ICML 2026 论文列表

Terminal embeddings have emerged as a powerful tool for dimension reduction. Given a set of points $P\subset \mathbb{R}^d$, a terminal embedding is a mapping $f:\mathbb{R}^d\rightarrow \mathbb{R}^t$ that preserves the pairwise distance between any pair of points $p\in P$ and $q\in \mathbb{R}^d$ up to small distortion under this mapping. Terminal embeddings have been particularly fruitful for constructing $k$-means and $k$-median coresets, where the objective is to find a typically weighted subset $\Omega$ of $P$ such that for any candidate solution, the cost of the clustering objective on $\Omega$ approximates the cost of the clustering objective on $P$ up to small distortion. Unfortunately, these techniques have not been extended to more complicated structures such as clustering time-series data under common straight-line interpolation between measurements. The main issue is that terminal embeddings, arguably the central technique in this line of research, cannot be linear and are thus not immediately suitable to preserve linear structures. In this work, we develop a generalization of terminal embeddings to affine line-segments that overcomes this issue. We showcase their applicability by using our lines-preserving terminal embeddings to obtain the first dimension-free coresets for clustering time-series under the Fréchet distance. The underlying dimension reduction uses Johnson-Lindenstrauss embeddings, and our experiments indicate that they compare favorably against PCA for real-world time-series.

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.

Molecular dynamics (MD) is a central computational tool in physics, chemistry, and biology, enabling quantitative prediction of experimental observables as expectations over high-dimensional molecular distributions such as Boltzmann distributions and transition densities. However, conventional MD is fundamentally limited by the high computational cost required to generate independent samples. Generative molecular dynamics (GenMD) has recently emerged as an alternative, learning surrogates of molecular distributions either from data or through interaction with energy models. While these methods enable efficient sampling, their transferability across molecular systems is often limited. In this work, we show that incorporating auxiliary sources of information can improve the data efficiency and generalization of transferable implicit transfer operators (TITO) for molecular dynamics. We find that coarse-grained TITO models are substantially more data-efficient than Boltzmann Emulators, and that incorporating protein language model (pLM) embeddings further improves out-of-distribution generalization. Our approach, PLaTITO, achieves state-of-the-art performance on equilibrium sampling benchmarks for out-of-distribution protein systems, including fast-folding proteins. We further study the impact of additional conditioning signals such as structural embeddings, temperature, and large-language-model-derived embeddings on model performance.

Document parsing, the task of extracting diverse content from PDFs while preserving their structural integrity, has been significantly advanced by Multimodal Large Language Models (MLLMs). These models have achieved remarkable success, largely driven by extensive post-training on massive datasets. This paper therefore undertakes a deep analysis of the two dominant adaptation strategies, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), prompted by a puzzling observation on the PDF-to-Markdown task: SFT makes a negligible impact, especially on parsing complex tables and formulas, while RL achieves substantial overall gains. To unravel the reasons, our systematic investigation reveals a clear and complementary division of labor: SFT primarily operates as a structure learner, biased towards mastering the low-entropy syntax of document layouts. While it learns the format of a table, it struggles to ensure the fidelity of its high-entropy cell content. Conversely, RL excels as a content refiner by optimizing a holistic reward that reflects final accuracy. We further ground this phenomenon in the distinct theoretical nature of their respective objective functions. Based on these findings, we introduce a unified strategy that explicitly harnesses their individual strengths while mitigating their weaknesses. This work shows that a deep understanding of post-training methods is key to unlocking performance beyond what data scaling alone can achieve.

Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen PDE coefficients or unseen physics. Prior works address this limitation with large scale multi physics pretraining followed by fine tuning, but this still requires examples from the new dynamics, falling short of true zero shot generalization. In this work, we propose a method to enhance generalization at test-time, i.e, without modifying pretrained weights. Building on DISCO, which provides a dictionary of neural operators trained across different dynamics, we introduce a neural operator splitting strategy that, at test time, searches over compositions of training operators to approximate unseen dynamics. On challenging out-of-distribution tasks including parameter extrapolation and novel combinations of physics phenomena, our approach achieves state-of-the-art zero shot generalization results, while being able to recover the underlying PDE parameters. These results underscore test-time computation as a key avenue for building flexible, compositional, and generalizable neural operators.

Discrete biological sequence optimization often requires goal-directed, parser-valid edits to an existing protein or molecule. Diffusion models support iterative refinement but do not expose a controllable discrete-edit interface, while autoregressive LLMs can be myopic when planning constrained edits over multiple steps. We introduce *STRIDE* (Sequence Trajectory Refinement via Iterative Discrete Editing), a post-training framework that trains an LLM to emit executable INSERT/DELETE/REPLACE trajectories for variable-length refinement. *STRIDE* first learns Levenshtein-aligned shortest-edit demonstrations, then uses supervised fine-tuning and group-based policy optimization to align trajectories with task rewards while preserving coherent editing. On an oracle-based full-action protein stress test, *STRIDE* raises success over Vanilla SFT from 42% to 89% and novelty among unique improvements from 47% to 97%. On instruction-conditioned molecular editing, the GSPO-aligned variant improves strict success, controllability, and SMILES validity over the SFT-only *STRIDE* model (code: https://github.com/daiheng-zhang/STRIDE).

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model’s “self-knowledge”, i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer’s correctness that is accessible to the model itself. However, we find that whether trained or training-free, an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM attempting the same task. Moreover, we hypothesize that a key factor in predicting model correctness, i.e., building a “Correctness Model” (CM), is exposure to a target model’s historical predictions. We use multiple methods to inject this historical correctness information, including training an LLM to predict the confidences of many other LLMs, i.e., creating a Generalized Correctness Model (GCM). We use GCMs and CMs as a lens for studying the source of correctness prediction ability and its generalization, studying the importance of answer phrasing, world-knowledge, performance history, in-context examples, and post-hoc calibration for correctness prediction. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU, TriviaQA, and Spider datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a cross-model skill learned by encoding correctness history rather than a model-specific skill reliant on introspection. Code: https://github.com/The-Inscrutable-X/CalibratedModelAgnosticCorrectness.

Neural operators have become a central tool in scientific machine learning for learning discretization-consistent solution operators, achieving strong results on partial differential equation (PDE) benchmarks. Physiological time series, however, are highly nonstationary and dominated by localized transient events, properties that can challenge both PDE-oriented neural operators and conventional deep models. We propose NeurOCNN, a neural-operator-based model for physiological signals that learns a robust function-to-label mapping. NeurOCNN integrates continuous-time, spline-parameterized convolutions to capture localized morphology with Fourier projection pooling for variable-to-fixed dimensional mapping, thereby enabling robust, discretization-invariant inference under zero-shot sampling-rate shifts. Empirically, NeurOCNN outperforms standard neural-operator baselines, achieves performance comparable to state-of-the-art methods, and maintains stable accuracy across multiple previously unseen evaluation sampling rates. The code is available at https://github.com/Idsl-group/NeurOCNN.

Physics obeys strict symmetries like rotational equivariance. However, the standard Transformer architectures widely used in physics foundation models do not enforce these constraints by construction. We introduce ReViT, a rotationally equivariant Vision Transformer framework for neural PDE solvers operating on grid-based physical fields that achieves exact equivariance for the discrete groups $C_4$ (2D) and the chiral octahedral group $O$ (3D), with bounded approximate $\mathrm{SO}(d)$ equivariance for continuous rotations. ReViT maps scalar and vector inputs into locally invariant representations derived from physics-based canonical bases, enabling the use of standard self-attention without symmetry violations. Built on a hierarchical Swin-style backbone with a precomputed reference basis pyramid, ReViT preserves equivariance across multi-scale operations. We evaluate ReViT on a wide range of 2D and 3D PDE benchmarks, such as Magnetohydrodynamics and Turbulent Channel Flows, demonstrating significant gains over state-of-the-art baselines. ReViT exhibits strong generalization, and reduces MSE by up to 65\% compared with the best-performing alternatives.

Physics-informed neural networks (PINNs) can be unreliable on PDEs with oscillatory, multiscale, stiff, or long-time solutions, and these difficulties worsen in high dimensions where collocation-based training yields large numerical integration error and high-variance gradients. We propose Low-Rank Fourier Sums (LoRFS), representing the solution as a low-rank sum of separable Fourier expansions (products of one-dimensional Fourier series across coordinates). This makes high-frequency structure explicit and enables closed-form evaluation of common physics-based objectives and their gradients (e.g., $L^2$ residual and variational losses), replacing sampling-based collocation estimates with analytic loss evaluation and eliminating sampling noise. We further provide theoretical results that clarify why LoRFS is particularly well suited to high-dimensional regimes. Across canonical PINN failure-mode benchmarks and their high-dimensional extensions, LoRFS consistently outperforms strong PINN baselines and remains stable in regimes where competing methods degrade.

In the agentic web era, LLM-based agents increasingly invoke web services as tools, yet most interfaces remain static endpoints that poorly express long-horizon workflows with loops, conditionals, joins, and retries. We present ToolPro, which represents an agent's tool intent as an executable tool program that compactly encodes multi-step service interactions with explicit effect types. ToolPro combines constraint-guided program construction, effect-aware replay for exactly-once state-modifying calls, and a profile-driven policy that decides when program execution outperforms stepwise calling. We instantiate ToolPro over MCP-style services with WebAssembly sandboxing and evaluate it on diverse workflows of real-world applications. ToolPro reduces end-to-end latency by up to 53.4% and client-side traffic by up to 96.1%, with larger gains under higher network latency and workflow complexity.

Oncologists are increasingly relying on multiple modalities to model the complexity of diseases. Within this landscape, transcriptomic and epigenetic data have proven to be particularly instrumental and play an increasingly vital role in clinical applications. However, their integration into multimodal models remains a challenge, especially considering their high dimensionality. In this work, we present a novel bimodal model that jointly learns representations of bulk RNA-seq and DNA methylation leveraging self-supervision from masked language modeling. We implement an architecture that reduces the memory footprint usually attributed to purely transformer-based models when dealing with long sequences. We demonstrate that the obtained bimodal embeddings can be used to fine-tune cancer-type classification and survival models that achieve state-of-the-art performance compared to unimodal models. Furthermore, we introduce a robust learning framework that maintains downstream task performance despite missing modalities, enhancing the model’s applicability in real-world clinical settings.

We study the error rate of LLMs on tasks like arithmetic that require a deterministic output, and repetitive processing of tokens drawn from a small set of alternatives. We argue that incorrect predictions arise when small errors in the attention mechanism accumulate to cross a threshold, and use this insight to derive a quantitative two-parameter relationship between the accuracy and the complexity of the task. The two parameters vary with the prompt and the model; they can be interpreted in terms of an elementary noise rate, and the number of plausible erroneous tokens that can be predicted. Our analysis is inspired by an "effective field theory'' perspective: the LLM's many raw parameters can be reorganized into just two parameters that govern the error rate. We perform extensive empirical tests, using Gemini 2.5 Flash, Gemini 2.5 Pro and DeepSeek R1, and find excellent agreement between the predicted and observed accuracy for a variety of tasks, although we also identify deviations in some cases. Our model provides an alternative to suggestions that errors made by LLMs on long repetitive tasks indicate the "collapse of reasoning'', or an inability to express "compositional'' functions. Finally, we show how to construct prompts to reduce the error rate.

Nowcasting forms the first line of defense against rapidly evolving weather hazards, where even minutes of delay can lead to severe societal impacts. However, existing systems predominantly extrapolate 2D radar reflectivity, which struggles under rapid intensification regimes. We introduce StormInsight, a multi-scale modeling framework that enables coherent reconstruction of the three-dimensional evolution of convective systems while explicitly conditioning on the ambient environment. StormInsight integrates multi-source observations—including radar, satellite, and station—with reanalysis fields through two components: (i) Storm Evolution Encoder that explicitly disentangles convective system state form vertical thermodynamic coupling and large-scale environmental forcing; (ii) Convective System Decoder that predicts future echos by adaptively aggregating cross-layer interactions conditioned on evolving environmental conditions. To support comprehensive evaluation, we build a new benchmark StormBench that integrates observational and reanalysis data across regions. On this benchmark, StormInsight consistently achieves the best performance, reducing MAE by 12.4% and improving the mCSI by 34.0%.

The training of deep Spiking Neural Networks (SNNs) has traditionally relied on Batch Normalization (BN), which stabilizes input currents and gradients during training. However, BN is not a universal solution. It is unsuitable for variable-length tasks and scenarios with reduced batch size, constraining the development of deep SNNs, where removing BN typically causes the training to fail to converge. This dependence stems not from a fundamental necessity of BN but from the current lack of reasonable initialization methods for SNNs. This paper addresses this core limitation by proposing SpikeInit, a novel initialization framework for SNNs. By modeling the response curve and gradient of spiking layers, SpikeInit initializes the weights and shape parameters of surrogate gradients to maintain stable firing rates during forward propagation and stable gradient magnitudes during backpropagation. Extensive experiments demonstrate that deep SNNs with SpikeInit can be trained stably without normalization and achieve superior performance compared to their normalized counterparts under identical settings. Furthermore, we demonstrate the scalability of SpikeInit by successfully training an ultra-deep, 1000-layer SNN without normalization. Our work provides a foundational step toward large-scale normalization-free SNN, liberating SNN design from the constraints of normalization.

Hebbian and anti-Hebbian plasticity are widely observed in the brain and are classically modeled as mechanistic, local homosynaptic rules stabilized by homeostatic constraints. This raises an identifiability question: does observing Hebbian/anti-Hebbian structure in synaptic updates uniquely imply an underlying Hebbian computation? We identify an alternative, emergent route. We show that near stationarity, L2 weight decay generically drives the \emph{learning-signal} component of many update rules to align with a Hebbian direction, with alignment increasing monotonically with decay strength. This Hebbian-like signature is not specific to SGD and can arise even for non-learning or random update rules long before learning has ceased. We further show that stochastic noise in the learning signal can induce anti-Hebbian alignment, yielding a simple tradeoff with weight decay and a phase boundary in regression settings. These mechanisms do not replace standard Hebbian theory; they can coexist with genuine Hebbian plasticity and complicate the interpretation of synaptic measurements, motivating experiments that distinguish mechanistic Hebbian computation from emergent Hebbian signatures.

We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch–Gordan tensor products. This is achieved by introducing a set of new efficient and powerful SO(2)-equivariant operations and performing all off-diagonal feature updates and message passing within SO(2) local frames, thereby eliminating the need of SO(3) tensor products. Moreover, a continuous SO(2) tensor product is performed within the SO(2) local frame at each node to fuse node features. Extensive experiments on the large QH9 and MD17 datasets demonstrate that our model achieves superior performance across a wide range of molecular structures and trajectories, highlighting its strong generalization capability. The proposed SO(2) operations on SO(2) local frames offer a promising direction for scalable and symmetry-aware learning of electronic structures. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/).

Learning-based methods have made significant progress in physics simulation, typically approximating dynamics with a monolithic end-to-end optimized neural network. Although these models offer an effective way to simulation, they may lose essential features compared to traditional numerical simulators, such as physical interpretability and reliability. Drawing inspiration from classical simulators that operate in a modular fashion, this paper presents Neural Modular Physics (NMP) for elastic simulation, which combines the approximation capacity of neural networks with the physical reliability of traditional simulators. Beyond the previous monolithic learning paradigm, NMP enables direct supervision of intermediate quantities and physical constraints by decomposing elastic dynamics into physically meaningful neural modules connected through intermediate physical quantities. With a specialized architecture and training strategy, our method transforms the numerical computation flow into a modular neural simulator, achieving improved physical consistency and generalizability. Experimentally, NMP demonstrates superior generalization to unseen initial conditions and resolutions, stable long-horizon simulation, better preservation of physical properties compared to other neural simulators, and greater feasibility in scenarios with unknown underlying dynamics than traditional simulators.

Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size ($N$), dataset size ($D$), and compute budget ($C$). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10× reduces validation loss by up to 3.2×. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to more total training data yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance.