ICML 2026 Papers

Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic location, however, distribute representational capacity uniformly across the globe, struggling at the fine-grained resolutions localized applications require. We propose a geographic location encoder built from spherical Slepian functions that concentrates representational capacity inside a region-of-interest and scales to high resolutions without extensive computational demands. For settings requiring global context, we present a hybrid Slepian-Spherical Harmonic encoder that efficiently bridges the tradeoff between local-global performance, while retaining desirable properties such as pole-safety and spherical-surface-distance preservation. Across five tasks spanning classification, regression, and image-augmented prediction, Slepian encodings outperform baselines and retain performance advantages across a wide variety of neural network architectures.

Symbolic regression aims to discover compact, interpretable mathematical expressions from data, but neural generation is challenging because expressions are tree-structured. Existing neural methods often linearize expression trees into token sequences, facilitating autoregressive modeling but obscuring hierarchical relations and complicating structure-dependent constraint enforcement. We propose GCN-SR, a graph-based symbolic regression framework that generates expressions in an explicit tree-aligned form, making structural context available during decoding. To enable batched generation over variable-topology expressions, we introduce Symbolic Perfect Binary Trees (SPBTs), a fixed-topology scaffold that preserves tree hierarchy while supporting graph-based node-attribute prediction. We further introduce Similarity-Weighted Policy Gradient (SWPG) to incorporate genetic programming (GP) refinement without directly imitating GP-refined elites; instead, refined expressions construct similarity-weighted rewards for samples drawn by the current generator. Experiments on standard symbolic regression benchmarks and ablations show that GCN-SR consistently improves exact recovery over strong neural and hybrid baselines under matched evaluation budgets.

Embedding physical intuition into network architectures allows the learning of dynamics that enforce fundamental properties, such as energy conservation laws, thereby leading to physically-plausible predictions. Yet, scaling these models to intrinsically high-dimensional dynamical systems remains a significant challenge. This paper introduces Reduced-order Hamiltonian Neural Network (RO-HNN), a novel physics-inspired neural network that combines the conservation laws of Hamiltonian mechanics with the scalability of model order reduction. RO-HNN is built on two core components: a novel geometrically-constrained symplectic autoencoder that learns a low-dimensional, structure-preserving symplectic submanifold, and a geometric Hamiltonian neural network that models the dynamics on the submanifold. Our experiments demonstrate that RO-HNN provides physically-consistent, stable, and generalizable predictions of complex high-dimensional dynamics, thereby effectively extending the scope of Hamiltonian neural networks to high-dimensional physical systems.

Electrocardiography (ECG) serves as an indispensable diagnostic tool in clinical practice, yet existing multimodal large language models (MLLMs) remain unreliable for ECG interpretation, often producing plausible but clinically incorrect analyses. To address this, we propose ECG-R1, the first reasoning ECG MLLM designed for reliable ECG interpretation via three innovations. First, we construct the interpretation corpus using \textit{Protocol-Guided Instruction Data Generation}, grounding interpretation in measurable ECG features and monograph-defined quantitative thresholds and diagnostic logic. Second, we present a modality-decoupled architecture with \textit{Interleaved Modality Dropout} to improve robustness and cross-modal consistency when either the ECG signal or ECG image is missing. Third, we present \textit{Reinforcement Learning with ECG Diagnostic Evidence Rewards} to strengthen evidence-grounded ECG interpretation. Additionally, we systematically evaluate the ECG interpretation capabilities of proprietary, open-source, and medical MLLMs, and provide the first quantitative evidence that severe hallucinations are widespread, suggesting that the public should not directly trust these outputs without independent verification. Code is available at \href{https://github.com/PKUDigitalHealth/ECG-R1}{here}.

Information design (ID) explores how a sender influence the optimal behavior of receivers to achieve specific objectives. While ID originates from everyday human communication, existing game-theoretic and learning methods often model information structures as numbers, which limits many applications to toy games. This work leverages LLMs and proposes a verbalized framework in Bayesian persuasion (BP), which extends classic BP to real-world games involving human dialogues for the first time. We map the BP to a verbalized mediator-augmented game, where LLMs instantiate the sender and receiver. To efficiently solve the verbalized game, we propose a generalized equilibrium-finding algorithm combining LLM and game solver. The algorithm is reinforced with techniques including verbalized commitment assumptions, verbalized obedience constraints, and information obfuscation. Experiments in dialogue scenarios, such as recommendation letters, law enforcement, diplomacy with press, validate that our framework can reproduce theoretical results in classic BP and discover effective persuasion strategies in more complex natural language and multi-stage scenarios.

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site (factorised) likelihood and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.

Machine learning interatomic potentials (MLIPs) achieve excellent accuracy when trained on large Density Functional Theory (DFT) data. To be useful in practice, they must often be adapted to target chemistries using small and expensive task-specific datasets. However, MLIPs transfer inconsistently across domains, with representations that often loose accessible composition and structure information. To address this, we present TriForces, a model-agnostic three-stream framework that separates composition and structure information, combined with self-supervised learning to preserve transferable representations. TriForces improves performance on MatBench and QM9 over baselines without needing DFT labels and enables efficient similar structure retrieval through its learned latent space. On OMat24, in limited-data training regime, TriForces reduces energy MAE by 57\% at 20K samples only and improves force MAE across sample sizes. We release pretrained TriForces variants across multiple MLIP architectures with code at https:/github.com/Ramlaoui/triforces.

The persistent storage requirements for high-resolution, spatiotemporally evolving fields governed by large-scale and high-dimensional partial differential equations (PDEs) have reached the petabyte-to-exabyte scale. Transient simulations modeling Navier-Stokes equations, magnetohydrodynamics, plasma physics, or binary black hole mergers generate data volumes that are prohibitive for modern high-performance computing (HPC) infrastructures. To address this bottleneck, we introduce ANTIC (Adaptive Neural Temporal in situ Compressor), an end-to-end in situ compression pipeline. ANTIC consists of an adaptive temporal selector tailored to high-dimensional physics that identifies and filters informative snapshots at simulation time, combined with a spatial neural compression module based on continual fine-tuning that learns residual updates between adjacent snapshots using neural fields. By operating in a single streaming pass, ANTIC enables a combined compression of temporal and spatial components and effectively alleviates the need for explicit on-disk storage of entire time-evolved trajectories. Experimental results demonstrate that ANTIC achieves storage reductions of approximately $\sim 400\times$ for 2D Kolmogorov flow simulations and $\sim 7000\times$ for large-scale physics simulations such as binary black hole mergers.

Spiking neural networks have attracted increasing attention for their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as a scalable alternative to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose here a spiking heterogeneous harmonic resonate-and-fire state space model (S$H^2$RFSSM), a second-order spiking SSM for classification and regression on ultra-long sequences. S$H^2$RFSSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. Furthermore, we introduce a kernel-based spiking regressor that enables accurate modelling of dependencies in sequences of up to 50k steps. We also observe a reduction in spiking operations and improved performance with heterogeneity and discretisation in harmonic resonate-and-fire neuronal layers. Overall, we evaluate Harmonic Resonate-and Fire layers across 17 diverse datasets, spanning sensors, time series, and classification to long-term forecasting. Our results demonstrate that S$H^2$RFSSM achieves superior long-range modelling capability with energy efficiency, positioning it as a strong candidate for signal processing on resource-constrained devices for human activity recognition, time series classification, and regression.

Trajectory Inference (TI) seeks to recover latent dynamical processes from snapshot data, where only independent samples from time-indexed marginals are observed. In applications such as single-cell genomics, destructive measurements make path-space laws non-identifiable from finitely many marginals, leaving held-out marginal prediction as the dominant but limited evaluation protocol. We introduce a general framework for estimating the Kullback–Leibler divergence (KL) between probability measures on function space, yielding a tractable, data-driven estimator that is scalable to realistic snapshot datasets. We validate the accuracy of our estimator on a benchmark suite, where the estimated functional KL closely matches the analytic KL. Applying this framework to synthetic and real scRNA-seq datasets, we show that current evaluation metrics often give inconsistent assessments, whereas path-space KL enables a coherent comparison of trajectory inference methods and exposes discrepancies in inferred dynamics, especially in regions with sparse or missing data. These results support functional KL as a principled criterion for evaluating trajectory inference under partial observability. Code available here: https://github.com/eurecom-probai/functional-kl.

Unraveling how macroscopic cognitive phenotypes emerge from microscopic neuronal connectivity remains one of the core pursuits of neuroscience. To this end, researchers typically leverage multi-modal information from structural connectivity (SC) and functional connectivity (FC) to complete downstream tasks. Recent methodologies explore the intricate coupling mechanisms between SC and FC, attempting to fuse their representations at the regional level. However, while these approaches do incorporate useful neuroscientific observations, they predominantly operate at a topological or architectural level and lack a principled formulation grounded in neural communication dynamics. Consequently, they are limited in quantifying how information is actually routed between neural regions, and thus cannot fully explain why SC and FC exhibit dynamic states of both coupling and heterogeneity. In this paper, we formulate multi-modal fusion through the lens of neural communication dynamics and propose the Adaptive Flow Routing Network (AFR-Net), a physics-informed framework that models how structural constraints give rise to functional communication patterns, enabling interpretable discovery of critical neural pathways. Extensive experiments demonstrate that AFR-Net significantly outperforms state-of-the-art baselines. The code is available at \url{https://github.com/Skyyyy0920/AFR-Net}.

This paper introduces a novel cross-physiology translation task: synthesizing sleep electroencephalography (EEG) from respiration signals. To address the significant complexity gap between the two modalities, we propose a waveform-conditional generative framework that preserves fine-grained respiratory dynamics while constraining the EEG target space through discrete tokenization. Trained on over 28,000 individuals, our model achieves a 7% Mean Absolute Error in EEG spectrogram reconstruction. Beyond reconstruction, the synthesized EEG supports downstream tasks with performance comparable to ground truth EEG on age estimation (MAE 5.0 vs. 5.1 years), sex detection (AUROC 0.81 vs. 0.82), and sleep staging (Accuracy 0.84 vs. 0.88), significantly outperforming baselines trained directly on breathing. Finally, we demonstrate that the framework generalizes to contactless sensing by synthesizing EEG from wireless radio-frequency reflections, highlighting the feasibility of remote, non-contact neurological assessment during sleep.

Neural simulators promise efficient surrogates for physics simulation, but scaling them is bottlenecked by the prohibitive cost of generating high-fidelity training data. Pre-training on abundant off-the-shelf geometries offers a natural alternative, yet faces a fundamental gap: supervision on static geometry alone ignores dynamics and can lead to negative transfer on physics tasks. We present GeoPT, a unified pre-trained model for general physics simulation based on lifted geometric pre-training. The core idea is to augment geometry with synthetic dynamics, enabling dynamics-aware self-supervision without physics labels. Pre-trained on over one million samples, GeoPT consistently improves industrial-fidelity benchmarks spanning fluid mechanics for cars, aircraft, and ships, and solid mechanics in crash simulation, reducing labeled data requirements by 20-60% and accelerating convergence by 2$\times$. These results show that lifting with synthetic dynamics bridges the geometry-physics gap, unlocking a scalable path for neural simulation and potentially beyond. Code is available at https://github.com/Physics-Scaling/GeoPT.

Large-scale molecular dynamics simulations are essential in understanding chemical and biological processes, necessitating the accurate and efficient modeling of interatomic interactions. Existing learning-based methods are generally based on message passing mechanisms; they are either not scalable or too coarse to offer accurate modeling. We propose a new message passing framework that can effectively and efficiently model interatomic interactions for simulating large-scale molecular dynamics at full atomic resolution. Specifically, our framework is stacked with a sequence of message passing neural network layers, each realizing the message passing over a distinct and dilated star-structured path. These star-structured paths are constructed progressively along dilated regions to capture the distance-dependent interactions. The crux of our framework is that it resolves the problem of dense interatomic interactions of large-scale atomic systems with sparser and region-based message passing graphs. We evaluate the framework on four benchmarks: MD22 (molecules with 42–370 atoms), Chignolin (a 166-atom protein featuring diverse conformations), the AdK dataset (a protein trajectory with up to 3,000 atoms), and the MISATO dataset (over 10,000 heterogeneous protein-ligand complexes with systems up to 40,000 atoms). Comprehensive evaluations demonstrate that our approach delivers state-of-the-art performance overall across various benchmarks. The code is provided on [Github](https://github.com/WanyuGroup/ICML2026-DKMP).

Long-term weather forecasting is critical for socioeconomic planning and disaster preparedness. While recent approaches employ finetuning to extend prediction horizons, they remain constrained by the issues of catastrophic forgetting, error accumulation, and high training overhead. To address these limitations, we present a novel pipeline across pretraining, finetuning and forecasting to enhance long‑context modeling while reducing computational overhead. First, we introduce an Efficient Multi‑scale Transformer (EMFormer) to extract multi‑scale features through a single convolution in both training and inference. Based on the new architecture, we further employ an accumulative context finetuning to improve temporal consistency without degrading short‑term accuracy. Additionally, we propose a composite loss that dynamically balances different terms via a sinusoidal weighting, thereby adaptively guiding the optimization trajectory throughout pretraining and finetuning. Experiments show that our approach achieves great performance in weather forecasting and extreme event prediction, substantially improving long-term forecast accuracy. Moreover, EMFormer demonstrates strong generalization on vision benchmarks (ImageNet-1K and ADE20K). Code: https://github.com/chenhao-zju/emformer

Sampling from unnormalized probability densities is a central challenge in computational science. Boltzmann generators are generative models that enable independent sampling from the Boltzmann distribution of physical systems at a given temperature. However, their practical success depends on data-efficient training, as both simulation data and target energy evaluations are costly. To this end, we propose off-policy log-dispersion regularization (LDR), a novel regularization framework that builds on a generalization of the log-variance objective. We apply LDR in the off-policy setting in combination with standard data-based training objectives, without requiring additional on-policy samples. LDR acts as a shape regularizer of the energy landscape by leveraging additional information in the form of target energy labels. The proposed regularization framework is broadly applicable, supporting unbiased or biased simulation datasets as well as purely variational training without access to target samples. Across all benchmarks, LDR improves both final performance and data efficiency, with sample efficiency gains of up to one order of magnitude.

We study dynamic regret minimization in non-stationary online learning, with a primary focus on follow-the-regularized-leader (FTRL) methods. FTRL is important for curved losses and for understanding adaptive optimizers such as Adam, yet existing dynamic regret analyses are less explored for FTRL. To address this, we build on the discounted-to-dynamic reduction and present a modular way to obtain dynamic regret bounds of FTRL-related problems. Specifically, we focus on two representative curved losses: linear regression and logistic regression. Our method not only simplifies existing proofs for the optimal dynamic regret of online linear regression, but also yields new dynamic regret guarantees for online logistic regression. Beyond online convex optimization, we apply the reduction to analyze the Adam optimizers, obtaining optimal convergence rates in stochastic, non-convex, and non-smooth settings. The reduction also enables a more detailed treatment of Adam with two discount parameters $(\beta_1,\beta_2)$, leading to new results for both clipped and clip-free variants of Adam optimizers.

Standard attention mechanisms in transformers employ static token representations that remain unchanged across all pair-wise computations in each layer. This limits their representational alignment with the potentially diverse dynamics of each token-pair interaction. While they excel in domains with relatively homogeneous relationships, standard attention may be inadequate in capturing heterogeneous inter-channel dependencies of multivariate time series (MTS) data where different channel-pair interactions within a single system may be governed by entirely different physical laws or temporal dynamics. To better align the attention mechanism for such domain phenomena, we propose attention with dynamic relational priming (prime attention). Prime attention modulates token representations for each token-pair, optimizing each pair-wise interaction for that specific relationship. Our results demonstrate that prime attention consistently outperforms standard attention across benchmarks, achieving up to 6.5\% improvement in forecasting accuracy. In addition, prime attention achieves comparable performance using up to 40\% less sequence length compared to standard attention, demonstrating its superior relational modeling capabilities and potential for data efficiency.

Graph neural network (GNN) potentials such as SchNet improve the accuracy and transferability of molecular dynamics (MD) simulation by learning many-body interactions, but remain slower than classical force fields due to fragmented kernels and memory-bound pipelines that underutilize GPUs. We show that a missing principle is making GNN-MD $\textit{IO-aware}$, carefully accounting for reads and writes between GPU high-bandwidth memory (HBM) and on-chip SRAM. We present $\texttt{FlashSchNet}$, an efficient and accurate IO-aware SchNet-style GNN-MD framework built on four techniques: (1) $\textit{flash radial basis}$, which fuses pairwise distance computation, Gaussian basis expansion, and cosine envelope into a single tiled pass, computing each distance once and reusing it across all basis functions; (2) $\textit{flash message passing}$, which fuses cutoff, neighbor gather, filter multiplication, and reduction to avoid materializing edge tensors in HBM; (3) $\textit{flash aggregation}$, which reformulates scatter-add via CSR segment reduce, reducing atomic writes by a factor of feature dimension and enabling contention-free accumulation in both forward and backward passes; (4) channel-wise 16-bit quantization that exploits the low per-channel dynamic range in SchNet MLP weights to further improve throughput with negligible accuracy loss. On a single NVIDIA RTX PRO 6000, $\texttt{FlashSchNet}$ achieves $\textbf{1000 ns/day}$ aggregate simulation throughput over 64 parallel replicas on coarse-grained (CG) protein containing 269 beads ($\textbf{6.5}$ $\mathbf{\times}$ faster than CGSchNet baseline with $\textbf{80\\% less}$ peak memory), surpassing widely used classical force fields ($\textit{e.g.}$, MARTINI) while retaining SchNet-level accuracy and transferability.