and generalizable DTI prediction.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a \emph{regularized mirror map} that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-$t$ prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-$t$ priors and primal-space guarantees for constrained generation, under $\varepsilon$-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

Estimating causal effects becomes particularly challenging when outcomes possess complex, non-Euclidean structures, where conventional approaches often fail to capture meaningful structural variation. We introduce a novel framework for topological causal inference, defining treatment effects through changes in the underlying topological structure of outcomes. In our framework, intervention-driven topological shifts across homology are summarized via power-weighted silhouettes. We propose a doubly robust estimator, derive its asymptotic properties, and develop a formal test for the null hypothesis of no topological effect. Empirical studies demonstrate that our approach reliably quantifies treatment effects and remains robust across diverse, complex outcome spaces.

Generalist multimodal large language models (MLLMs) have achieved impressive performance across a wide range of vision-language tasks. However, their performance on medical tasks—particularly in zero-shot settings where generalization is critical—remains suboptimal. A key research gap is the limited understanding of why medical MLLMs underperform in medical image interpretation. **In this work**, we present a pioneering systematic investigation into the visual grounding capabilities of state-of-the-art medical MLLMs. To disentangle *visual grounding* from *semantic grounding*, we design VGMED, a novel evaluation dataset developed with expert clinical guidance, explicitly assessing the visual grounding capability of medical MLLMs. We introduce new quantitative metrics and conduct detailed qualitative analyses. Our study across **eight** state-of-the-art (SOTA) medical MLLMs validates that they often fail to ground their predictions in clinically relevant image regions. We note that this finding is specific to medical image analysis; in contrast, prior work has shown that MLLMs are capable of grounding their predictions in the correct image regions when applied to natural scene images. Motivated by these findings, we propose VGRefine, a simple yet effective inference-time method that refines attention distribution to improve visual grounding in medical settings. Our approach achieves SOTA performance across 6 diverse Med-VQA benchmarks (over 110K VQA samples from 8 imaging modalities) without requiring additional training or external expert models. Overall, our work, for the first time, systematically validates inadequate visual grounding as one of the key contributing factors for medical MLLMs' under-performance. Code and additional experiments are included in the Supp.

Transformer-based language models rely on positional encoding (PE) to handle token order and support context length extrapolation. However, existing PE methods lack theoretical clarity and rely on limited evaluation metrics to substantiate their extrapolation claims. We propose the Bayesian Attention Mechanism (BAM), a theoretical framework that formulates positional encoding as a prior within a probabilistic model. BAM unifies existing methods (e.g., NoPE and ALiBi) and motivates a new Generalized Gaussian positional prior that substantially improves long-context generalization. Empirically, BAM enables accurate information retrieval at $500\times$ the training context length, outperforming previous state-of-the-art context length generalization by more than $25\times$ in retrieval accuracy while maintaining comparable perplexity and introducing minimal additional parameters.