ICLR 2026 Papers

The vulnerability of deep neural networks to adversarial examples poses significant challenges to their reliable deployment. Among existing empirical defenses, adversarial training and robust distillation have proven the most effective. In this paper, we identify a property originally associated with model intellectual property, i.e., probability sparsity induced by nasty training, and demonstrate that it can also provide interpretable improvements to adversarial robustness. We begin by analyzing how nasty training induces sparse probability distributions and qualitatively explore the spatial metric preferences this sparsity introduces to the model. Building on these insights, we propose a simple yet effective adversarial training method, nasty adversarial training (NAT), which incorporates probability sparsity as a regularization mechanism to boost adversarial robustness. Both theoretical analysis and experimental results validate the effectiveness of NAT, highlighting its potential to enhance the adversarial robustness of deep neural networks in an interpretable manner.

Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.g., cycles and cliques) to boost the expressive power of message-passing neural networks. In turn, however, these structures are typically identified a priori through an unsupervised graph lifting operation. Notwithstanding, this choice is crucial and may have a drastic impact on a TNN's performance on downstream tasks. To circumvent this issue, we propose $\partial$lift (DiffLift), a general framework for learning graph liftings to hypergraphs, cellular- and simplicial complexes in an end-to-end fashion. In particular, our approach leverages learned vertex-level latent representations to identify and parameterize distributions over candidate higher-order cells for inclusion. This results in a scalable model which can be readily integrated into any TNN. Our experiments show that $\partial$lift outperforms existing lifting methods on multiple benchmarks for graph and node classification across different TNN architectures. Notably, our approach leads to gains of up to 45% over static liftings, including both connectivity- and feature-based ones.

Large language model (LLM) applications such as agents and domain-specific reasoning increasingly rely on context adaptation, modifying model inputs with instructions, strategies, or evidence, rather than weight updates. While prior methods improve usability, they often suffer from a brevity bias, discarding domain-specific insights in favor of short summaries, and from context collapse, where iterative rewriting erodes details over time. Building on the adaptive memory introduced by Dynamic Cheatsheet, we present ACE (**A**gentic **C**ontext **E**ngineering), a framework that treats contexts as evolving playbooks that accumulate, refine, and organize strategies through a modular process of generation, reflection, and curation. ACE prevents collapse by applying structured, incremental updates that preserve detailed knowledge and scale with long-context models. Across agentic and domain-specific benchmarks, ACE consistently outperforms strong baselines, improving application performance by 9.0\% while reducing adaptation latency and rollout cost. Notably, ACE could adapt effectively without labeled supervision, instead leveraging natural execution feedback, and on the AppWorld leaderboard it matches the top-1-ranked production-level agent while using a smaller open-source model. These results demonstrate that comprehensive, evolving contexts enable scalable, efficient, and self-improving LLM systems.

Search-augmented large language models (LLMs) trained with reinforcement learning (RL) have achieved strong results on open-domain question answering (QA), but training still remains a significant challenge. The optimization is often unstable due to sparse rewards and difficult credit assignments across reasoning and tool calls. To address this, we introduce Turn-Level Information Potential Reward Shaping (TIPS), a simple framework that assigns dense, turn-level rewards to each reasoning + tool-call segment based on the increased likelihood of the correct answer under a teacher model. By leveraging the potential-based reward shaping, TIPS offers fine-grained and policy-invariant guidance that overcomes the limitations of outcome-only optimization. Evaluated on seven QA benchmarks, TIPS consistently outperforms GRPO/PPO baselines and substantially improves training stability. For instance, with a Qwen-2.5 7B Instruct model, TIPS improves the average Exact Match score by 11.8% and F1 by 13.6% relative to PPO. Our results demonstrate that turn-level information-potential reward shaping provides an effective and general solution to sparse-reward credit assignment for multi-turn LLM reasoning.

Trained Transformers have been shown to compute abstract features that appear redundant for predicting the immediate next token. We identify which components of the gradient signal from the next-token prediction objective give rise to this phenomenon, and we propose a method to estimate the influence of those components on the emergence of specific features. After validating our approach on toy tasks, we use it to interpret the origins of the world model in OthelloGPT and syntactic features in a small language model. Finally, we apply our framework to a pretrained LLM, showing that features with extremely high or low influence on future tokens tend to be related to formal reasoning domains such as code. Overall, our work takes a step toward understanding hidden features of Transformers through the lens of their development during training.

Molecular dynamics (MD) simulations underpin modern computational drug discovery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need for repeated quantum-mechanical force calculations, enabling significant speedups over conventional pipelines. Yet many such methods typically enforce strict equivariance and rely on sequential rollouts, thus limiting their flexibility and simulation efficiency. They are also commonly single-task, trained on individual molecules and fixed time frames, which restricts generalization to unseen compounds and extended timesteps. To address these issues, we propose Atomistic Transformer Operator for Molecules (ATOM), a pretrained transformer neural operator for multi-task molecular dynamics. ATOM adopts a quasi-equivariant design that does not require an explicit molecular graph and employs a temporal attention mechanism to enable accurate, parallel decoding of multiple future states. To support operator pretraining across chemicals and timescales, we curate TG80, a large, diverse, and numerically stable MD dataset with over 2.5 million femtoseconds of trajectories across 80 compounds. ATOM achieves state-of-the-art performance on established single-task benchmarks, such as MD17, RMD17, and MD22. After multi-task pretraining on TG80, ATOM shows exceptional zero-shot and robust generalization to unseen molecules across varying time horizons. We believe ATOM represents a significant step toward accurate, efficient, and transferable molecular dynamics models.

3D Gaussian Splatting (3DGS) has emerged as a dominant novel-view synthesis technique, but its high memory consumption severely limits its applicability on edge devices. A growing number of 3DGS compression methods have been proposed to make 3DGS more efficient, yet most only focus on storage compression and fail to address the critical bottleneck of rendering memory. To address this problem, we introduce MEGS², a novel memory-efficient framework that tackles this challenge by jointly optimizing two key factors: the total primitive number and the parameters per primitive, achieving unprecedented memory compression. Specifically, we fully replace the memory-intensive Spherical Harmonics with lightweight, arbitrarily oriented and prunable Spherical Gaussian lobes as our color representations. More importantly, we propose a unified soft pruning framework that models primitive-number and lobe-number pruning as a single constrained optimization problem. Experiments show that MEGS² achieves a 50% static VRAM reduction and a 40% rendering VRAM reduction compared to existing methods, while maintaining comparable rendering quality.

Combinatorial generalization (CG)—generalizing to unseen combinations of known semantic factors—remains a grand challenge in machine learning. While symmetry-based methods are promising, they learn from observed data and thus fail at what we term $\textbf{symmetry generalization}$: extending learned symmetries to novel data. We tackle this by proposing a novel framework that endows the latent space with the structure of a $\textbf{symmetric space}$, a class of manifolds whose geometric properties provide a principled way to extend these symmetries. Our method operates in two steps: first, it imposes this structure by learning the underlying algebraic properties via the $\textbf{Cartan decomposition}$ of a learnable Lie algebra. Second, it uses $\textbf{geodesic symmetry}$ as a powerful self-supervisory signal to ensure this learned structure extrapolates from observed samples to unseen ones. A detailed analysis on a synthetic dataset validates our geometric claims, and experiments on standard CG benchmarks show our method significantly outperforms existing approaches.

Video diffusion transformers (vDiTs) have made tremendous progress in text-to-video generation, but their high computational demands pose a major challenge for practical deployment. While existing studies propose acceleration methods to reduce workload at various granularities, they often rely on heuristics, limiting their applicability. We introduce Astraea, a framework that searches for near-optimal configurations for vDiT-based video generation with a performance target. At its core, Astraea proposes a lightweight token selection mechanism and a memory-efficient, GPU-parallel sparse attention strategy, enabling linear reductions in execution time with minimal impact on generation quality. Meanwhile, to determine optimal token reduction for different timesteps, we further design a search framework that leverages a classic evolutionary algorithm to automatically determine the distribution of the token budget effectively. Together, Astraea achieves up to 2.4x inference speedup on a single GPU with great scalability (up to 13.2x speedup on 8 GPUs) while retaining better video quality compared to the state-of-the-art methods (<0.5% loss on the VBench score compared to the baseline vDiT models).

Dense retrievers play a vital role in accessing external and specialized knowledge to augment language models (LMs). Training dense retrievers typically requires annotated query-document pairs, which are costly to create and scarce in specialized domains (e.g., code) or in complex settings (e.g., requiring reasoning). These practical challenges have sparked growing interest in self-supervised retriever learning. Since LMs are trained to capture token-level dependencies through a self-supervised learning objective (i.e., next token prediction), we can analogously cast retrieval as learning dependencies among chunks of tokens. This analogy naturally leads to the question: How can we adapt self‑supervised learning objectives in the spirit of language modeling to train retrievers? To answer this question, we introduce Revela, a unified and scalable training framework for self-supervised retriever learning via language modeling. Revela models semantic dependencies among documents by conditioning next token prediction on local and cross-document context through an in-batch attention mechanism. This attention is weighted by retriever-computed similarity scores, enabling the retriever to be optimized as part of language modeling. We evaluate Revela on domain-specific (CoIR), reasoning-intensive (BRIGHT), and general-domain (BEIR) benchmarks across various retriever backbones. Without annotated or synthetic query-document pairs, Revela surpasses larger supervised models and proprietary APIs on both CoIR and BRIGHT. It achieves BEIR's unsupervised SoTA with ~1000x less training data and 10x less compute. Performance increases with batch size and model size, highlighting Revela's scalability and its promise for self‑supervised retriever learning.

Imagine trying to understand the shape of a teapot by viewing it from the front—you might see the spout, but completely miss the handle. Some perspectives naturally provide more information than others. How can an AI system determine which viewpoint offers the most valuable insight for accurate and efficient 3D object reconstruction? Active view selection (AVS) for 3D reconstruction remains a fundamental challenge in computer vision. The aim is to identify the minimal set of views that yields the most accurate 3D reconstruction. Instead of learning radiance fields, like NeRF or 3D Gaussian Splatting, from a current observation and computing uncertainty for each candidate viewpoint, we introduce a novel AVS approach guided by neural uncertainty maps predicted by a lightweight feedforward deep neural network, named UPNet. UPNet takes a single input image of a 3D object and outputs a predicted uncertainty map, representing uncertainty values across all possible candidate viewpoints. By leveraging heuristics derived from observing many natural objects and their associated uncertainty patterns, we train UPNet to learn a direct mapping from viewpoint appearance to uncertainty in the underlying volumetric representations. Next, our approach aggregates all previously predicted neural uncertainty maps to suppress redundant candidate viewpoints and effectively select the most informative one. Using these selected viewpoints, we train 3D neural rendering models and evaluate the quality of novel view synthesis against other competitive AVS methods. Remarkably, despite using half of the viewpoints than the upper bound, our method achieves comparable reconstruction accuracy. In addition, it significantly reduces computational overhead during AVS, achieving up to a 400 times speedup along with over 50\% reductions in CPU, RAM, and GPU usage compared to baseline methods. Notably, our approach generalizes effectively to AVS tasks involving novel object categories, without requiring any additional training. We will release all code, models, and datasets.

Data pruning (DP), as an oft-stated strategy to alleviate heavy training burdens, reduces the volume of training samples according to a well-defined pruning method while striving for near-lossless performance. However, existing approaches, which commonly select highly informative samples, can lead to biased gradient estimation compared to full-dataset training. Furthermore, the analysis of this bias and its impact on final performance remains ambiguous. To address these challenges, we propose OrderDP, a plug-and-play framework that aims to obtain stable, unbiased, and near-lossless training acceleration with theoretical guarantees. Specifically, OrderDP first randomly selects a subset and then chooses the top-$q$ samples, where unbiasedness is established with respect to a surrogate loss. This ensures that OrderDP conducts unbiased training in terms of the surrogate objective. We further establish convergence and generalization analyses, elucidating how OrderDP affects optimal performance and enables well-controlled acceleration while ensuring guaranteed final performance. Empirically, we evaluate OrderDP against comprehensive baselines on CIFAR-10, CIFAR-100, and ImageNet-1K, demonstrating competitive accuracy, stable convergence, and exact control---all with a simpler design and faster runtime, while reducing training cost by over 40\%. Delivering both strong performance and computational efficiency, our method serves as a robust and easily adaptable tool for data-efficient learning.

The discontinuous operations inherent in quantization and sparsification introduce a long-standing obstacle to backpropagation, particularly in ultra-low precision and sparse regimes. While the community has long viewed quantization as unfriendly to gradient descent due to its lack of smoothness, we pinpoint—for the first time—that the key issue is the absence of a proper gradient path that allows training to learn robustness to quantization noise. The standard Straight-Through Estimator (STE) exacerbates this with its well-understood mismatch: a quantization-aware forward pass but oblivious backward pass, leading to unmanaged error and instability. We solve this by explicitly modeling quantization as additive noise, making the full forward-backward path well-defined without heuristic gradient estimation. As one natural solution, we introduce a denoising dequantization transform derived from a principled ridge regression objective, creating an explicit, corrective gradient path that makes learning robust to the noise STE bypasses. We extend this to sparsification by treating it as a special form of quantization that zeros out small values. Our unified framework trains models at arbitrary precisions and sparsity levels with off-the-shelf recipes, enabling stable A1W1 and sub-1-bit networks where others falter. It yields state-of-the-art results, mapping efficiency frontiers for modern LLMs and providing a theoretically grounded path to hyper-efficient neural networks.

Visual manipulation localization (VML) aims to identify tampered regions in images and videos, a task that has become increasingly challenging with the rise of advanced editing tools. Existing methods face two main issues: resolution diversity, where resizing or padding distorts forensic traces and reduces efficiency, and the modality gap, as images and videos often require separate models. To address these challenges, we propose RelayFormer, a unified framework that adapts to varying resolutions and modalities. RelayFormer partitions inputs into fixed-size sub-images and introduces Global-Local Relay (GLR) tokens, which propagate structured context through a global-local relay attention (GLRA) mechanism. This enables efficient exchange of global cues, such as semantic or temporal consistency, while preserving fine-grained manipulation artifacts. Unlike prior methods that rely on uniform resizing or sparse attention, RelayFormer naturally scales to arbitrary resolutions and video sequences without excessive overhead. Experiments across diverse benchmarks demonstrate that RelayFormer achieves state-of-the-art performance with notable efficiency, combining resolution adaptivity without interpolation or excessive padding, unified modeling for both images and videos, and a strong balance between accuracy and computational cost.

While traditional time-series classifiers assume full sequences at inference, practical constraints (latency and cost) often limit inputs to partial prefixes. The absence of class-discriminative patterns in partial data can significantly hinder a classifier’s ability to generalize. This work uses knowledge distillation (KD) to equip partial time series classifiers with the generalization ability of their full-sequence counterparts. In KD, high-capacity teacher transfers supervision to aid student learning on the target task. Matching with teacher features has shown promise in closing the generalization gap due to limited parameter capacity. However, when the generalization gap arises from training-data differences (full versus partial), the teacher’s full-context features can be an overwhelming target signal for the student’s short-context features. To provide progressive, diverse, and collective teacher supervision, we propose Generative Diffusion Prior Distillation (GDPD), a novel KD framework that treats short-context student features as degraded observations of the target full-context features. Inspired by the iterative restoration capability of diffusion models, we learn a diffusion-based generative prior over teacher features. Leveraging this prior, we posterior-sample target teacher representations that could best explain the missing long-range information in the student features and optimize the student features to be minimally degraded relative to these targets. GDPD provides each student feature with a distribution of task-relevant long-context knowledge, which benefits learning on the partial classification task. Extensive experiments across earliness settings, datasets, and architectures demonstrate GDPD’s effectiveness for full-to-partial distillation.

Brain-like intelligent systems need brain-like learning methods. Equilibrium Propagation (EP) is a biologically plausible learning framework with strong potential for brain-inspired computing hardware. However, existing implementations of EP suffer from instability and prohibitively high computational costs. Inspired by the structure and dynamics of the brain, we propose a biologically plausible Feedback-regulated REsidual recurrent neural network (FRE-RNN) and study its learning performance in EP framework. Feedback regulation enables rapid convergence by attenuating feedback signals and reducing the disturbance of feedback path to feedforward path. The improvement in convergence property reduces the computational cost and training time of EP by orders of magnitude, delivering performance on par with backpropagation (BP) in benchmark tasks. Meanwhile, residual connections with brain-inspired topologies help alleviate the vanishing gradient problem that arises when feedback pathways are weak in deep RNNs. Our approach substantially enhances the applicability and practicality of EP. The techniques developed here also offer guidance to implementing in-situ learning in physical neural networks.

In Reward Learning (ReL), we are given feedback on an unknown target reward, and the goal is to use this information to recover it in order to carry out some downstream application, e.g., planning. When the feedback is not informative enough, the target reward is only partially identifiable, i.e., there exists a set of rewards, called the feasible set, that are equally plausible candidates for the target reward. In these cases, the ReL algorithm might recover a reward function different from the target reward, possibly leading to a failure in the application. In this paper, we introduce a general ReL framework that permits to quantify the drop in "performance" suffered in the considered application because of identifiability issues. Building on this, we propose a robust approach to address the identifiability problem in a principled way, by maximizing the "performance" with respect to the worst-case reward in the feasible set. We then develop Rob-ReL, a ReL algorithm that applies this robust approach to the subset of ReL problems aimed at assessing a preference between two policies, and we provide theoretical guarantees on sample and iteration complexity for Rob-ReL. We conclude with some numerical simulations to illustrate the setting and empirically characterize Rob-ReL.

Linear modeling methods like Mamba have been merged as the effective backbone for the 3D object detection task. However, previous Mamba-based methods utilize the bidirectional encoding for the whole non-empty voxel sequence, which contains abundant useless background information in the scenes. Though directly encoding foreground voxels appears to be a plausible solution, it tends to degrade detection performance. We attribute this to the response attenuation and restricted context representation in the linear modeling for fore-only sequences. To address this problem, we propose a novel backbone, termed Fore-Mamba3D, to focus on the foreground enhancement by modifying Mamba-based encoder. The foreground voxels are first sampled according to the predicted scores. Considering the response attenuation existing in the interaction of foreground voxels across different instances, we design a regional-to-global slide window (RGSW) to propagate the information from regional split to the entire sequence. Furthermore, a semantic-assisted and state spatial fusion module (SASFMamba) is proposed to enrich contextual representation by enhancing semantic and geometric awareness within the Mamba model. Our method emphasizes foreground-only encoding and alleviates the distance-based and causal dependencies in the linear autoregression model. The superior performance across various benchmarks demonstrates the effectiveness of Fore-Mamba3D in the 3D object detection task.

Vision-language reinforcement learning (RL) has primarily focused on narrow domains (e.g. geometry or chart reasoning). This leaves broader training scenarios and resources underexplored, limiting the exploration and learning of Vision Language Models (VLMs) through RL. We find video games inherently provide rich visual elements and mechanics that are easy to verify. To fully use the multimodal and verifiable reward in video games, we propose Game-RL, constructing diverse game tasks for RL training to boost VLMs general reasoning ability. To obtain training data, we propose Code2Logic, a novel approach that adapts game code to synthesize game reasoning task data, thus obtaining the GameQA dataset of 30 games and 158 tasks with controllable difficulty gradation. Unexpectedly, training solely on GameQA would help VLMs obtain better out of domain generalization, demonstrating the value of Game-RL for enhancing VLMs general reasoning. Furthermore, this suggets that RL can lead to generalizable improvements in VLMs' reasoning abilities, and notably, video games may serve as valuable scenarios and resources to bring this generalization.