ICML 2026 Papers

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Attention is the critical component of a transformer. Yet the quadratic computational complexity of vanilla full attention in the input size and the inability of its linear attention variant to focus have been challenges for computer vision tasks. We provide a mathematical definition of generalized attention and formulate both vanilla softmax attention and linear attention within the general framework. We prove that generalized attention disperses, that is, as the number of keys tends to infinity, the query assigns equal weights to all keys. Motivated by the dispersion property and recent development of Mamba form of attention, we design Scalable and Efficient Mamba like Attention (SEMA) which utilizes token localization to avoid dispersion and maintain focusing, complemented by theoretically consistent arithmetic averaging to capture global aspect of attention. We support our approach on Imagenet-1k where classification results show that SEMA is a scalable and effective alternative beyond linear attention, outperforming recent vision Mamba models on increasingly larger scales of images at similar model parameter sizes. Source code can be found at: https://github.com/nhatthanhtran/SEMA.

Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for meta-learning showing that the adaptation gain (expected fidelity improvement from task-specific gradient steps) saturates exponentially with gradient steps and scales linearly with task variance, providing a quantitative criterion for when adaptation justifies its overhead. Validation on quantum gate calibration shows negligible benefits for low-variance tasks but > 40% fidelity gains on two-qubit gates under extreme out-of-distribution conditions (10× the training noise), with implications for reducing per-device calibration time on cloud quantum processors. Further validation on classical linear-quadratic control confirms these laws emerge from general optimization geometry rather than quantum-specific physics. We further introduce a few-shot pre-adaptation protocol that estimates the optimal adaptation budget from $N =3–5$ probe steps within 3–19% relative error across out-of-distribution regimes.

Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research. In particular, it is unclear where along the noise schedule memorization is induced, how data geometry influences it, and how phenomena at different noise scales interact. We introduce a geometric framework that partitions the noise schedule into three regimes based on the coverage properties of training data by Gaussian shells and the concentration behavior of the posterior, which we argue are two fundamental objects governing memorization and generalization in diffusion models. This perspective reveals that memorization risk is highly non-uniform across noise levels. We further identify a danger zone at medium noise levels where memorization is most pronounced. In contrast, both the small and large noise regimes resist memorization, but through fundamentally different mechanisms: small noise avoids memorization due to limited training coverage, while large noise exhibits low posterior concentration and admits a provably near linear Gaussian denoising behavior. For the medium noise regime, we identify geometric conditions through which we propose a geometry-informed targeted intervention that mitigates memorization.

Continuous-time, event-native spiking neural networks (SNNs) operate strictly on spike events, treating spike timing and ordering as the representation rather than an artifact of time discretization. This viewpoint aligns with biological computation and with the native resolution of event sensors and neuromorphic processors, while enabling compute and memory that scale with the number of events. However, two challenges hinder practical, end-to-end trainable event-based SNN systems: 1) exact charge--fire--reset dynamics impose inherently sequential processing of input spikes, and 2) precise spike times must be solved without time bins. We address both. First, we use parallel associative scans to consume multiple input spikes at once, yielding up to 44x speedups over sequential simulation while retaining exact hard-reset dynamics. Second, we implement differentiable spike time solvers that compute spike times to machine-precision without discrete-time approximations or restrictive analytic assumptions. We demonstrate the viability of training SNNs using our solutions on four event-based datasets on GPUs.

In this paper, we tackle a fundamental problem in high-dimensional statistics, namely, learning Single Index Models (SIMs) robustly in the presence of heavy-tailed noise and an adversary that can corrupt a constant fraction of both covariates and responses. Prior research on efficient robust recovery only focuses on monotonic link functions or only limit themselves to Phase Retrieval. Provable efficient robust recovery guarantees for generic nonlinear link functions have remained elusive. In this paper, we obtain the first near-linear time, optimal-sample-complexity robust recovery algorithm for a wide class of nonlinear non-monotonic link functions. Critical to our result is an improved understanding of the squared-loss landscape: we identify a sufficient condition under which a broad class of non linear link functions admit a dimension-independent constant-radius convex basin around the ground truth, establishing statistical identifiability beyond previously known cases. We also leverage second-order Stein's identities to identify a structural condition, that we term Expected Squared Convexity (ESC), that acts as a sufficient condition for spectral initialization techniques to obtain an estimator within the convex basin with error $O(\epsilon^{1/4})$, even under heavy-tailed noise and strong adversarial contamination. This robust initialization technique can be combined with a robust gradient descent phase to break the spectral error barrier, achieving an improved estimation error of $O(\sigma\sqrt{\epsilon})$. Our non-convex optimization framework gives the first efficient sample and time complexity robust recovery results for activation functions such as GeLU and Swish that act as building blocks of modern deep-learning architectures.

Reconstructing high-fidelity RAW sensor data from processed RGB images is a fundamental yet ill-posed problem, plagued by irreversible information loss and complex non-linear ISP transformations. While generative models offer high-quality reconstruction, they suffer from prohibitive computational costs. Conversely, dominant regression-based methods are fast but susceptible to incoherent observational deviations, often yielding over-smoothed predictions that drift from the authentic signal manifold. To reconcile this trade-off, we propose SHADE, a Single-step Homogeneous Aligned DEterministic flow framework. We validate that, unlike point-to-point regression, the single-step deterministic flow captures global transport trends and enables intrinsic robustness against input perturbations. Furthermore, we introduce Homogeneous Representation Alignment to maximize fidelity. By leveraging a homogeneously initialized student-teacher DINO pair, this mechanism enforces alignment within a shared feature space, significantly amplifying the representational capacity. Extensive experiments demonstrate that SHADE achieves state-of-the-art performance on multiple benchmarks, establishing a new paradigm for accurate and efficient sensor data reconstruction.

While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology. The gradients from the PDE residuals and boundary constraints oppose each other, trapping the model in local minima. Current solutions, such as adaptive weighting or hard constraints, either fail to fundamentally resolve this ill-conditioning or are limited to simple geometries. In this study, we systematically analyze the possible causes of this gradient pathology from the perspectives of loss landscapes and optimization dynamics. Based on the obtained conclusion, we propose Constraint-Aligned loss with Manifold Lifting (CAML). By reformulating all zeroth-order terms into aligned constraints, our method effectively mitigates gradient conflicts. In addition, we introduce a delay factor to help the optimizer skip the high-curvature area. Experiments demonstrate that our CAML significantly enhances numerical stability and efficiency in highly complex PINN problems. Our code is open-sourced on [CAML](https://github.com/YichenLuo-0/CAML).

We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of $K$ items from a ground set of size $N$ and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a $0$-$1$ mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and characterize the induced statistical-computational trade-offs. As an application, we develop a best assortment identification algorithm for MNL bandits with linear utilities and non-uniform revenues, and prove an instance-dependent sample complexity of $\tilde{\mathcal{O}}\big(\frac{d \log N}{\Delta^2}\big)$, where $d$ is the feature dimension, $N$ is the number of arms, and $\Delta$ is the minimum revenue gap.

Genome language models (gLM) have the potential to further understanding of regulatory genomics without requiring labeled data. Most gLMs are pretrained using sequence reconstruction tasks inspired by natural language processing, but recent studies have shown that these gLMs often fail to capture biological signal. To overcome this, we introduce pretraining tasks that predict the rate of evolution. These tasks are designed so that they can be composed with sequence reconstruction, enabling a controlled comparison of predicting sequence only, evolutionary rate only, or both. To address gaps in existing evaluations, we developed a suite of biologically grounded benchmarks. Across these tasks, and for established variant effect prediction benchmarks, models pretrained on both sequence and evolutionary rate outperform those trained on sequence alone, and training on evolutionary rate can make the even the relatively small models in our work competitive with much larger existing gLMs for some tasks on the human genome. These results establish evolution as a key training target for genome-scale models.

Stock markets are one of the most complex systems in the modern world, where prices emerge from billions of decentralized interactions among heterogeneous participants in an ever-evolving information landscape. While high-fidelity simulation is important for understanding market dynamics, existing approaches face a persistent trade-off between structural and behavioral fidelity. To this end, we propose MarketSim, a large-scale stock market simulation framework with generative agents. MarketSim introduces a hierarchical multi-agent architecture that decouples strategic reasoning from high-frequency execution, enabling LLM agents to operate in a nanosecond-resolution, NASDAQ-like continuous double auction market. Building on this, we simulate over 15,000 heterogeneous market participants whose interactions shape and are shaped by an evolving market environment grounded in more than 12k real-world news articles, policy documents, and earnings reports. To evaluate our proposed MarketSim, we develop a comprehensive benchmark that includes stocks from 8 GICS sectors and 3 representative real-world scenarios, along with 5 stylized facts for market complexity and 5 price-related statistical metrics. Extensive experiments demonstrate that MarketSim not only captures key complexity properties of real-world markets, but also outperforms state-of-the-art baselines in tracking high-frequency price dynamics with an average MAPE of 3.48%, providing a scalable testbed for market analysis.

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack a reweighting procedure required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a framework for reduced-order generative modeling with importance sampling in coarse-grained coordinate space. CG-BGs generate samples using a flow-based model and reweight them using a learned potential of mean force (PMF). We show that the PMF can be learned from rapidly converged trajectories via enhanced sampling force matching. Experiments demonstrate that CG-BGs capture solvent-mediated interactions in highly reduced representations while substantially reducing computational cost relative to atomistic BGs, providing a practical route toward equilibrium sampling of larger molecular systems.

Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification.

Real-world degradations, such as noise, blur, and low resolution, significantly impair the performance of Multi-modal Large Language Models (MLLMs) in document understanding tasks. Despite recent advancements, progress in this field remains stifled by two critical bottlenecks: the scarcity of large-scale, aligned training data necessary for learning robustness, and the lack of transferable restoration solutions across diverse MLLM architectures. To bridge the data gap, we first present DocRobust-VQA, a large-scale dataset explicitly constructed to support robustness training. Comprising 189K aligned clean/corrupted document image pairs and 417K QA pairs, it provides the first substantial corpus for fine-tuning MLLMs to handle varying degradation conditions. Leveraging this data, we propose Uni-DocRobust, a universal plug-and-play framework that decouples restoration capabilities from specific visual encoders. Our method employs a frozen Universal Restoration Core pre-trained in a canonical feature space via multi-teacher distillation, which can be seamlessly integrated into target MLLMs (e.g., Qwen-VL, InternVL) through lightweight Feature Adapters. Extensive experiments demonstrate that Uni-DocRobust significantly enhances robust performance on MLLMs and enables a cost-effective ``pre-train once, deploy everywhere'' paradigm for robust MLLM deployment.

High-order relations involving multiple interacting entities are commonly encountered, particularly in biomedical domains. Existing relational learning methods typically learn static entity representations and assume symmetric relation inference, which can be inadequate for capturing context-dependent entity functions and the inherent asymmetry of high-order relations. In this paper, we propose Contextualized High-order Contrastive Learning (CONTEXTOR), a general and plug-and-play framework that formulates high-order relation inference as a dynamic query–response process. Specifically, CONTEXTOR decomposes each high-order relation into multiple incomplete query tuples and their corresponding response entities. Given a query tuple, we contextualize candidate response entity representations via an asymmetric conditional modulation, and align queries with their corresponding contextualized responses through multi-fold contrastive learning. Extensive experiments on benchmark datasets spanning multiple biomedical tasks demonstrate that CONTEXTOR consistently outperforms existing methods across diverse evaluation settings. Code is available at https://github.com/ZJUDataIntelligence/CONTEXTOR.

Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy–latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy–latency constraints, considering code distances up to $d=9$ (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize with general vector fields as well as choose other selection criteria beyond minimal energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.

Designing RNA sequences that reliably fold into specific secondary structures is essential for understanding their biological functions but remains a challenging computational problem. We propose CocoRNA, a cooperative multi-agent reinforcement learning framework for RNA inverse design. CocoRNA simplifies the design task by decomposing it into smaller sub-problems, each solved collaboratively by multiple agents. This approach reduces the complexity of the problem and improves the exploration of design policies. During training, a centralized critic uses global structural information to guide the agents, enabling them to jointly optimize their design strategies. As a result, CocoRNA learns high-quality RNA design policies that generalize effectively to unseen structures without additional training. Experiments on the Rfam dataset demonstrate that CocoRNA substantially outperforms state-of-the-art methods in both success rate and design speed. Further experiments on other biological sequence design tasks highlight the effectiveness and broad potential of CocoRNA for complex design tasks.

Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured coarse-to-fine refinement for climate forecasting without updating backbone parameters. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR is architecture-agnostic across the three TSFM backbones evaluated per site (TimesFM, TimeGPT, TabPFN) and consistently lowers test-set MSE on three South Australian sites and three additional regions outside South Australia. Applied to TimesFM, the wrapper reduces one-month-ahead SPEI MSE by up to 18.9\% across the three South Australian sites (mean reduction $\approx$18.7\%). Overall, RGMR provides a practical route for deploying frozen TSFMs in regional climate forecasting workflows.