ICML 2026 Papers

Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit *exact inversion*, an inaccuracy that is unacceptable in precision-critical applications. Existing inversion methods suffer from poor stability and low order of convergence, and are strictly limited to the ODE setting. In this work, we propose *Rex*, a family of reversible exponential (stochastic) Runge-Kutta solvers obtained by applying Lawson methods to convert any explicit (stochastic) Runge-Kutta scheme into an algebraically reversible one for both diffusion ODEs *and* SDEs. Beyond a rigorous theoretical analysis---establishing arbitrary-order convergence and a non-zero region of linear stability---we empirically demonstrate that *Rex* achieves near-machine-precision reconstruction and improves Boltzmann sampling with flow models as well as image generation and editing with diffusion models.

Affective and cognitive disorders manifest as distributed, time-varying brain network dynamics across regions, channels, and time, challenging robust representation learning from EEG/sEEG for clinical diagnosis. We propose **RECTOR** (Masked **Re**gion–**C**hannel–**T**emp**or**al Modeling), an end-to-end self-supervised framework that unifies joint region-channel-temporal representation learning beyond fixed anatomical priors. At its core, **RECTOR-SA** is a hierarchical, block-sparse self-attention induced by Adaptive Functional Partitioning that evolves region structures from static anatomical definitions to adaptive functional regions. The self-supervision is driven by **Masked Topology and Representation Learning**, which jointly optimizes three complementary objectives: Masked Predictive Modeling, Topological Structure Modeling, and Cross-View Consistency. Across diverse benchmarks, RECTOR sets a new state-of-the-art in EEG emotion recognition and sEEG task-engagement classification. Crucially, its strong robustness to missing channels and cross-montage generalization underscores its potential for large-scale pre-training on heterogeneous EEG/sEEG, providing interpretable insights at both region and channel levels.

Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$\%.

We study a class of iterated empirical risk minimization (ERM) procedures in which two successive ERMs are performed on the same dataset, and the predictions of the first estimator enter as an argument in the loss function of the second. This setting, which arises naturally in active learning and reweighting schemes, introduces intricate statistical dependencies across samples and fundamentally distinguishes the problem from classical single-stage ERM analyses. For linear models trained with a broad class of convex losses on Gaussian mixture data, we derive a sharp asymptotic characterization of the test error in the high-dimensional regime where the sample size and ambient dimension scale proportionally. Our results provide explicit, fully asymptotic predictions for the performance of the second-stage estimator despite the reuse of data and the presence of prediction-dependent losses. We apply this theory to revisit a well-studied pool-based active learning problem, removing oracle and sample-splitting assumptions made in prior work. We uncover a fundamental tradeoff in how the labeling budget should be allocated across stages, and demonstrate a double-descent behavior of the test error driven purely by data selection, rather than model size or sample count.

While heavy-tailed synaptic weight distributions are pervasive in biological neural networks, their computational role---particularly in relation to generalization---remains poorly understood. To address this, we develop a novel optimal-transport-based optimization algorithm that incorporates key biological constraints, including Dale’s principle and heavy-tailed synaptic statistics, to train recurrent neural networks (RNNs) on a wide range of cognitive tasks. We show that these biologically constrained, heavy-tailed RNNs exhibit substantially improved generalization, which we further characterize within a PAC-Bayes framework. Our theoretical analysis and numerical experiments reveal two complementary mechanisms underlying this generalization enhancement. Topologically, heavy-tailed connectivity induces an effectively low-rank structure, which in turn yields low-dimensional neural dynamics. Geometrically, heavy-tailed connectivity intrinsically shapes task variable representations to lie near a linear manifold, thereby improving generalization for a linear readout strategy. Together, these results identify heavy-tailed connectivity as a biologically grounded intrinsic mechanism that promotes low-rank structure and favorable representational geometry, leading to improved generalization in flexible cognitive tasks.

Large language models (LLMs) are on the rise for accelerating scientific discovery, most recently in advanced tasks such as generating valid scientific hypotheses. Yet in many discovery settings, the goal is not to identify a single best hypothesis since validation can be noisy and expensive, and scientists benefit from a set of high-quality alternative hypotheses that hedge against downstream uncertainty for the best solutions. Nevertheless, commonly used evolutionary search recipes tend to prioritize optimization over exploration in hypothesis generation, and the resulting selection pressure during the search process leads to diversity collapse. Motivated by these limitations, we formulate hypothesis search as a sampling problem, where the objective is to efficiently produce diverse, high-quality hypotheses under a fixed validation budget. Building on this perspective, we propose EvoDiverse, an evolutionary framework inspired by the classical parallel tempering algorithm that searches hypotheses at multiple temperature levels and enables principled information exchange across temperatures to improve exploration without disrupting convergence. Across domains including molecular discovery, equation discovery, and algorithm discovery, our approach consistently improves both hypothesis quality and diversity under the same validation budget, and produces candidates that remain robust under more expensive downstream computational validations.

Real-world time-series data often suffer from missing observations, hindering long-range temporal modeling. However, most existing imputation methods formulate imputation as conditional reconstruction over limited context, which restricts temporal information propagation and fails to explicitly model temporal evolution. To overcome this limitation, we propose the Conditional Temporal Inference Paradigm (CTIP), which formulates time-series imputation as conditional inference along temporal evolution. Under this paradigm, we introduce CBiT, which leverages a history compression mechanism to encode long-range history into a compact latent space for history-conditioned temporal imputation. In addition, we adopt a partitioned modeling strategy that distinguishes historical context and temporal imputation targets with only linear-time complexity. Extensive experiments on multiple public benchmarks show that CBiT improves imputation accuracy by reducing Masked MAE and Masked RMSE by 27.3% and 18.6%, respectively, across different missing rates.

Physics-Informed Neural Networks (PINNs) represent a significant advancement in computational methods for solving partial differential equations (PDEs). However, the adoption of deeper neural network architectures presents significant challenges, as they struggle to address differential-related complications that arise during the computation of derivatives over the input of PINNs. These complications extend beyond traditional vanishing and exploding gradients to include vanishing and exploding differentials, with both phenomena becoming more severe as networks grow deeper. By examining the computation graph of derivatives in deep neural networks, we identify key bottlenecks causing numerical instabilities in deep architectures. In response, we introduce a novel approach that utilizes Coupling Layers with carefully regulated spectral norms of Jacobian matrices to stabilize and facilitate deep PINN training, effectively addressing differential-related challenges and improving model stability. Our proposed architecture successfully mitigates the fundamental constraints of deeper PINNs while maximizing their capabilities through consistent differential propagation. Comprehensive evaluations show that our approach surpasses conventional shallow PINN methods and alternative deep PINN designs across a range of challenging problems.

Mixture-of-Experts (MoE) architectures provide strong scalability for large language models, but their large expert parameter footprint poses challenges for efficient deployment. Expert pruning is widely used to reduce model size and inference cost; however, existing approaches are token-agnostic, treating all tokens equally when estimating expert importance. This uniform treatment dilutes the contributions of informative tokens and leads to suboptimal pruning decisions. To address this fundamental limitation, we propose **Step** (**S**elective **T**oken-guided **E**xpert **P**runing), a token-aware framework that rethinks expert pruning from the perspective of selective token guidance. By incorporating loss-aware expert evaluation and a lightweight knowledge-preserving mechanism, **Step** reduces information loss while removing redundant experts. Extensive experiments across different MoE architectures and model scales demonstrate the effectiveness of **Step**. On the 30B Qwen3 MoE model with 50\% expert sparsity, **Step** achieves nearly a 50\% reduction in memory usage with minimal performance degradation, delivers a 1.5$\times$ throughput improvement, and completes the entire pruning process within 10 minutes.

Multi-compartment Hodgkin–Huxley (HH) models provide a principled framework for predicting neural dynamics and responses to electrical stimulation. However, fitting HH biophysical parameters typically requires intracellular recordings, which are invasive and low-throughput, limiting the ability to capture the geometry and cell-specific properties of many neurons in a given neural circuit. Multi-electrode arrays (MEAs) offer a scalable alternative—high-density extracellular measurements from full neural populations—but HH model complexity has so far precluded reliable biophysical inference from extracellular data alone. Here, we introduce a framework to rapidly infer HH parameters from designed features of extracellular MEA measurements by leveraging differentiable biophysical simulation and simulation-based inference, unlocking a wide range of downstream applications. In this work, we focus on a central goal of translational neuroengineering: predicting neural spiking responses to candidate neurostimulation patterns that would take hours to measure clinically. To validate our approach, we collected hundreds of hours of stimulation and recording data from isolated macaque retina with a 30 µm-pitch 512-electrode array. Our framework predicted previously unseen multi-electrode stimulation responses with 90.4\% accuracy using HH models fit from only a few minutes of recording, replacing hours of stimulus testing.

Training deep spiking neural networks (SNNs) remains challenging due to sharp loss landscapes and temporal inconsistency caused by surrogate gradients. To address these challenges, we propose a unified framework: adaptive and asymmetric surrogate gradients (A$^2$SG). The adaptive gradients adjust an effective window for spatio-temporal adaptation, reducing spatial gradient variation and maintaining directional consistency of gradients over time. The asymmetric gradients reflect neuronal dynamics by assigning larger gradients to neurons with higher membrane potentials, and we prove that they yield lower variation than symmetric surrogates. Our analysis further establishes a direct connection between local gradient variation and the curvature of the loss landscape, providing a principled explanation for how A$^2$SG promotes convergence to flatter minima and improves generalization. We conduct extensive experiments on diverse models, including CNN-based and Transformer-based SNNs, across various tasks such as image classification using both static and neuromorphic datasets, as well as segmentation. The results demonstrate that A$^2$SG consistently improves accuracy and energy efficiency, establishing it as a general and reliable solution for training deep SNNs.Our code is available at https://github.com/KIST-NCL/A2SG.git.

Representations of the world, arguably, contain information about features (e.g. something is blue, something is a circle) but also information about which features are part of the same object (e.g. the circle is blue), which we call binding information. Any system with the ability to understand scenes with multiple objects must be able to solve the binding problem: it needs to know which features belong together. However, despite work showing that Vision Transformers (ViTs) know which patches belong together, it is not known whether current deep learning models learn to exhibit binding information, i.e., for features. We may believe that there is not much binding information, after all misattributing features to wrong objects is a common failure of ViT-based architectures, especially in scenes with objects sharing features. Here we formalize the binding problem with an information-theoretic approach, and introduce a probing method to measure binding information in model representations. We perform experiments on ViTs, measuring binding from different components of the architecture, such as the image summary token [CLS] or the spatial tokens. We use datasets with different binding challenges, such as feature sharing, occlusion, and natural features, while comparing the performance of several pre-trained ViTs. Overall, our research demonstrates binding as a key ingredient to strong visual recognition and reasoning.

While AI-generated hallucinations pose considerable risks, the underlying cognitive mechanisms by which humans can successfully recognize or be misled by these hallucinations remain unclear. To address this problem, this paper explores humans' neural dynamics to characterize how the brain processes hallucinated content. We record EEG signals from 27 participants while they are performing a verification task to judge the correctness of image descriptions generated by a multi-modal large language model (MLLM). Based on an averaged event-related potential (ERP) study, we reveal that multiple cognitive processes, e.g., semantic integration, inferential processing, memory retrieval, and cognitive load, exhibit distinct patterns when humans process hallucinated versus non-hallucinated content. Notably, neural responses to hallucinations that were misjudged versus correctly judged by human participants showed significant differences. This indicates that misjudged AI-generated hallucinations failed to trigger the standard neurocognitive fact verification pathway. The detailed code can be accessed openly through https://github.com/Promise-Z5Q2SQ/EEG-Hallucination.

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory costs for higher-order targets. We propose the Cartesian Environment Interaction Tensor Network (CEITNet), an approach that constructs a multi-channel Cartesian local environment tensor for each atom and performs flexible many-body mixing via learnable channel-space interactions. By performing learning in channel space and using Cartesian tensor bases to assemble equivariant outputs, CEITNet enables efficient construction of high-order tensor. Across benchmark datasets for order-2 dielectric, order-3 piezoelectric, and order-4 elastic tensor prediction, CEITNet surpasses prior high-order prediction methods on key accuracy criteria while offering high computational efficiency.

Graph Neural Networks (GNNs) have revolutionized Neural Force Fields for atomistic simulations, achieving near-quantum accuracy at reduced cost, yet adapting these models to new chemical systems requires expensive retraining of foundation models. Inspired by model merging in vision and language processing, we introduce GFFMERGE, the first principled framework for closed-form model merging in GNNs. We exploit the linear structure of message-passing layers and formulate merging as a convex embedding-alignment problem with an analytical solution. Through the first systematic benchmarking of model merging for GNNs, we show that existing methods designed for vision and language catastrophically fail on force field regression, while GFFMERGE recovers performance approaching gold standard joint training. Across molecular (MD17, MD22), solid-state (LiPS20), and large-scale graph benchmarks, GFFMERGE and GNNMERGE (its generic GNN counterpart) achieve 5-27$\times$ speedups while enabling modular composition of specialized models. Remarkably, our closed-form solution alone outperforms all baseline methods before fine-tuning and provides superior initialization for faster, data-efficient convergence.

Modeling the interplay between external stimuli and internal neural representations is a pivotal research area for Brain-Computer Interfaces (BCIs). A major limitation of prior work is the prevailing paradigm of specialized, single-task models, which curtails versatility and neglects inter-task synergies. To address this, we propose Mind-Omni, the first versatile framework that unifies seven distinct encoding and decoding tasks through a discrete diffusion paradigm. At its core is a novel Brain Tokenizer that transforms heterogeneous, continuous brain signals into standardized, discrete tokens. This enables direct, token-level interactions for mutual understanding and generation between any two or more modalities within a shared semantic space. To unlock advanced reasoning capabilities, we further curate a specialized Brain Question Answering (BQA) instruction-tuning dataset. Our model not only establishes a new state-of-the-art among multi-task unified frameworks but also provides strong evidence for multi-task synergy. By demonstrating performance competitive with, and at times superior to, larger specialized models, our work offers a powerful new paradigm for neural modeling and paves the way for foundation models of neural activity.

Handwritten Text Recognition (HTR) is computationally imbalanced in two ways: most image pixels are background, and many width-axis sequence positions are blank-dominated. This creates a mismatch for Spiking Neural Networks (SNNs): handwriting is observed as a static image, whereas spiking computation unfolds over timesteps. We propose Spike-HTR, a hybrid spiking recognizer that controls both the number of spiking steps and the number of width positions processed by the deep sequence mixer. To make a static image suitable for short-horizon spiking inference, InkCoder converts it into a coarse-to-fine input stream, where early steps cover broad stroke regions and later steps emphasize sharper stroke details. To reduce sequence computation, a CTC-guided length reducer keeps likely character or uncertain positions and compresses long blank-dominated stretches before deep mixing. With $T{=}2$, Spike-HTR trains only on target data, decodes without language models or lexicons, and reaches validation/test CERs of 3.5/5.4, 2.3/2.5, and 4.2/3.9 on IAM, LAM, and READ2016. Codes are available at https://github.com/QomolangmaH/SpikeHTR.

Many fields collect large-scale temporal data through repeated measurements (`trials’), where each trial is labeled with a set of metadata variables spanning several categories. For example, a trial in a neuroscience study may be linked to a value from category (a): task difficulty, and category (b): animal choice. A critical challenge in time-series analysis is to understand how these labels are encoded within the multi-trial observations, and disentangle the distinct effect of each label entry across categories. Here, we present MILCCI, a novel data-driven method that i) identifies the interpretable components underlying the data, ii) captures cross-trial variability, and iii) integrates label information to understand each category's representation within the data. MILCCI extends a sparse per-trial decomposition that leverages label similarities within each category to enable subtle, label-driven cross-trial adjustments in component compositions and to distinguish the contribution of each category. MILCCI also learns each component’s corresponding temporal trace, which evolves over time within each trial and varies flexibly across trials. We demonstrate MILCCI’s performance through both synthetic and real-world examples, including voting patterns, online page view trends, and neuronal recordings.

Spiking Neural Networks (SNNs), with their event-driven and biologically inspired mechanisms, are well-suited for energy-efficient neuromorphic hardware. Neural coding, which is critical to SNNs, determines how information is represented via spikes. While Time-to-First-Spike (TTFS) coding uses a single spike per neuron to offer extreme sparsity and energy efficiency, it often suffers from unstable training and low accuracy due to its sparse firing. To address these challenges, we propose a training framework that incorporates parameter initialization, training normalization, a temporal output decoder, and a re-evaluation of the pooling layer. The proposed parameter initialization and training normalization mitigate signal diminishing and gradient vanishing, which helps stabilize training. Our output decoder aggregates temporal spikes to encourage earlier firing, thereby reducing latency. The re-evaluation of the pooling layer demonstrates that max-pooling violates single-spike constraints, which should be avoided, whereas average-pooling preserves them. Experiments show that our framework stabilizes and accelerates training, reduces latency, and achieves state-of-the-art accuracy for step-by-step TTFS SNNs on MNIST ($99.48\%$), Fashion-MNIST ($92.90\%$), CIFAR10 ($90.56\%$), CIFAR100 ($70.27\%$) and DVS Gesture ($95.83\%$).