ICML 2026 Papers

Mental rotation—the ability to compare objects seen from different viewpoints—is a fundamental example of mental simulation and spatial world modeling in humans. Here we propose a mechanistic model of human mental rotation, leveraging recent advances in deep, equivariant, and neuro-symbolic learning. Our model consists of three stacked components: (1) an equivariant neural encoder, producing 3D spatial representations of objects from images, (2) a neuro-symbolic object encoder, deriving symbolic objects descriptions from these spatial representations, and (3) a neural decision agent, comparing these symbolic descriptions to prescribe rotation simulations in 3D latent space via a recurrent pathway. Our model design is guided by the existing experimental literature on mental rotation, which we complemented with experiments in VR where participants could at times manipulate the objects to compare. Our model captures well the performance, response times and behavior of participants in our and others' experiments, and through ablation studies we demonstrate the necessity of each component. Our work adds to a recent collection of deep neural models of human spatial reasoning, further demonstrating the potency of integrating deep, equivariant, and symbolic representations to model the human mind.

Autonomous AI agents powered by large language models (LLMs) are increasingly capable of running a full cycle of scientific research, yet we still lack reliable ways to verify that their discoveries are correct. Because novel findings demand costly real-world validation, existing benchmarks fall back on LLM-as-judge scoring of generated papers or single leaderboard metrics, both coarse proxies for scientific reasoning. We introduce FIRE-BENCH (Full-cycle Insight Rediscovery Evaluation), which instead asks agents to rediscover established, verifiable findings from recent, high-impact machine learning research. Given only a high-level research question from a published study, an agent must independently design experiments, run them, and draw evidence-backed conclusions, scored against the study's documented findings. Across state-of-the-art agents with frontier backbones such as gpt-5, even the strongest reaches limited rediscovery success (<50 F1), with high run-to-run variance and recurring failures in experimental design, execution, and evidence-based reasoning. Beyond diagnosing current systems, FIRE-BENCH shows that open-ended discovery can be evaluated rigorously and verifiably, laying a foundation for building reliable environments that improve agents.

High-fidelity vehicle aerodynamics analysis is bottlenecked by costly CFD simulations. Neural surrogates accelerate prediction but lack inverse design capabilities, while existing generative optimization methods suffer from unstable convergence and frequent engineering constraint violations. We present UniDrag, a unified framework bridging multi-field aerodynamic prediction with robust differentiable shape optimization. Given a vehicle geometry, UniDrag predicts surface pressure, volume flow fields, drag coefficient $C_d$, and a streamwise build-up profile localizing drag contributions. Our architecture combines enhanced Physics-Sliced Attention (ePSA), Gated Expert Routing, and Modality-Protected Learning to prevent negative transfer across output modalities. At deployment, the frozen surrogate enables gradient-based optimization via Free-Form Deformation with engineering constraints. We introduce Expectation-over-Transformation to prevent adversarial exploitation of surrogate fragility. We curate a large-scale dataset of 15,000 vehicle geometries spanning four body types with GPU-accelerated LBM simulations. On this benchmark, UniDrag achieves $C_d$ prediction $R^2$ of 0.937 (+7.6\% over baselines) and 13.7\% mean CFD-verified drag reduction with 100\% success rate and only 21.3~mm average displacement (0.46\% vehicle length).

Oscillatory neural signals such as electroencephalography (EEG) and local field potentials (LFPs) show phase relationships that coordinate communication across brain regions. Modern recordings capture hundreds of channels across many frequency bins, yet standard phase analyses are restricted to only a few variables. The Torus Graph (TG) model, an exponential-family distribution over phases whose univariate and pairwise potentials generalize von Mises distributions, infers principled structure among oscillations but models only static, undirected dependencies and is limited to $\sim \! 100$ variables because its score matching inference scales as $\mathcal{O}(d^{6})$. We introduce a stochastic score matching procedure that reduces the per-iteration cost to $\mathcal{O}(d^{2})$, enabling inference on datasets with thousands of variables. This scalable foundation supports analyses of 1,860 frequency-phase features from multi-electrode LFPs and enables two extensions previously inaccessible to TGs or classical circular statistics: (i) a TG Hidden Markov Model capturing state-dependent phase-coupling changes (e.g., spindle-related states during sleep) and (ii) an autoregressive TG inferring directional interactions via transfer-entropy estimation. Applied to LFP recordings, these models reveal state-dependent phase-interaction patterns between wakefulness and NREM sleep. Together, they enable systematic, large-scale mapping of dynamic and directional phase relationships across brain and cognitive states.

Predictive coding networks are neural models that perform inference through an iterative energy minimization process, whose operations are local in space and time. While effective in shallow architectures, they suffer significant performance degradation beyond five to seven layers. In this work, we show that this degradation is caused by exponentially imbalanced errors between layers during weight updates, and by predictions from the previous layers not being effective in guiding updates in deeper layers. Furthermore, when training models with skip connections, the energy propagated by the residuals reaches higher layers faster than that propagated by the main pathway, affecting test accuracy. We address the first issue by introducing a novel precision-weighted optimization of latent variables that balances error distributions during the relaxation phase, the second issue by proposing a novel weight update mechanism that reduces error accumulation in deeper layers, and the third one by using auxiliary neurons that slow down the propagation of the energy in the residual connections. Empirically, our methods achieve performance comparable to backpropagation on deep models such as ResNets, opening new possibilities for predictive coding in complex tasks.

Tensor-valued prediction is fundamental to geometric deep learning, yet uncertainty quantification (UQ) for such outputs remains an open challenge. While E(3)-equivariant neural networks excel at point estimates, they lack rigorous confidence measures. We focus on symmetric rank-2 tensor prediction, where the target has six Kelvin-Mandel coordinates and full uncertainty is represented by a $6\times6$ covariance matrix. We introduce a framework for E(3)-equivariant UQ, modeling the full predictive distribution where both mean and covariance preserve rotational symmetry. Our approach decomposes the covariance into irreducible representations $\mathrm{Sym}^2(\rho_c) \cong 2\times(l=0) \oplus 2\times(l=2) \oplus 1\times(l=4)$. By mapping from the flat Lie algebra $\mathfrak{sym}(6)$ to the curved SPD manifold via matrix exponentiation, we strictly ensure positive-definite covariances while maintaining exact equivariance. Furthermore, we formulate a Log-Euclidean Equivariant Scoring Objective (LE-ESO)---a robust surrogate loss based on the Multivariate Laplace distribution---providing robustness to heavy-tailed errors and stable optimization. Validation on ModelNet40 inertia tensors and Materials Project dielectric tensors demonstrates that our method achieves competitive performance and provides physically consistent, symmetry-preserving uncertainty estimates with useful risk and OOD sensitivity.

Millimeter-wave (mmWave) sensing enables privacy-preserving, always-on edge perception, but its measurements are often sparse, temporally irregular, and corrupted by high-frequency noise. Existing mmWave pipelines predominantly rely on artificial neural networks (ANNs), which achieve robustness through extensive preprocessing or deep architectures, thereby limiting their efficiency on edge devices. In this work, we study spiking neural networks (SNNs) for mmWave sensing from a mechanism–data alignment perspective. By leveraging the low-pass filtering behavior of leaky integrate-and-fire (LIF) dynamics, we analyze how their implicit temporal filtering interacts with the frequency structure of mmWave signals. Our analysis shows that when discriminative information resides in low-to-mid frequencies, LIF dynamics can inherently suppress high-frequency noise, clarifying when and why SNNs outperform ANNs. Based on this insight, we derive a principled criterion for configuring the membrane decay factor by matching the effective bandwidth of LIF dynamics to the data’s discriminative spectral content. Experimental results across four widely used mmWave datasets validate the proposed frequency-matching hypothesis, yielding an average test-accuracy improvement of 6.22% and a 3.64× reduction in theoretical energy consumption relative to ANN baselines, under a unified evaluation protocol.

Though biological foundation models (Bio-FMs) have delivered strong performance across biomedical tasks, their robustness to small-but-real perturbations is underexplored. In this work, we ask: Are Bio-FMs robust for real-world use? What perturbations compromise their reliability? Our pilot study suggests that due to subtle biological data curation issues and common machine-learning (ML) processing choices, Bio-FMs suffer from two complementary perturbation sources: biologically plausible perturbations (capturing experimental corruptions and curation artifacts) and ML-induced transformations (capturing preprocessing, data augmentation, and embedding choices). Guided by this taxonomy, we design perturbation suites that mimic corruptions frequently encountered in biological experiments, and we systematically probe how transformations in the ML pipeline reshape model behavior. By conducting 2,128 experiments over 11 state-of-the-art Bio-FMs on 7 bio-tasks, we show that most Bio-FMs are vulnerable to both biological perturbations and ML transformations, revealing underappreciated robustness gaps that can directly translate into deployment risk. Interestingly, we find that subtle biological perturbations, which are often imperceptible to current measurement tools, can induce severe discrepancies in Bio-FM outputs and lead to critical failures, yet cryo-EM models (e.g., CryoDRGN) exhibit a surprising level of robustness even under worst-case perturbations. Our study for the first time surfaces critical failure modes and provides a principled perspective for evaluating the robustness of Bio-FMs.

Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets.

Efficiently training recurrent neural networks on long sequences remains an open challenge. The standard global paradigm, backpropagation through time (BPTT), suffers from vanishing and exploding gradients and memory costs that scale linearly with sequence length. Conversely, biologically inspired local learning rules are memory-efficient but typically introduce severe bias. To bridge this gap, we introduce Criticality-driven Online Local Alignment (COLA). By leveraging the long-range spatiotemporal correlations inherent to the critical regime, COLA enables a strictly local learning rule to approximate global error propagation, thereby combining online efficiency with gradient descent precision. Theoretically, for a recurrent neural network with $H$ hidden units, COLA requires only an $O(H)$ auxiliary state and constant activation memory, completely independent of sequence length. Empirically, COLA is competitive with BPTT on standard benchmarks and demonstrates superior robustness on stability-sensitive tasks. Finally, we conduct a rigorous analysis of the approximation error to provide a theoretical foundation for reliable online learning. Code is available at \url{https://github.com/Criticality-Cognitive-Computation-Lab/COLA}

Understanding complex interactions between brain regions is critical for early neurodegenerative disease classification such as Alzheimer’s Disease (AD) and Parkinson’s Disease (PD). While graph-based models are widely used to analyze brain networks, most existing approaches primarily focus on pairwise interactions between directly connected nodes, limiting their ability to capture higher-order dependencies across multiple regions. Although hypergraph-based methods have been proposed to model higher-order relations, many rely on predefined hyperedges or restrict learning to hyperedge weights, reducing flexibility and limiting their capacity to capture multi-resolution structural patterns. In this regard, we introduce an adaptive multi-scale hyperedge learning framework, i.e., MuHL, which constructs hierarchical node features and dynamically learns high-order interaction through continuous hyper-edge construction over multi-resolution graph signals. Extensive experiments on multiple brain network benchmarks demonstrate that MuHL consistently improves disease classification performance across different stages, and further identifies key regions of interest (ROIs) and their group-wise interactions from the learned hyperedges that are associated with disease progression, highlighting its potential as a powerful tool for brain network analysis with neurodegenerative disorders.

Spiking Neural Networks (SNNs) emulate the spiking behavior of biological neurons and are promising for energy-efficient neuromorphic computing. A widely used strategy to train SNNs is to convert pretrained Artificial Neural Networks (ANNs), where the accuracy and efficiency are determined by the spike encoding scheme. Traditional methods based on spike count or timing severely underutilize the available encoding space, leading to large accuracy degradation under low-timestep constraints. More expressive alternatives involve complex dynamics, which hinder scalability and practical deployment. To address these challenges, we propose Temporal Weighted Encoding (TWE). Spikes are implicitly assigned exponentially decaying weights through a recursive integration, drawing an analogy to a temporal bit sequence. We systematically analyze the temporal mismatch caused by this weight pattern and propose temporal relaxation and threshold relaxation to resolve this issue, enabling fast and accurate activation encoding. Extensive experiments demonstrate that TWE achieves negligible conversion loss with significantly fewer timesteps, offering a scalable and efficient solution for SNN deployment.

In network neuroscience, functional brain systems are often characterized using separate yet related graph-theoretic or spectral descriptors, overlooking how these properties covary and partially overlap across individuals and conditions. We anticipate that dense, weighted functional connectivity graphs lie on a low-dimensional latent geometry along which both topological and spectral structures vary smoothly at the population level. Although graph-based deep learning offers a powerful framework for modeling these brain connectomes, supervised approaches are constrained by the limited availability of labeled data. Existing unsupervised graph representation methods also typically focus on node-level embeddings, which are limited in capturing compact graph-level representations that preserve information from dense functional connectomes. To address these gaps, we learn compact brain graph representations using a graph transformer autoencoder, where domain-specific, aligned functional gradient geometry provides an inductive bias to guide learning. Despite being trained in a fully unsupervised manner, our approach meaningfully separates cognitive states and enables decoding of visual stimuli, with performance further improved by incorporating neural dynamics. In parallel, to enable generation of synthetic brain graphs, we fit a diffusion model to the learned latent representation and decode samples back to dense connectomes.

Transformer-based Spiking Neural Networks (SNNs) combine Transformer performance with SNN energy efficiency through an event-driven self-attention mechanism. However, Spiking Transformers still lag behind their Artificial Neural Network (ANN) counterparts. Most existing studies address this issue through new architectural designs, yet few have explored optimization algorithms tailored to Spiking Transformers. We substantiate the excessive noise problem in Spiking Transformer training by quantitatively defining parameter-update noise and, based on this definition, providing theoretical analysis and experimental validation. To address this problem, we propose AdaS, an adaptive gradient descent method for Spiking Transformers. AdaS reduces excessive noise by adaptively incorporating a gradient update component into adaptive optimization. Instead of simply removing noise, AdaS maintains it at an appropriate level to preserve its generalization benefits, thereby improving the performance of Spiking Transformers. We conduct extensive experiments on various Spiking Transformer architectures and datasets from both computer vision and natural language processing. The results demonstrate that the proposed AdaS consistently enhances performance across different Spiking Transformers, validating its effectiveness and generalizability. This work is among the first systematic studies of optimizer design specifically for Spiking Transformers, offering a practical tool to narrow the accuracy gap with ANNs while preserving the energy advantages of spike-based computation. Code is available at https://github.com/CayleyZ/AdaS.

Existing EEG models are limited by electrode heterogeneity and rigid "channel-first" architectures that treat sensors as independent features. We propose Brain Signal Rendering (BSR), which reinterprets EEG as a physical projection of neural activity and transforms raw signals into structured spatiotemporal tensors (termed Spectrum Videos), enabling the transfer of rich priors from video foundation models. By utilizing VideoMAE for self-supervised pre-training, BSR learns robust, layout-agnostic spatiotemporal representations that preserve neural topology. We further employ subject-level few-shot learning and introduce cross-montage fine-tuning to rigorously evaluate generalization across subjects and electrode configurations. Experiments show that VideoMAE model integrated with the BSR framework significantly outperforms state-of-the-art spectrum based methods, providing a scalable and data-efficient foundation for generalizable EEG modeling. Our code is available at [https://github.com/yanweifu-sii/BSR-VideoMAE](https://github.com/yanweifu-sii/BSR-VideoMAE).

Density functional theory (DFT) is the most widely used method for calculating molecular properties; however, its accuracy is often insufficient for quantitative predictions. Coupled cluster (CC) theory is the most successful method for achieving accuracy beyond DFT and predicting properties that closely align with experiment. It is known as the ``gold standard'' of quantum chemistry. Unfortunately, the high computational cost of CC limits its widespread applicability. In this work, we present the Molecular Orbital Learning Model (MoLe), an equivariant machine learning model that directly predicts CC's core mathematical objects, the excitation amplitudes, from the mean-field Hartree-Fock molecular orbitals as inputs. We test various aspects of our model and demonstrate its very high data efficiency and remarkable out-of-distribution generalization to larger molecules and off-equilibrium geometries, despite being trained only on small equilibrium geometries. Finally, we also examine its ability to reduce the number of cycles required to converge CC calculations. MoLe can set the foundations for high-accuracy wavefunction-based ML architectures to accelerate molecular design and complement force-field approaches.

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.

Spiking Neural Networks (SNNs) can achieve competitive performance by converting already existing well-trained Artificial Neural Networks (ANNs), avoiding further costly training. This property is particularly attractive in Reinforcement Learning (RL), where training through environment interaction is expensive and potentially unsafe. However, existing conversion methods perform poorly in continuous control, where suitable baselines are largely absent. We identify error amplification as the key cause: small action approximation errors become temporally correlated across decision steps, inducing cumulative state distribution shift and severe performance degradation. To address this issue, we propose Cross-Step Residual Potential Initialization (CRPI), a lightweight gradient-free mechanism that carries over residual membrane potentials across decision steps to suppress temporally correlated errors. Experiments on continuous control benchmarks with both vector and visual observations demonstrate that CRPI can be integrated into existing conversion pipelines and substantially recovers lost performance. Our results highlight continuous control as a critical and challenging benchmark for ANN-to-SNN conversion, where small errors can be strongly amplified and impact performance. Code is available at https://github.com/xuzijie32/ANN2SNN-CRPI.

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.