ICLR 2026 Papers

Despite impressive capabilities, LLMs' successes often rely on pattern-matching behaviors, yet these are also linked to OOD generalization failures in compositional tasks. However, behavioral studies commonly employ task setups that allow multiple generalization sources (e.g., algebraic invariances, structural repetition), obscuring a precise and testable account of how well LLMs perform generalization through pattern matching and their limitations. To address this ambiguity, we first formalize pattern matching as functional equivalence, i.e., identifying pairs of subsequences of inputs that consistently lead to identical results when the rest of the input is held constant. Then, we systematically study how decoder-only Transformer and Mamba behave in controlled tasks with compositional structures that isolate this mechanism. Our formalism yields predictive and quantitative insights: (1) Instance-wise success of pattern matching is well predicted by the number of contexts witnessing the relevant functional equivalence. We prove a tight sample complexity bound of learning a two-hop structure by identifying the exponent of the data scaling law for perfect in-domain generalization. Our empirical results align with the theoretical prediction, under 20× parameter scaling and across architectures. (3) Path ambiguity is a structural barrier: when a variable influences the output via multiple paths, models fail to form unified intermediate state representations, impairing accuracy and interpretability. (4) Chain-of-Thought reduces data requirements yet does not resolve path ambiguity. Hence, we provide a predictive, falsifiable boundary for pattern matching and a foundational diagnostic for disentangling mixed generalization mechanisms.

Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions via ordinary or stochastic differential equations (ODEs/SDEs), holding significant promise for generative modeling. While previous studies have analyzed the finite-time convergence rate of discrete-time implementations for SDEs, the ODE counterpart remains largely unexplored. In this work, we bridge this gap by presenting a rigorous finite-time convergence analysis of numerical implementations for ODEs in the framework of stochastic interpolants. We establish novel discrete-time total variation error bounds for two widely used numerical solvers: the first-order forward Euler method and the second-order Heun's method. Our analysis also yields optimized iteration complexity results and step size schedules that enhance computational efficiency. Notably, when specialized to the diffusion model setting, our theoretical guarantees for the second-order method improve upon prior results in terms of both smoothness requirements and dimensional dependence. Our theoretical findings are corroborated by numerical and image generation experiments, which validate the derived error bounds and complexity analyses.

Recent advances in illumination control extend image-based methods to video, yet still facing a trade-off between lighting fidelity and temporal consistency. Moving beyond relighting, a key step toward generative modeling of real-world scenes is the joint control of camera trajectory and illumination, since visual dynamics are inherently shaped by both geometry and lighting. To this end, we present Light-X, a video generation framework that enables controllable rendering from monocular videos with both viewpoint and illumination control. 1) We propose a disentangled design that decouples geometry and lighting signals: geometry and motion are captured via dynamic point clouds projected along user-defined camera trajectories, while illumination cues are provided by a relit frame consistently projected into the same geometry. These explicit, fine-grained cues enable effective disentanglement and guide high-quality illumination. 2) To address the lack of paired multi-view and multi-illumination videos, we introduce Light-Syn, a degradation-based pipeline with inverse-mapping that synthesizes training pairs from in-the-wild monocular footage. This strategy yields a dataset covering static, dynamic, and AI-generated scenes, ensuring robust training. Extensive experiments show that Light-X outperforms baseline methods in joint camera–illumination control. Besides, our model surpasses prior video relighting methods in text- and background-conditioned settings. Ablation studies further validate the effectiveness of the disentangled formulation and degradation pipeline. Code, data and models will be made public.

In-context Learning (ICL) is an emerging few-shot learning paradigm based on modern Language Models (LMs), yet its inner mechanism remains unclear. In this paper, we investigate the mechanism through a novel perspective of information removal. Specifically, we demonstrate that in the zero-shot scenario, LMs encode queries into non-selective representations in hidden states containing information for all possible tasks, leading to arbitrary outputs without focusing on the intended task, resulting in near-zero accuracy. Meanwhile, we find that selectively removing specific information from hidden states by a low-rank filter effectively steers LMs toward the intended task. Building on these findings, by measuring the hidden states on carefully designed metrics, we observe that few-shot ICL effectively simulates such task-oriented information removal processes, selectively removing the redundant information from entangled non-selective representations, and improving the output based on the demonstrations, which constitutes a key mechanism underlying ICL. Moreover, we identify essential attention heads inducing the removal operation, termed Denoising Heads, which enables the ablation experiments blocking the information removal operation from the inference, where the ICL accuracy significantly degrades, especially when the correct label is absent from the few-shot demonstrations, confirming both the critical role of the information removal mechanism and denoising heads.

Video Class-Incremental Learning (VCIL) seeks to develop models that continuously learn new action categories over time without forgetting previously acquired knowledge. Unlike traditional Class-Incremental Learning (CIL), VCIL introduces the added complexity of spatiotemporal structures, making it particularly challenging to mitigate catastrophic forgetting while effectively capturing both frame-shared semantics and temporal dynamics. Existing approaches either rely on exemplar rehearsal, raising concerns over memory and privacy, or adapt static image-based methods that neglect temporal modeling. To address these limitations, we propose Spatiotemporal Preservation and Routing (StPR), a unified and exemplar-free VCIL framework that explicitly disentangles and preserves spatiotemporal information. We begin by introducing Frame-Shared Semantics Distillation (FSSD), which identifies semantically stable and meaningful channels by jointly considering channel-wise sensitivity and classification contribution. By selectively regularizing these important semantic channels, FSSD preserves prior knowledge while allowing for adaptation. Building on this preserved semantic space, we further design a Temporal Decomposition-based Mixture-of-Experts (TD-MoE), which dynamically routes task-specific experts according to temporal dynamics, thereby enabling inference without task IDs or stored exemplars. Through the synergy of FSSD and TD-MoE, StPR progressively leverages spatial semantics and temporal dynamics, culminating in a unified, exemplar-free VCIL framework. Extensive experiments on UCF101, HMDB51, SSv2 and Kinetics400 show that our method outperforms existing baselines while offering improved interpretability and efficiency in VCIL. Code is available in the supplementary materials.

Large language models excel at generating individual functions or single files of code, yet generating complete repositories from scratch remains a fundamental challenge. This capability is key to building coherent software systems from high-level specifications and realizing the full potential of automated code generation. The process requires planning at two levels: deciding what features and modules to build (proposal stage) and defining their implementation details (implementation stage). Current approaches rely on natural language planning, which often produces unclear specifications, misaligned components, and brittle designs due to its inherent ambiguity and lack of structure. To address these limitations, we introduce the Repository Planning Graph (RPG), a structured representation that encodes capabilities, file structures, data flows, and functions in a unified graph. By replacing free-form natural language with an explicit blueprint, RPG enables consistent long-horizon planning for repository generation. Building on RPG, we develop ZeroRepo, a graph-driven framework that operates in three stages: proposal-level planning, implementation-level construction, and graph-guided code generation with test validation To evaluate, we construct RepoCraft, a benchmark of six real-world projects with 1,052 tasks. On RepoCraft, ZeroRepo produces nearly 36K Code Lines and 445K Code Tokens, on average 3.9× larger than the strongest baseline (Claude Code), and 68× larger than others. It also achieves 81.5% coverage and 69.7% test accuracy, improving over Claude Code by 27.3 and 35.8 points. Further analysis shows that RPG models complex dependencies, enables more sophisticated planning through near-linear scaling, and improves agent understanding of repositories, thus accelerating localization. Our data and code are available at https://github.com/microsoft/RPG-ZeroRepo.

Large language models (LLMs) are widely used as reference-free evaluators via prompting, but this “LLM-as-a-Judge” paradigm is costly, opaque, and sensitive to prompt design. In this work, we investigate whether smaller models can serve as efficient evaluators by leveraging internal representations instead of surface generation. We uncover a consistent empirical pattern: small LMs, despite with weak generative ability, encode rich evaluative signals in their hidden states. This motivates us to propose the Semantic Capacity Asymmetry Hypothesis: evaluation requires significantly less semantic capacity than generation and can be grounded in intermediate representations, suggesting that evaluation does not necessarily need to rely on large-scale generative models but can instead leverage latent features from smaller ones. Our findings motivate a paradigm shift from LLM-as-a-Judge to Representation-as-a-Judge, a decoding-free evaluation strategy that probes internal model structure rather than relying on prompted output. We instantiate this paradigm through INSPECTOR, a probing-based framework that predicts aspect-level evaluation scores from small model representations. Experiments on reasoning benchmarks (GSM8K, MATH, GPQA) show that INSPECTOR substantially outperforms prompting-based small LMs and closely approximates full LLM judges, while offering a more efficient, reliable, and interpretable alternative for scalable evaluation.

Multi-modal Large Language Models (MLLMs) represent a significant advancement in artificial intelligence. Among the growing capabilities exhibited by MLLMs, abilities to understand and reason in real-world environments stand out as particularly vital as a fundamental prerequisite for a wide array of real-world applications. The current methods for evaluating MLLMs often fall short in their ability to comprehensively assess these crucial capabilities. However, being able to reason on complex environment-scale spaces, for example, room spaces, building spaces, and even urban spaces, and to predict the future and plan actions, is essential for humans and various autonomous agents to survive in the real physical world. To address these gaps, we propose a visual-question-answering benchmark, **SpaCE-Eval** (**Spa**tial Reasoning, **C**ommonsense Knowledge and **E**nvironment Interaction) in the real world, designed to evaluate some of MLLM’s most important reasoning abilities in real-world environments. As the name suggests, it challenges the models to reason on complex spatial scenarios, invoke commonsense knowledge of the physical world, and interact with the environment. The dataset consists of all new diagrams purposefully produced by humans, where diagram-question pairs are meticulously refined and selected through a rigorous pipeline. Additionally, with the benchmark, we evaluate a selection of leading MLLMs, both proprietary and open source. The results suggest that a significant enhancement of MLLMs in reasoning in the real physical world is necessary to realise more advanced general artificial intelligence.

Efficient deployment of deep neural networks increasingly relies on Post-Training Quantization (PTQ). Logarithmic PTQ, in particular, promises multiplier-free hardware efficiency, but its performance is often limited by the nonlinear and symmetric quantization grid and standard rounding-to-nearest (RTN) approach. While learnable rounding has significantly advanced linear PTQ, its application to the non-linear and often discrete nature of logarithmic domain remains unexplored. This paper introduces learnable Logarithmic Adaptive Rounding Techniques (LogART) that pioneer task-aware learnable rounding specifically for the logarithmic domain. LogART further extends the learnable rounding strategy to flexibly support outlier-aware, asymmetric, and hardware-friendly dynamic logarithmic bases, determined in a distribution-aware manner using an efficient search strategy. Extensive experiments demonstrate that LogART achieves state-of-the-art accuracy while maintaining efficiency in quantizing models across various architectures and ultra-low bitwidths, outperforming existing logarithmic PTQ methods and paving the way for more effective hardware deployment. The code is available at https://github.com/logart-lab/logart.

We investigate theoretical guarantees for the \emph{false-negative rate} (FNR)—the fraction of true causal edges whose orientation is not recovered, under single-variable random interventions and an $\epsilon$-interventional faithfulness assumption that accommodates latent confounding. For sparse Erdős--Rényi directed acyclic graphs, where the edge probability scales as $p_e = \Theta(1/d)$, we show that the FNR concentrates around its mean at rate $O\bigl(\tfrac{\log d}{\sqrt d}\bigr)$, implying that large deviations above the expected error become exponentially unlikely as dimensionality increases. This concentration ensures that derived upper bounds hold with high probability in large-scale settings. Extending the analysis to generalized Barabási--Albert graphs reveals an even stronger phenomenon: when the degree exponent satisfies $\gamma > 3$, the deviation width scales as $O\bigl(d^{\beta - \frac{1}{2}}\bigr)$ with $\beta = 1/(\gamma - 1) < \frac{1}{2}$, and hence vanishes in the limit. This demonstrates that heterogeneous, heavy-tailed degree structures commonly observed in empirical networks can intrinsically regularize causal discovery by reducing variability in orientation error. These finite-dimension results provide the first dimension-adaptive, faithfulness-robust guarantees for causal structure recovery, and challenge the intuition that high dimensionality and network heterogeneity necessarily hinder accurate discovery. Our simulation results corroborate these theoretical predictions, showing that the FNR indeed concentrates and often vanishes in practice as dimensionality grows.

Using Reinforcement Learning with Verifiable Rewards (RLVR) to optimize Large Language Models (LLMs) can be conceptualized as progressively editing a query's 'Reasoning Tree'. This process involves exploring nodes (tokens) and dynamically modifying the model's policy at each node. When combined with data scheduling, this process yields further gains in data efficiency and accuracy. However, existing RLVR data scheduling methods typically rely on path-based metrics to rank queries, overlooking the reasoning tree structures of these queries. In this paper, we introduce a novel metric, namely **Reasoning Score (r-score)**, which measures the query's learning difficulty based on the structure of its reasoning tree. Based on the r-score, we propose the **Reasoning Tree Schedule (Re-Schedule)**, a scheduling algorithm that constructs a curriculum progressing from structurally simple (high r-score) to complex (low r-score) queries. Experiments on six math-reasoning benchmarks show that Re-Schedule significantly improves average accuracy, achieving gains of up to 3.2\%. These strong results validate our approach and demonstrate that a structural understanding of the reasoning tree provides a more powerful and principled foundation for RLVR data scheduling.

Differentially private (DP) transfer learning, i.e., fine-tuning a pretrained model on private data, is the current state-of-the-art approach for training large models under privacy constraints. We focus on two key hyperparameters in this setting: the clipping bound $C$ and batch size $B$. We show a clear mismatch between the current theoretical understanding of how to choose an optimal $C$ (stronger privacy requires smaller $C$) and empirical outcomes (larger $C$ performs better under strong privacy), caused by changes in the gradient distributions. Assuming a limited compute budget (fixed epochs), we demonstrate that the existing heuristics for tuning $B$ do not work, while cumulative DP noise better explains whether smaller or larger batches perform better. We also highlight how the common practice of using a single $(C,B)$ setting across tasks can lead to suboptimal performance. We find that performance drops especially when moving between loose and tight privacy and between plentiful and limited compute, which we explain by analyzing clipping as a form of gradient re-weighting and examining cumulative DP noise.

Diffusion models demonstrate outstanding performance in image generation, but their multi-step inference mechanism requires immense computational cost. Previous works accelerate inference by leveraging layer or token cache techniques to reduce computational cost. However, these methods fail to achieve superior acceleration performance in few-step diffusion transformer models due to inefficient feature caching strategies, manually designed sparsity allocation, and the practice of retaining complete forward computations in several steps in these token cache methods. To tackle these challenges, we propose a differentiable layer-wise sparsity optimization framework for diffusion transformer models, leveraging token caching to reduce token computation costs and enhance acceleration. Our method optimizes layer-wise sparsity allocation in an end-to-end manner through a learnable network combined with a dynamic programming solver. Additionally, our proposed two-stage training strategy eliminates the need for full-step processing in existing methods, further improving efficiency. We conducted extensive experiments on a range of diffusion-transformer models, including DiT-XL/2, PixArt-$\alpha$, FLUX, and Wan2.1. Across these architectures, our method consistently improves efficiency without degrading sample quality. For example, on PixArt-$\alpha$ with 20 sampling steps, we reduce computational cost by 54% while achieving generation metrics that surpass those of the original model, substantially outperforming prior approaches. These results demonstrate that our method delivers large efficiency gains while often improving generation quality. .

An important aspect subtending language understanding and production is the ability to independently encode positional and symbolic information of the words within a sentence. In Transformers, positional information is typically encoded using Positional Encodings (PEs). One such popular PE, namely Rotary PE (RoPE), has been widely used due to its empirical success. Recently, it has been argued that part of RoPE's success emerges from its ability to encode robust positional and semantic information using large and small frequencies, respectively. In this work, we perform a deeper dive into the positional versus symbolic dichotomy of attention heads behavior, both at the theoretical and empirical level. We provide general definitions of what it means for a head to behave positionally or symbolically, prove that these are two mutually exclusive behaviors and develop a metric to quantify them. We apply our framework to analyze Transformer-based LLMs using RoPE and find that all heads exhibit a strong correspondence between behavior and frequency use. Finally, we introduce canonical tasks designed to be either purely positional or symbolic, and demonstrate that the Transformer performance causally relates to the ability of attention heads to leverage the appropriate frequencies. In particular, we show that we can control the Transformer performance by controlling which frequencies the attention heads can access. Altogether, our work provides a detailed understanding of RoPE, and how its properties relate to model behavior.

Vision–Language Models (VLMs) show promise as zero-shot goal-conditioned value functions, but their frozen pre-trained representations limit generalization and temporal reasoning. We introduce VITA, a zero-shot value function learning method that enhances both capabilities via test-time adaptation. At inference, a lightweight adaptation module is updated via a gradient step on a meta-learned self-supervised loss, such that each test-time update improves value estimation. By updating sequentially over a trajectory, VITA encodes history into its parameters, addressing the temporal reasoning limitations. To mitigate shortcut learning, we propose a dissimilarity-based sampling strategy that selects semantically diverse segments of the trajectory during training. In real-world robotic manipulation tasks, VITA generalizes from a single training environment to diverse out-of-distribution tasks, environments, and embodiments, outperforming the state-of-the-art zero-shot method using autoregressive VLMs. Furthermore, we demonstrate that VITA’s zero-shot value estimates can be utilized for reward shaping in offline reinforcement learning, resulting in multi-task policies on the Meta-World benchmark that exceed the performance of those trained with the simulation’s fuzzy-logic dense rewards.

Single‑molecule localization microscopy (SMLM) allows reconstructing cellular organelles and biology-relevant structures far beyond the limited spatial resolution imposed by optics constrains, using tagged biomolecule positions. Currently, efficient SMLM requires non‑overlapping emitting fluorophores, to ensure proper image deconvolution leading to long acquisition times that hinders live‑cell imaging. Recent deep‑learning approaches can handle denser emissions, but they rely on variants of non‑maximum suppression (NMS) layers, which are unfortunately non‑differentiable and may discard true positives with their local fusion strategy. In this presentation, we reformulate the SMLM training objective as a set‑matching problem, deriving an optimal‑transport loss that eliminates the need for NMS during inference and enables end‑to‑end training. Additionally, we propose an iterative neural network that integrates knowledge of the microscope’s optical system inside our model. Experiments on synthetic benchmarks and real biological data show that both our new loss function and architecture surpass the state of the art at moderate and high emitter densities. Code is available at \url{anonymized_url}.

Actor–critic (AC) algorithms underpin many of today’s most successful reinforcement learning (RL) applications, yet their finite-time convergence in realistic settings remains largely underexplored. Existing analyses often rely on oversimplified formulations and are largely confined to linear function approximation. In practice, however, nonlinear approximations with deep neural networks dominate AC implementations, leaving a substantial gap between theory and practice. In this work, we provide the first finite-time analysis of single-timescale AC with deep neural network approximation in continuous state-action spaces. In particular, we consider the challenging time-average reward setting, where one needs to simultaneously control three highly-coupled error terms including the reward error, the critic error, and the actor error. Our novel analysis is able to establish convergence to a stationary point at a rate $\widetilde{\mathcal{O}}(T^{-1/2})$, where $T$ denotes the total number of iterations, thereby providing theoretical grounding for widely used deep AC methods. We substantiate these theoretical guarantees with experiments that confirm the proven convergence rate and further demonstrate strong performance on MuJoCo benchmarks.

We introduce k-NLPmeans and k-LLMmeans, text-clustering variants of k-means that periodically replace numeric centroids with textual summaries. The key idea—summary-as-centroid—retains k-means assignments in embedding space while producing human-readable, auditable cluster prototypes. The method is LLM-optional: k-NLPmeans uses lightweight, deterministic summarizers, enabling offline, low-cost, and stable operation; k-LLMmeans is a drop-in upgrade that uses an LLM for summaries under a fixed per-iteration budget whose cost does not grow with dataset size. We also present a mini-batch extension for real-time clustering of streaming text. Across diverse datasets, embedding models, and summarization strategies, our approach consistently outperforms classical baselines and approaches the accuracy of recent LLM-based clustering without extensive LLM calls. Finally, we provide a case study on sequential text streams and release a StackExchange-derived benchmark for evaluating streaming text clustering.

Self-supervised learning (SSL) has emerged as a powerful pretraining strategy to learn transferable representations from unlabeled data. Yet, it remains unclear how long SSL models should be pretrained for such representations to emerge. Contrary to the prevailing heuristic that longer pretraining translates to better downstream performance, we identify a transferability trade-off: across diverse SSL settings, intermediate checkpoints often yield stronger out-of-domain (OOD) generalization, whereas additional pretraining primarily benefits in-domain (ID) accuracy. From this observation, we hypothesize that SSL progresses through learning phases that can be characterized through the lens of critical periods (CP). Prior work on CP has shown that supervised learning models exhibit early phases of high plasticity, followed by a consolidation phase where adaptability declines but task-specific performance keeps increasing. Since traditional CP analysis depends on supervised labels, for SSL we rethink CP in two ways. First, we inject deficits to perturb the pretraining data and measure the quality of learned representations via downstream tasks. Second, to estimate network plasticity during pretraining we compute the Fisher Information matrix on pretext objectives, quantifying the sensitivity of model parameters to the supervisory signal defined by the pretext tasks. We conduct several experiments to demonstrate that SSL models do exhibit their own CP, with CP closure marking a sweet spot where representations are neither underdeveloped nor overfitted to the pretext task. Leveraging these insights, we propose CP-guided checkpoint selection as a mechanism for identifying intermediate checkpoints during SSL that improve OOD transferability. Finally, to balance the transferability trade-off, we propose CP-guided self-distillation, which selectively distills layer representations from the sweet spot (CP closure) checkpoint into their overspecialized counterparts in the final pretrained model.