ICLR 2026 Papers

Learning dynamical systems that respect physical symmetries and constraints remains a fundamental challenge in data-driven modeling. Integrating physical laws with graph neural networks facilitates principled modeling of complex N-body dynamics and yields accurate and permutation-invariant models. However, training graph neural networks with iterative, gradient-descent-based optimization algorithms (e.g., Adam, RMSProp, LBFGS) often leads to slow training, especially for large, complex systems. In comparison to 15 different optimizers, we demonstrate that Hamiltonian Graph Networks (HGN) can be trained 150-600× faster - but with comparable accuracy - by replacing iterative optimization with random feature-based parameter construction. We show robust performance in diverse simulations, including N-body mass-spring and molecular dynamics systems in up to $3$ dimensions and 10,000 particles with different geometries, while retaining essential physical invariances with respect to permutation, rotation, and translation. Our proposed approach is benchmarked using a NeurIPS 2022 Datasets and Benchmarks Track publication to further demonstrate its versatility. We reveal that even when trained on minimal 8-node systems, the model can generalize in a zero-shot manner to systems as large as 4096 nodes without retraining. Our work challenges the dominance of iterative gradient-descent-based optimization algorithms for training neural network models for physical systems.

Large Language Models (LLMs) are increasingly deployed in human–AI collaborative decision-making systems, where they are expected to align precise formal representations with ambiguous natural language. However, their ad hoc strategies for resolving ambiguity often lead to hallucinations and inconsistencies. We formalize this setting via probabilistic Minimally Adequate Teachers (pMATs) that (i) answer membership queries with fixed but possibly flipped labels, and (ii) return valid counterexamples to hypothesis equivalence. We present **CAPAL** (**C**lass-query **A**ctive, **P**ersistent-noise-**A**ware **L**earning), an active algorithm for learning deterministic finite automata (DFAs) that remains correct under persistent membership noise without demonstrations. CAPAL augments the classic \$L^\star\$ loop with two components grounded in our implementation: (1) a *class query* realized as a statistical same-state test that compares disagreements between two prefixes against a noise-floor estimate \$\hat{\eta}\$ with Hoeffding tolerances; (2) a *discrimination tree* that selects a near-minimal discriminator, keeping the core suffix set small. An efficient micro-bootstrap and cache-reuse scheme estimates \$\hat{\eta}\$ with few new queries. We prove convergence given a perfect language-equivalence oracle and show substantial membership-query savings in practice. Our evaluation across multiple benchmarks, including RegexLib and KB13, demonstrates that this approach enhances both the efficiency and robustness of DFA learning under noisy oracles, supporting the view of LLMs as fallible yet useful collaborators for synthesizing verifiable formal artifacts.

Super-resolving climate data is crucial for fine-grained decision-making in various domains, ranging from agriculture to environmental conservation. However, existing super-resolution approaches struggle to generate the high-frequency spatial information present in climate data, especially over regions showing complex terrain variability. A key obstacle lies in a frequency bias existing in both deep neural networks (DNNs) and climate data: DNNs exhibit such bias by overfitting to low-frequency information, which is further exacerbated by the prevalence of low-frequency components in climate data (e.g., plains, oceans). As a consequence, geography-dependent high-frequency details are hard to reconstruct from coarse climate inputs with DNNs. To improve the fidelity of climate super-resolution (SR), we introduce GeoFAR: by explicitly encoding climatic patterns at different frequencies, while learning implicit geographical neural representations (i.e., related to location and elevation), our approach provides frequency-aware and geography-informed representations for climate SR, thereby reconstructing fine-grained climate information at high resolution. Experiments show that GeoFAR is a model-agnostic approach that can mitigate high-frequency prediction errors in both deterministic and generative SR models, demonstrating state-of-the-art performance across various spatial resolutions, atmospheric variables, and downscaling ratios. Datasets and code will be released.