ICLR 2026 Papers

Modeling 3D dynamics is a fundamental problem in multi-body systems across scientific and engineering domains and has important practical implications in trajectory prediction and simulation. While recent GNN-based approaches have achieved strong performance by enforcing geometric symmetries, encoding high-order features or incorporating neural-ODE mechanics, they typically depend on explicitly observed structures and inherently fail to capture the unobserved interactions that are crucial to complex physical behaviors and dynamics mechanism. In this paper, we propose PAINET, a principled SE(3)-equivariant neural architecture for learning all-pair interactions in multi-body systems. The model comprises: (1) a novel physics-inspired attention network derived from the minimization trajectory of an energy function, and (2) a parallel decoder that preserves equivariance while enabling efficient inference. Empirical results on diverse real-world benchmarks, including human motion capture, molecular dynamics, and large-scale protein simulations, show that PAINET consistently outperforms recently proposed models, yielding 4.7% to 41.5% error reductions in 3D dynamics prediction with comparable computation costs in terms of time and memory. Our codes, baseline models and datasets are available at https://anonymous.4open.science/r/PAINET-4668.

Synaptic plasticity is a fundamental substrate for learning and memory, where different synapse types exhibit distinct plasticity mechanisms. However, how functional behaviors emerge from heterogeneous synaptic plasticity mechanisms remains poorly understood. Here, we introduce a computational framework that harnesses Darwinian evolutionary principles to discover biologically plausible, heterogeneous synaptic plasticity rules within a biologically realistic model of the mouse primary visual cortex. Specifically, we parameterize several key factors related to synaptic plasticity, including presynaptic and postsynaptic spikes, their associated eligibility traces, and neuromodulatory signals. By integrating these factors via a truncated Taylor expansion, we construct a large-scale search space of candidate plasticity rules, with each rule containing over 2.6k optimizable parameters. Each rule is subsequently evaluated on both cross-domain visual task performance and biological validity. Leveraging a multi-objective evolutionary algorithm, we effectively navigate this high-dimensional search space to identify plasticity rules that are both biologically plausible and yield high task performance. We uncover diverse families of high-performing plasticity rules that achieve similar behavioral outcomes despite markedly different mathematical formulations, suggesting that real-world synaptic learning mechanisms may exhibit computational degeneracy. We further show that these biologically plausible rules are not only robust across network scales but also enable few-shot learning, offering a computational explanation for the emergence of innate ability.

Despite substantial progress in video understanding, most existing datasets are limited to Earth’s gravitational conditions. However, microgravity alters human motion, interactions, and visual semantics, revealing a critical gap for real-world vision systems. This presents a challenge for domain-robust video understanding in safety-critical space applications. To address this, we introduce MicroG-4M, the first benchmark for spatio-temporal and semantic understanding of human activities in microgravity. Constructed from real-world space missions and cinematic simulations, the dataset includes 4,759 clips covering 50 actions, 1,238 context-rich captions, and over 7,000 question–answer pairs on astronaut activities and scene understanding. MicroG-4M aims to support three core tasks: fine-grained multi-label action recognition, temporal video captioning, and visual question answering, thereby enabling a comprehensive evaluation of both spatial localization and semantic reasoning in microgravity contexts. We establish baselines using state-of-the-art models. All data, annotations, and code will be made publicly available upon decision.

In organic reaction prediction, many recent approaches ranging from traditional task-specific models to Large Language Models (LLMs), have demonstrated notable success. However, these methods are inherently data-driven, exhibit constrained interpretability, and have hit fundamental performance bottlenecks. To overcome these limitations, we present Reaction-Thinker, a hybrid, knowledge‑and-data‑driven system that is enhanced by Retrieval‑Augmented Generation (RAG) and powered by advanced reasoning, improving both the interpretability of prediction process and the explainability of results. We develop similar-case retrieval database and train a RAG‑based LLM through supervised fine-tuning (SFT) to apply both reaction types and similar reaction cases as knowledge. We also construct a reaction reasoning chain-of-thought (CoT) dataset and train a reasoning-based LLM through SFT, then further optimize it using Group Relative Policy Optimization (GRPO). Experimental results show that our method outperforms all compared LLMs and task-specific models, achieving the highest accuracy (Exact Match) and fingerprint similarity (FTS). Ablation study indicates improvements in relative accuracy of 7.5% and 13.9% for RAG and GRPO, respectively. Further analysis of mispredictions reveals limitations in conventional evaluation metrics, which motivates our proposed benchmarking refinement.

Graph Neural Networks (\textsc{Gnn}s) are increasingly being deployed in sensitive, user-centric applications where regulations such as the GDPR mandate the ability to remove data upon request. This has spurred interest in graph unlearning, the task of removing the influence of specific training data from a trained \textsc{Gnn} without retraining from scratch. While several unlearning techniques have recently emerged, the field lacks a principled benchmark to assess whether these methods truly provide a practical alternative to retraining and, if so, how to choose among them for different workloads. In this work, we present the first systematic benchmark for \textsc{Gnn} unlearning, structured around three core desiderata: \emph{efficiency} (is unlearning faster than retraining?), \emph{utility} (does the unlearned model preserve predictive performance and align with the retrained gold standard?), and \emph{forgetting} (does the model genuinely eliminate the influence of removed data?). Through extensive experiments across diverse datasets and deletion scenarios, we deliver a unified assessment of existing approaches, surfacing their trade-offs and limitations. Crucially, our findings show that most unlearning techniques are not yet practical for large-scale graphs. At the same time, our benchmarking yields actionable guidelines on when unlearning can be a viable alternative to retraining and how to select among methods for different workloads, thereby charting a path for future research toward more practical, scalable, and trustworthy graph unlearning.

Within the context of representation learning for Earth observation, geographic Implicit Neural Representations (INRs) embed low-dimensional location inputs (longitude, latitude) into high-dimensional embeddings, through models trained on geo-referenced satellite, image or text data. Despite the common aim of geographic INRs to distill Earth's data into compact, learning-friendly representations, we lack an understanding of how much information is contained in these Earth representations, and where that information is concentrated. The intrinsic dimension of a dataset measures the number of degrees of freedom required to capture its local variability, regardless of the ambient high-dimensional space in which it is embedded. This work provides the first study of the intrinsic dimensionality of geographic INRs. Analyzing INRs with ambient dimension between 256 and 512, we find that their intrinsic dimensions fall roughly between 2 and 10 and are sensitive to changing spatial resolution and input modalities during INR pre-training. Furthermore, we show that the intrinsic dimension of a geographic INR correlates with downstream task performance and can capture spatial artifacts, facilitating model evaluation and diagnostics. More broadly, our work offers an architecture-agnostic, label-free metric of information content that can enable unsupervised evaluation, model selection, and pre-training design across INRs.

Alzheimer’s Disease (AD) is a progressive neurodegenerative disorder and a leading cause of dementia worldwide. Accurate diagnosis requires integrating diverse patient data modalities. With the rapid advancement of foundation models in neurobiology and medicine, integrating foundation models from various modalities has emerged as a promising yet underexplored direction for multi-modal AD diagnosis. A central challenge is enabling effective interaction among these models without disrupting the robust, modality-specific representations learned from large-scale pretraining. To address this, we propose a novel multi-modal framework for AD diagnosis that enables joint interaction among uni-modal foundation models through modality-anchored interaction. In this framework, one modality and its corresponding foundation model are designated as an anchor, while the remaining modalities serve as auxiliary sources of complementary information. To preserve the pre-trained representation space of the anchor model, we propose modality-aware Q-formers that selectively map auxiliary modality features into the anchor model’s feature space, enabling the anchor model to jointly process its own features together with the seamlessly integrated auxiliary features. We evaluate our method on AD diagnosis and progression prediction across four modalities: sMRI, fMRI, clinical records, and genetic data. Our framework consistently outperforms prior methods in two modality settings, and further demonstrates strong generalization to external datasets and other neurodegenerative diseases such as Parkinson’s disease.

The classical optimal transport such as Kantorovich's optimal transport and partial optimal transport could be too restrictive in applications due to the full-mass or fixed-mass preservation constraints. To remedy this limitation, we propose elastic optimal transport (ELOT) which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It aims to answer the problem of how to transport the probability mass adaptively between probability distributions, which is a fundamental topic in various areas of artificial intelligence. The strength of elastic optimal transport is its capability to transport adaptive-mass in the light of the geometry structure of the problem itself. As an application example in machine learning, we apply elastic optimal transport to both unsupervised domain adaptation and partial domain adaptation tasks. It adaptively transports masses from source domain to target domain by taking domain shift into consideration and respecting the ubiquity of noises or outliers in the data, in order to improve the generalization performance. The experiment results on the benchmarks show that ELOT significantly outperforms the state-of-the-art methods. As a powerful distribution matching tool, elastic optimal transport might be of interests to the broad areas such as artificial intelligence, healthcare, physics, operations research, urban science, etc. The source code is available in the supplementary material.

Molecular dynamics (MD) simulation has long been the principal computational tool for exploring protein conformational landscapes, but its application is limited by high computational cost. We present ProTDyn, a foundation protein language model that unifies conformational ensemble generation and multi-timescale dynamics modeling within a single framework. Unlike prior approaches that treat these tasks separately, ProTDyn allows flexible i.i.d ensemble sampling and dynamic trajectory simulation. Across diverse protein systems, ProTDyn yields thermodynamically consistent ensembles, faithfully reproduces dynamical properties over multiple timescales, and generalizes to proteins beyond its training data—offering a scalable and efficient alternative to conventional MD simulations.

State-of-the-art machine learning often follows a two-stage process: $(i)$ pre-training on large, general-purpose datasets; $(ii)$ fine-tuning on task-specific data. In fine-tuning, selecting training examples that closely reflect the target distribution is crucial. However, it is often the case that only a few samples are available from the target distribution. Existing data selection methods treat these target samples as a validation set and estimate the effect of adding or removing a single sample from the training pool by performing inference on the validation set. We propose a simpler and faster alternative that inverts the usual role of train and validation: we perform inference on the training pool before and after fine-tuning on the validation set. We then select samples whose predictions change the most. Our key insight is that the training samples most affected by fine-tuning on a small validation set tend to be the most beneficial for reducing test loss on the target distribution. Experiments on instruction tuning and named entity recognition tasks show that, in most cases, our method achieves lower test log-loss than state-of-the-art approaches. We support our findings with theoretical analysis.

Unlike the foundation model scaling laws seen in natural language processing and computer vision, biological foundation models scale relatively poorly. For example, the ESM-2 family of protein language models plateaus at 650M-3B parameters on ProteinGym benchmarks. We address this limitation by introducing Reverse Distillation, a principled framework that decomposes large protein language model representations into orthogonal subspaces guided by smaller models of the same family. We hypothesize that this decomposition matches the natural hierarchy of protein properties, where broad features like secondary structure are robustly captured by compact, smaller models while the residual capacity of larger models specializes in protein-family specific functions. Our method is theoretically grounded and enables monotonic scaling---larger reverse-distilled models consistently outperform their smaller counterparts, overcoming the scaling plateau. Moreover, on ProteinGym benchmarks, reverse-distilled ESM-2 variants broadly outperform their respective baseline models at the same embedding dimensionality. Our approach offers a generalizable framework for disentangling hierarchical feature spaces in foundation model embeddings, with potential applications across biology and other domains where scaling challenges persist.

Facility Location is a fundamental problem in clustering and unsupervised learning. Recently, significant attention has been given to studying this problem in the classical online setting enhanced with machine learning advice. While (almost) tight bounds exist for the fractional version of the problem, the integral version remains less understood, with only weaker results available. In this paper, we address this gap by presenting the first online rounding algorithms for the facility location problem, and by showing their applications to online facility location with machine learning advice.

Lane-level navigation is critical for geographic information systems and navigation-based tasks, offering finer-grained guidance than road-level navigation by standard definition (SD) maps. However, it currently relies on expansive global HD maps that cannot adapt to dynamic road conditions. Recently, online perception (OP) maps have become research hotspots, providing real-time geometry as an alternative, but lack the global topology needed for navigation. To address these issues, Online Navigation Refinement (ONR), a new mission is introduced that refines SD-map-based road-level routes into accurate lane-level navigation by associating SD maps with OP maps. The map-to-map association to handle many-to-one lane-to-road mappings under two key challenges: (1) no public dataset provides lane-to-road correspondences; (2) severe misalignment from spatial fluctuations, semantic disparities, and OP map noise invalidates traditional map matching. For these challenges, We contribute: (1) Online map association dataset (OMA), the first ONR benchmark with 30K scenarios and 2.6M annotated lane vectors; (2) MAT, a transformer with path-aware attention to aligns topology despite spatial fluctuations and semantic disparities and spatial attention for integrates noisy OP features via global context; and (3) NR P-R, a metric evaluating geometric and semantic alignment. Experiments show that MAT outperforms existing methods at 34 ms latency, enabling low-cost and up-to-date lane-level navigation.

The intrinsic dynamics of an object governs its physical behavior in the real world, playing a critical role in enabling physically plausible interactive simulation with 3D assets. Existing methods have attempted to infer the intrinsic dynamics of objects from visual observations, but generally face two major challenges: one line of work relies on manually defined constitutive priors, making it difficult to align with actual intrinsic dynamics; the other models intrinsic dynamics using neural networks, resulting in limited interpretability and poor generalization. To address these challenges, we propose VisionLaw, a bilevel optimization framework that infers interpretable expressions of intrinsic dynamics from visual observations. At the upper level, we introduce an LLMs-driven decoupled constitutive evolution strategy, where LLMs are prompted as a physics expert to generate and revise constitutive laws, with a built-in decoupling mechanism that substantially reduces the search complexity of LLMs. At the lower level, we introduce a vision-guided constitutive evaluation mechanism, which utilizes visual simulation to evaluate the consistency between the generated constitutive law and the underlying intrinsic dynamics, thereby guiding the upper-level evolution. Experiments on both synthetic and real-world datasets demonstrate that VisionLaw can effectively infer interpretable intrinsic dynamics from visual observations. It significantly outperforms existing state-of-the-art methods and exhibits strong generalization for interactive simulation in novel scenarios.

While recent advances in machine learning have equipped Weather Foundation Models (WFMs) with substantial generalization capabilities across diverse downstream tasks, the escalating computational requirements associated with their expanding scale increasingly hinder practical deployment. Current Parameter-Efficient Fine-Tuning (PEFT) methods, designed for vision or language tasks, fail to address the unique challenges of weather downstream tasks, such as variable heterogeneity, resolution diversity, and spatiotemporal coverage variations, leading to suboptimal performance when applied to WFMs. To bridge this gap, we introduce WeatherPEFT, a novel PEFT framework for WFMs incorporating two synergistic innovations. First, during the forward pass, Task-Adaptive Dynamic Prompting (TADP) dynamically injects the embedding weights within the encoder to the input tokens of the pre-trained backbone via internal and external pattern extraction, enabling context-aware feature recalibration for specific downstream tasks. Furthermore, during backpropagation, Stochastic Fisher-Guided Adaptive Selection (SFAS) not only leverages Fisher information to identify and update the most task-critical parameters, thereby preserving invariant pre-trained knowledge, but also introduces randomness to stabilize the selection. We demonstrate the effectiveness and efficiency of WeatherPEFT on three downstream tasks, where existing PEFT methods show significant gaps versus Full-Tuning, and WeatherPEFT achieves performance parity with Full-Tuning using fewer trainable parameters. The code of this work is available at https://anonymous.4open.science/r/WeatherPEFT-A068.

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.

Conditional generation models for longitudinal sequences can produce new or modified trajectories given a conditioning input. However, they often lack control over when the condition should take effect (timing) and which variables it should influence (scope). Most methods either operate only on univariate sequences or assume that the condition alters all variables and time steps. In scientific and clinical settings, interventions instead begin at a specific moment, such as the time of drug administration or surgery, and influence only a subset of measurements while the rest of the trajectory remains unchanged. CLEF learns temporal concepts that encode how and when a condition alters future sequence evolution. These concepts allow CLEF to apply targeted edits to the affected time steps and variables while preserving the rest of the sequence. We evaluate CLEF on 8 datasets spanning cellular reprogramming, patient health, and sales, comparing against 9 state-of-the-art baselines. CLEF improves immediate sequence editing accuracy by 16.28% (MAE) on average against their non-CLEF counterparts. Unlike prior models, CLEF enables one-step conditional generation at arbitrary future times, outperforming their non-CLEF counterparts in delayed sequence editing by 26.73% (MAE) on average. We test CLEF under counterfactual inference assumptions and show up to 63.19% (MAE) improvement on zero-shot conditional generation of counterfactual trajectories. In a case study of patients with type 1 diabetes mellitus, CLEF identifies clinical interventions that generate realistic counterfactual trajectories shifted toward healthier outcomes.

Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student attains a low-rank structure in its first-layer weights when trained with stochastic gradient descent (SGD) and a strong regularizer. This structural property is known to reduce sample complexity of generalization. Indeed, in a second step, the same authors establish algorithm-specific learning guarantees under additional assumptions. In this paper, we focus exclusively on the structure discovery aspect and study it under weaker assumptions, more specifically: we allow (a) NNs of arbitrary size and depth, (b) with all parameters trainable, (c) under any smooth loss function, (d) tiny regularization, and (e) trained by any method that attains a second-order stationary point (SOSP), e.g. perturbed gradient descent (PGD). At the core of our approach is a key $\textit{derandomization}$ lemma, which states that optimizing the function $E_{x} \left[g_{\theta}(Wx + b)\right]$ converges to a point where $W = 0$, under mild conditions. The fundamental nature of this lemma directly explains structure discovery and has immediate applications in other domains including an end-to-end approximation for MAXCUT, and computing Johnson-Lindenstrauss embeddings.

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.