ICML 2026 Papers

Learning mesh-based operators from data can match training objectives while implicitly violating algebraic consistency constraints that classical discretizations satisfy by construction. Such violations can introduce near-kernel directions, degrade conditioning as resolution increases, and distort the low-frequency spectral structure on which downstream solvers and diagnostics rely. This work introduces a low-overhead compatibility certificate for learned operator pairs, together with a closed-form projection that maps a learned pair to its Frobenius-nearest chain-compatible operator. The certificate provides an explicit distance-to-compatibility and yields perturbation bounds for the discrete operator. These bounds imply stability guarantees for elliptic solves and for low-frequency spectral counts, provided a spectral gap separates the kernel from the rest of the spectrum and boundary treatments are well posed. Experiments on standard elliptic problems show that defect-aware training prevents condition-number blow-up at higher resolutions, improves robustness under mesh and topological distribution shifts, and maintains predictive accuracy relative to unconstrained learning. Overall, these results support the use of deployment-neutral, computable algebraic consistency checks to detect and control failure modes that are not revealed by loss values alone.

Recent advances in large language models have accelerated neural theorem proving (NTP). Isabelle is a mature and important formal theorem prover that has been widely used in software and hardware verification. However, progress in the Isabelle setting remains limited. Existing approaches either optimize search strategies or train on highly imbalanced raw proof corpora. At the same time, the specialized structure of Isabelle proofs limits the effectiveness of general-purpose data selection methods. To address these challenges, we adopt a data-centric framework for neural theorem proving in Isabelle. We characterize high-quality formal proof data along three complementary dimensions—proof complexity, semantic coverage, and reasoning diversity (PSR)—and propose a PSR-guided data selection pipeline to construct a compact, high-quality training subset. In addition, we leverage verifier feedback as a dynamic data signal during inference, introducing a dynamic feedback-based prompt optimization that iteratively incorporates Isabelle verifier feedback to guide proof generation. We construct and release a 4k high-quality Isabelle dataset based on the PSR criterion. On the miniF2F-test, fine-tuning solely on PSR-selected data achieves 84.8% Pass@64. When further combined with dynamic feedback–based prompt optimization, the full framework improves performance to 90.6% Pass@64, establishing a new state of the art for neural theorem proving in Isabelle.

Alzheimer’s disease (AD) alters brain electrophysiology and disrupts multichannel EEG dynamics, making accurate and clinically useful EEG-based diagnosis increasingly important for screening and disease monitoring. However, many existing approaches rely on black-box classifiers and do not explicitly model the latent event timing and cross-channel coordination behind their decisions. To address these limitations, we propose LERD, an end-to-end Bayesian latent event--relational dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations. LERD combines a continuous-time event inference module with a stochastic event-generation process to capture flexible temporal patterns, while incorporating an electrophysiology-inspired dynamical prior to guide learning in a principled way. We further provide theoretical analysis that yields a tractable IVP-based KL regularizer and stability guarantees for the inferred relational dynamics. Extensive experiments on synthetic benchmarks and two real-world AD EEG cohorts demonstrate that LERD consistently outperforms strong baselines and yields physiology-aligned rate, timing, and graph summaries that help characterize group-level dynamical differences.

Comprehensive urban understanding requires integrating macroscopic spatial structure with fine-grained street-level semantics. However, existing urban Multimodal Large Language Models (MLLMs) primarily rely on satellite imagery, limiting their ability to capture detailed urban appearance and cross-view relationships. We propose \textbf{UrbanMLLM}, a unified MLLM that jointly learns from satellite and street-view imagery for cross-view urban perception and reasoning. To support this, we construct a large-scale dataset with paired cross-view urban images, geospatial alignment, and textual annotations. UrbanMLLM introduces a cross-view perceiver to explicitly model interactions between satellite and street-view representations, and adopts a structural interleaved pre-training paradigm that organizes cross-view image–text content as coherent urban documents to enhance cross-view knowledge fusion. We evaluate UrbanMLLM on 13 diverse urban understanding tasks spanning satellite, street-view, and cross-view settings. Experimental results demonstrate consistent improvements over strong open-source and proprietary MLLMs, highlighting effectiveness and scalability of UrbanMLLM for urban environment understanding.

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks (lrRNNs) to infer low-dimensional latent dynamics and connectivity from observed activity, enabling a mechanistic interpretation of the dynamics. However, standard approaches for training lrRNNs can recover spurious structures irrelevant to the underlying dynamics. We first characterize the identifiability of connectivity structures in lrRNNs and determine conditions under which a unique solution exists. To find such solutions, we develop an inference framework based on maximum entropy and continuous normalizing flows (CNFs), trained via flow matching. Instead of estimating a single connectivity matrix, our method learns a distribution over connection weights that is maximally unbiased over unidentifiable components while matching the observed dynamics. This approach captures complex yet necessary distributions such as heavy-tailed connectivity found in empirical data. We validate our method on synthetic datasets with connectivity structures that generate multistable attractors, limit cycles, and ring attractors, and demonstrate its applicability in recordings from rat frontal cortex during decision-making. Our framework shifts circuit inference from recovering connectivity to identifying which connectivity structures are computationally required, and which are artifacts of underconstrained inference.

Spiking Neural Networks (SNNs) offer an energy--efficient route to 3D spatio--temporal perception, yet they lag behind Artificial Neural Networks (ANNs) due to weak pretraining and heavy inference stacks, limiting generalization and multimodal reasoning (e.g., zero--shot 3D classification and open--world QA). We present a universal \textbf{S}pike--based \textbf{V}ision--\textbf{L}anguage pretraining framework (SVL) that equips SNNs with open--world 3D understanding while preserving end--to--end spike efficiency. SVL comprises two core components: (i) {Multi--scale Triple Alignment} (MTA), a label--free triplet contrastive objective aligning 3D, image, and text; and (ii) {Re--parameterizable Vision--Language Integration} (Rep--VLI), which converts offline text embeddings into lightweight weights for text--encoder--free inference. Moreover, we present the first fully spike--driven point Transformer, {Spike-driven PointFormer}, whose 3D spike--driven self--attention (3D-SDSA) reduces interactions to sparse additions, enabling faster, more efficient training. Extensive experiments show that SVL attains strong zero--shot 3D classification (85.4% top--1) and consistently outperforms prior SNNs on downstream tasks (e.g., +6.1% 3D cls, +2.1% DVS actions, +1.1% detection, +2.1% segmentation) while enabling open--world 3D question answering, sometimes outperforming ANNs. To the best of our knowledge, SVL represents the first scalable, generalizable, and hardware-friendly paradigm for 3D open-world understanding, effectively bridging the gap between SNNs and ANNs in complex open-world understanding tasks.

Despite the high accuracy of EEG-based emotion recognition, existing models remain opaque "black boxes", lacking semantic grounding between abstract neural features and human-interpretable states. In this paper, we reframe EEG explainability as a cross-modal generation task, shifting the paradigm from feature attribution to behavioral visualization. We introduce Facial Emoji Proxy Modeling, a novel framework that translates high-dimensional EEG signals into identity-anonymized facial emojis. Guided by the neuroscientific inspiration of neural-facial association, this approach grounds neural representations in the manifold of observable facial dynamics. Technically, our framework integrates FMENet, a specialized backbone modeling expression-relevant spatial synergies, and the Facial Emoji Learning Branch (FELB), which treats emoji reconstruction as a structured semantic regularizer. Extensive experiments on EAV and MMER benchmarks demonstrate that our method achieves state-of-the-art accuracy among EEG-only models. Crucially, it generates semantically faithful facial animations that provide a transparent, privacy-preserving window into the brain's emotional evolution, effectively allowing users to ``see the emotion'' directly from neural signals. Code is available at https://github.com/xian-sh/SeeEmotion

Humans abstract experiences into structured representations to facilitate pattern inference and knowledge transfer. While the hippocampal-entorhinal (HPC-MEC) circuit is known to represent both spatial and conceptual spaces, the mechanisms for concurrently extracting abstract structures from continuous, high-dimensional dynamics remain poorly understood. We propose a brain-inspired hierarchical model that simultaneously infers latent transitions and constructs a predictive visual world model. Our architecture employs an inverse model for structural extraction alongside an HPC-MEC coupling model that dissociates relational structures (MEC) from integrated episodic scenes (HPC). Using rotation dynamics as a benchmark, we demonstrate the model's capacity for structural abstraction. By leveraging velocity-driven path integration, the framework enables robust prediction and structural reuse across diverse contexts, thereby achieving structural generalization. This work provides a novel computational framework for understanding how brain-inspired, self-supervised learning of world models facilitates the acquisition of reusable abstract knowledge.

Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations. However, the full scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear residual networks, we show that the set of width- and depth-stable feature-learning parameterisations for PC is exactly the same as for BP. Moreover, under any of these parameterisations, the PC energy with equilibrated activities converges to the quadratic BP loss when the model width is much larger than the depth, resulting in PC computing the same gradients as BP. Experiments show that, as long as an activity equilibrium is reached, convergence to BP holds for nonlinear models including convolutional networks and transformers. Overall, this work constrains the types of parameterisation that are scalable with PC, while showing a way in which BP can be effectively implemented with only local updates in much wider than deep networks like the brain.

Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by introduce the Cartesian-3j symbol and Cartesian Generalized Clebsch-Gordan Coefficients, which serve as direct analogues of the Wigner-3j symbol and Generalized Clebsch-Gordan coefficients defined for ST coupling. We extend the e3nn library to support ICT product, and use this framework to build Cartesian counterparts of MACE, NequIP, and Allegro, allowing the first controlled comparison where architectures are held fixed and only the tensor basis is changed. Our experiments show that irreducible Cartesian models can achieve accuracy comparable to spherical counterparts, but direct Cartesianization incurs unfavorable compute and memory scaling, motivating dedicated Cartesian architectural choices. Leveraging ICTs and our framework, we introduce TACE-v1-OAM-M and demonstrate that it achieves competitive performance on Matbench Discovery compared to state-of-the-art ST models.

Network pruning, which removes less important parameters or architectures, is often expected to improve efficiency while preserving performance. However, this expectation does not consistently hold across language tasks: pruned models can perform well on non-generative tasks but frequently fail in generative settings. To demystify how such discrepancies arise under pruning, we analyze network pruning from a representation-hierarchy perspective, decomposing the internal computation of language models into three sequential spaces: \textit{embedding} (hidden representations), \textit{logit} (pre-softmax outputs), and \textit{probability} (post-softmax distributions). While representations in the embedding and logit spaces are largely robust to pruning-induced perturbations, the subsequent nonlinear transformation from logits to the probability space amplifies such deviations, whose persistence across time steps leads to substantial degradation during generation. By contrast, the stability of the categorical-token probability subspace, together with the robustness of the embedding space, supports the effectiveness of pruning for non-generative tasks such as retrieval and multiple-choice classification. Our representation-level analysis disentangles the effects of pruning across tasks and offers practical guidance for applying pruning effectively. The code is available in the \href{https://github.com/CASE-Lab-UMD/Pruning-on-Representations}{project repository}.

Multi-modal object Re-Identification (ReID) aims to retrieve the same object across different modalities by exploiting their complementary visual information. Recent advances leverage Multi-modal Large Language Models (MLLMs) to generate descriptive textual annotations as auxiliary supervision. However, existing approaches usually adopt these generated texts directly, overlooking the varying correspondence degrees between visual and textual modalities. Such neglect may lead the model to treat strong- and weak-correspondence image–text pairs equally, limiting its ability to learn discriminative associations and hindering effective optimization. To overcome this limitation, we propose a Correspondence Cognitive Learning (CCL) framework that explicitly models the correspondence degree and facilitates a progressive learning process from easy to hard pairs. CCL is composed of two synergistic modules. The Correspondence-Guided Semantic Refinement (CGSR) module dynamically refines visual representations using text semantics according to the correspondence difficulty estimated from the previous epoch, thereby enhancing feature alignment under imperfect associations. The Cognitive-Driven Dynamic Optimization (CDDO) module presents a self-paced weighting mechanism that adaptively adjusts the optimization focus by emphasizing easy pairs at the early stage and gradually integrating harder ones as training evolves. Together, these modules enhance feature-level alignment and optimization adaptivity, yielding robust and discriminative multi-modal representations. Extensive experiments on three multi-modal object ReID benchmarks demonstrate the superior performance of our method.

Understanding how educational social dynamics evolve is critical for informing effective educational policies and counterfactual interventions. However, traditional methods face a fundamental dilemma: observational studies often lack causal power, while controlled experiments are frequently constrained by ethical concerns. Although LLM-based multi-agent simulations offer a scalable **in silico** alternative, existing approaches remain limited by weak psychological grounding and insufficient measurement of latent psychological states. To address this, we introduce **EduMirror**, a multi-agent simulator for the scientific study of educational social dynamics. We provide configurable education-oriented agent forms, including value-driven agents grounded in psychological needs and social value orientation, together with a dual-track measurement protocol for quantifying observable behaviors and latent psychological states. We validate the realism and usability of EduMirror through case studies on school bullying and group cooperation, as well as broader evaluations across diverse educational scenarios. The results show that EduMirror generates educational social dynamics that are realistic, theory-consistent, and measurable by empirical criteria. These properties enable structured **in silico** educational research, providing a computational tool for hypothesis testing and counterfactual intervention analysis in educational science. Project page: *https://edumirror.net*.

Conditionally positive definite (CPD) kernels are defined with respect to a function class $\mathcal{F}$. It is well known that such a kernel $K$ is associated with its native space (defined analogously to an RKHS), which in turn gives rise to a learning method --- called conditional kernel ridge regression (conditional KRR) due to its analogy with KRR --- where the estimated regression function is penalized by the square of its native space norm. This method is of interest because it can be viewed as classical linear regression, with features specified by $\mathcal{F}$, followed by the application of standard KRR to the residual (unexplained) component of the target variable. Methods of this type have recently attracted increasing attention. We study the statistical properties of this method by reducing its behavior to that of KRR with another fixed kernel, called the residual kernel. Our main theoretical result shows that such a reduction is indeed possible, at the cost of an additional term in the expected test risk, bounded by $\mathcal{O}(1/\sqrt{N})$, where $N$ is the sample size and the hidden constant depends on the class $\mathcal{F}$ and the input distribution. This reduction enables us to analyze conditional KRR in the case where $K$ is positive definite and $\mathcal{F}$ is given by the first $k$ principal eigenfunctions in the Mercer decomposition of $K$. We also consider the setting where $\mathcal{F}$ consists of $k$ random features from a random feature representation of $K$. It turns out that these two settings are closely related. Both our theoretical analysis and experiments confirm that conditional KRR outperforms standard KRR in these cases whenever the $\mathcal{F}$-component of the regression function is more pronounced than the residual part.

Recent Spiking Transformer models have explored a variety of attention mechanisms beyond standard dot-product formulations. However, many existing similarity-based spiking attention formulations remain inherently sensitive to firing density, causing neurons with high spike rates to dominate attention scores regardless of semantic relevance. This density bias is particularly problematic in event-driven spiking representations, where sparse spike patterns often carry critical information. To address this limitation, we rethink spiking attention from a set-theoretic perspective. We propose DiceFormer, a novel Spiking Transformer architecture driven by Spike Dice Attention (SDA). Unlike traditional approaches, SDA replaces density-sensitive measures with a set similarity function derived from the Dice coefficient. By explicitly normalizing for firing density, SDA focuses on spike co-occurrence rather than high firing rates. We primarily evaluate DiceFormer on the challenging audio domain, where spike sparsity varies substantially across inputs. On AudioSet-20k, DiceFormer achieves a SOTA mAP of 0.161 with 54.3M parameters, outperforming prior SNN-based approaches and substantially narrowing the performance gap with ANN-based models. We also introduce Lin-SDA, a linearized version for computation efficiency, while achieving performance comparable to SDA. Beyond audio, we evaluate the effectiveness of SDA on CIFAR-100 to verify its applicability to the vision domain.

High-resolution (HR) image perception presents a key bottleneck for multimodal large language models (MLLMs). While visual search offers a promising solution, existing methods struggle with the trade-off between coverage and efficiency. Visual expert-assisted search is efficient but prone to blind spots when proposals fail, whereas scan-based search guarantees coverage at the cost of computational redundancy and semantic fragmentation. To address this dilemma, we introduce CVSearch, a training-free adaptive framework that dynamically schedules search strategies via an Assess-then-Search workflow. Specifically, CVSearch first invokes expert-assisted search when global information is insufficient, and only triggers a novel semantic-aware scanning mechanism upon failure. Distinct from rigid grid partitioning, this efficient scanning paradigm incorporates Semantic Guided Adaptive Patching to decompose images into semantically consistent regions, effectively mitigating object fragmentation. Furthermore, we devise a Dynamic Bottom-Up Search strategy driven by a Visual Complexity prior to enable efficient and precise iterative exploration of local details. Extensive experiments on HR benchmarks demonstrate that CVSearch achieves state-of-the-art accuracy while substantially improving search efficiency. Code is released at https://github.com/liliupeng28/ICML26-CVSearch.

Although Federated Learning (FL) offers advantages in privacy-preserving for cross-device collaborative learning, its practical deployment remains severely constrained by heterogeneous hardware resources and non-IID (non-independent and identically distributed) data across devices. Sub-model extraction has emerged as a widely adopted strategy for enabling collaborative training among devices with heterogeneous models. However, existing sub-model extraction methods in FL typically rely on coarse-grained stochastic selection or rigid rule-based neuron selection, which severely limits training performance. Specifically, stochastic strategies lead to severe parameter conflicts under non-IID data distributions, while rule-based approaches lack diversity in neuron selection per device, preventing comprehensive parameter optimization. To address this problem, this paper presents a novel sub-model extraction-based FL framework, named SpineFL, which adopts a backbone-sharing mechanism and an activation-guided pruning strategy for sub-model extraction. Specifically, SpineFL decomposes each global model layer into two portions: i) a mandatory backbone shared by all the sub-models to maintain model generalization, and ii) a dynamic portion for sub-model extraction. SpineFL adopts the activation-guided selection strategy to probabilistically select neurons according to their activation frequency from the dynamic portion to generate sub-model, where neurons exhibiting higher historical activation are more likely to be included, thereby simultaneously addressing parameter conflicts while preserving selection diversity. Experimental results demonstrate that compared with state-of-the-art heterogeneous FL methods, SpineFL can achieve up to 3.28% accuracy improvement.

Notification dispatch plays a critical role in large-scale user engagement, involving complex trade-offs across notification timing, presentation style, multiple outcomes, and constraints. In this paper, we formulate it as a constrained optimization over bundle treatments that jointly specify timing and presentation style, aiming to maximize incremental Daily Active Users (DAU) subject to platform-level budget and device vendor-specific quota constraints. The problem is challenging due to multi-dimensional, small-effect uplift estimation and large-scale constrained optimization. To address these challenges, we propose $\textbf{B}$undle $\textbf{U}$plift $\textbf{O}$ptimization with $\textbf{P}$runed $\textbf{L}$agrangian-based $\textbf{R}$elaxation (BUOPLR), a two-stage notification dispatch method that decouples uplift estimation from constrained decision-making. BUOPLR first learns bundle-level, multi-outcome small uplift through an architecture that captures cross-treatment and cross-outcome relationships, and then performs scalable assignment by restricting the decision space and applying Lagrangian relaxation to a small set of global constraints. Offline experiments show BUOPLR outperforms state-of-the-art methods, and online A/B tests increase DAU by 0.5\%. BUOPLR is now deployed on Kuaishou, a large-scale short video platform serving over 100 million users daily.

The realization of autonomous scientific experimentation is currently limited by LLMs' struggle to grasp the strict procedural logic and accuracy required by biological protocols. To address this fundamental challenge, we present BioProBench, a comprehensive resource for procedural reasoning in biology. BioProBench is grounded in BioProCorpus, a foundational collection of 27,000 human-written protocols. From this corpus, we systematically constructed a dataset of over 550,000 task instances, offering both a large-scale training resource and a rigorous benchmark with novel metrics. Evaluating 10 mainstream LLMs, we find that while general comprehension is high, performance drops significantly on tasks demanding deep reasoning, quantitative precision, and safety awareness. To demonstrate the value of BioProCorpus in mitigating these issues, we developed \textbf{ProAgent}, grounded in our corpus, ProAgent substantially advances the state-of-the-art. Code and data are available at: https://github.com/YuyangSunshine/bioprotocolbench and https://huggingface.co/datasets/BioProBench/BioProBench .