ICLR 2026 论文列表

Semantic representations can be framed as a structured, dynamic knowledge space through which humans navigate to retrieve and manipulate meaning. To investigate how humans traverse this geometry, we introduce a framework that represents concept production as navigation through embedding space. Using different transformer text embedding models, we construct participant-specific semantic trajectories based on cumulative embeddings and extract geometric and dynamical metrics, including distance to next, distance to centroid, entropy, velocity, and acceleration. These measures capture both scalar and directional aspects of semantic navigation, providing a computationally grounded view of semantic representation search as movement in a geometric space. We evaluate the framework on four datasets across different languages, spanning different property generation tasks: Neurodegenerative, Swear verbal fluency, Property listing task in Italian, and in German. Across these contexts, our approach distinguishes between clinical groups and concept types, offering a mathematical framework that requires minimal human intervention compared to typical labor-intensive linguistic pre-processing methods. Comparison with a non-cumulative approach reveals that cumulative embeddings work best for longer trajectories, whereas shorter ones may provide too little context, favoring the non-cumulative alternative. Critically, different embedding models yielded similar results, highlighting similarities between different learned representations despite different training pipelines. By framing semantic navigation as a structured trajectory through embedding space, bridging cognitive modeling with learned representation, thereby establishing a pipeline for quantifying semantic representation dynamics with applications in clinical research, cross-linguistic analysis, and the assessment of artificial cognition. https://github.com/jesuinovieira/semtraj-iclr2026

Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However, excessive latent states and interactions from mechanistic models can lead to training inefficiency and over-fitting, limiting practical effectiveness of hybrid neural ODEs. In response, we propose a new hybrid pipeline for automatic state selection and structure optimization in mechanistic neural ODEs, combining domain-informed graph modifications with data-driven regularization to sparsify the model for improving predictive performance and stability while retaining mechanistic plausibility. Experiments on synthetic and real-world data show improved predictive performance and robustness with desired sparsity, establishing an effective solution for hybrid model reduction in healthcare applications.

The alignment of Large Language Models (LLMs) and brain activity provides a powerful framework to advance our understanding of cognitive neuroscience and artificial intelligence. In this work, we zoom into one of the fundamental units of LLMs—the transformer block—to provide the first systematic computational neuroanatomy of its internal operations and human brain acitivity during language processing. Analyzing 21 state-of-the-art LLMs across five model families, we extract and evaluate 13 distinct intermediate states per transformer block—from initial layer normalization through attention mechanisms to feed-forward networks (FFNs). Our analysis reveals three key findings: (1) The commonly used hidden states in LLMs are surprisingly suboptimal, with over 90\% of brain voxels in sensory and language regions better explained by previously unexplored intermediate computations; (2) Different computational stages within a single transformer block map to anatomically distinct brain systems, revealing an intra-block hierarchy where early attention states align with sensory cortices while later FFN states correspond to association areas—mirroring the cortical processing hierarchy; (3) Rotary Positional Embeddings (RoPE) specifically enhance alignment along the brain's auditory processing streams. Per-head queries with RoPE best explain 74\% of auditory cortex activity compared to 8\% without RoPE, providing the first neurobiological validation of this architectural component in LLMs. Building on these insights, we propose MindTransformer, a feature selection framework that learns brain-aligned representations from all intermediate states. MindTransformer achieves significant brain alignment performance, with correlation improvements in primary auditory cortex exceeding gains from 456× model scaling. Our computational neuroanatomy approach opens new directions for understanding both biological intelligence through the lens of transformer computations and artificial intelligence through principles of brain organization.

As large language models (LLMs) continue to revolutionize AI research, there is a growing interest in building large-scale brain foundation models to advance neuroscience. While most existing brain foundation models are pre-trained on time-series signals or connectome features, we propose a novel graph-based pre-training paradigm for constructing a brain graph foundation model. In this paper, we introduce the Brain Graph Foundation Model, termed BrainGFM, a unified framework that leverages graph contrastive learning and graph masked autoencoders for large-scale fMRI-based pre-training. BrainGFM is pre-trained on a diverse mixture of brain atlases with varying parcellations, significantly expanding the pre-training corpus and enhancing the model’s ability to generalize across heterogeneous fMRI-derived brain representations. To support efficient and versatile downstream transfer, we integrate both graph prompts and language prompts into the model design, enabling BrainGFM to flexibly adapt to a wide range of atlases, neurological and psychiatric disorders, and task settings. Furthermore, we employ meta-learning to optimize the graph prompts, facilitating strong generalization to previously unseen disorders under both few-shot and zero-shot learning conditions via language-guided prompting. BrainGFM is established on 27 neuroimaging datasets spanning 25 common neurological and psychiatric disorders, encompassing 2 types of brain atlases (functional and anatomical) across 8 widely used parcellations, and covering over 25,000 subjects, 60,000 fMRI scans, and a total of 400,000 graph samples aggregated across all atlases and parcellations. The code is available at https://github.com/weixinxu666/BrainGFM.

Machine-Learned Interatomic Potentials (MLIPs) require vast amounts of atomic structure data to learn forces and energies, and their performance continues to improve with training set size. Meanwhile, the even greater quantities of accompanying data in the Hamiltonian matrix $\mathbf{H}$ behind these datasets has so far gone unused for this purpose. Here, we provide a recipe for integrating the orbital interaction data within $\mathbf{H}$ towards training pipelines for atomic-level properties. We first introduce HELM ('Hamiltonian-trained Electronic-structure Learning for Molecules'), a state-of-the-art Hamiltonian prediction model which bridges the gap between Hamiltonian prediction and universal MLIPs by scaling to $\mathbf{H}$ of structures with 100+ atoms, high elemental diversity, and large basis sets including diffuse functions. To accompany HELM, we release a curated Hamiltonian matrix dataset, 'OMol\_CSH\_58k', with unprecedented elemental diversity (58 elements), molecular size (up to 150 atoms), and basis set (def2-TZVPD). Finally, we introduce 'Hamiltonian pretraining' as a method to extract meaningful descriptors of atomic environments even from a limited number atomic structures, and repurpose this shared embedding space to improve performance on energy-prediction in low-data regimes. Our results highlight the use of electronic interactions as a rich and transferable data source for representing chemical space.

Diffusion language models have recently emerged as a competitive alternative to autoregressive language models. Beyond next-token generation, they are more efficient and flexible by enabling parallel and any-order token generation. However, despite empirical successes, their computational power and fundamental limitations remain poorly understood. In this paper, we formally study whether non-autoregressive generation in Masked Diffusion Models (MDM) enables solving problems beyond the reach of Auto-Regressive Models (ARM). Our results show that MDM with sufficiently large context length is computationally universal with decoding steps matching the optimal parallel time complexity in PRAM. However, when controlling for other factors, MDM's flexibility to generate in any-order does not expand what ARM can already solve. To address this, we propose a new form of generation called any-process generation, which extends MDM with capabilities to remask, insert and delete tokens, allowing self-correction, length-variable editing, and adaptive parallelism. Theoretically and empirically, we demonstrate these capabilities enable scalability to significantly harder reasoning problems that are otherwise intractable for ARM and vanilla MDM. Additionally, they prove essential for generation tasks where objects naturally evolve through non-sequential processes, crucial for extending current LLMs beyond natural language to domains such as coding and science.

The problem of physical dynamics, which involves predicting the 3D trajectories of particles, is a fundamental task with wide-ranging applications across science and engineering. However, accurately forecasting long-horizon trajectories from initial states remains challenging, due to complex particle interactions and entangled multi-scale dynamics involving both low- and high-frequency components. To address this, we propose a novel knowledge-distillation-based framework, SGDD (Spectral-Guided Dynamics Distillation), which integrates a spectral-guided enhancement to adaptively prioritize key frequency components within a unified spatio-temporal representation. Through knowledge distillation, SGDD leverages future trajectories as privileged information during training, guiding a teacher encoder to generate comprehensive dynamics representations while a student encoder approximates them using only the initial state. This enables the student to generate effective dynamics representations at inference, even without privileged information, thereby enabling accurate long-horizon trajectory prediction. Experimental results on molecule, protein, and human motion datasets demonstrate that our method achieves more accurate and stable long-term predictions than previous physical dynamics models, successfully capturing the complex spatio-temporal structures of real-world systems.

We introduce *Einstein Fields*, a neural representation designed to compress computationally intensive *four-dimensional* numerical relativity simulations into compact implicit neural network weights. By modeling the *metric*, the core tensor field of general relativity, Einstein Fields enable the derivation of physical quantities via automatic differentiation. Unlike conventional neural fields (e.g., signed distance, occupancy, or radiance fields), Einstein Fields fall into the class of *Neural Tensor Fields* with the key difference that, when encoding the spacetime geometry into neural field representations, dynamics emerge naturally as a byproduct. Our novel implicit approach demonstrates remarkable potential, including continuum modeling of four-dimensional spacetime, mesh-agnosticity, storage efficiency, derivative accuracy, and ease of use. It achieves up to a $\mathtt{4,000}$-fold reduction in storage memory compared to discrete representations while retaining a numerical accuracy of five to seven decimal places. Moreover, in single precision, differentiation of the Einstein Fields-parameterized metric tensor is up to five orders of magnitude more accurate compared to naive finite differencing methods. We demonstrate these properties on several canonical test beds of general relativity and numerical relativity simulation data, while also releasing an open-source $\mathtt{JAX}$-based library: https://github.com/AndreiB137/EinFields, taking the first steps to studying the potential of machine learning in numerical relativity.

Accurately solving partial differential equations (PDEs) on arbitrary geometries and a variety of meshes is an important task in science and engineering applications. In this paper, we propose Adaptive Fourier Mamba Operators (AFMO), which integrates reproducing kernels for state-space models (SSMs) rather than the kernel integral formulation of SSMs. This is achieved by constructing Takenaka-Malmquist systems for the PDEs. AFMO offers new representations that align well with the adaptive Fourier decomposition (AFD) theory and can approximate the solution manifold of PDEs on a wide range of geometries and meshes. In several challenging benchmark PDE problems in the field of fluid physics, solid physics, and finance on point clouds, structured meshes, regular grids, and irregular domains, AFMO consistently outperforms state-of-the-art solvers in terms of relative $L^2$ error. Overall, this work presents a new paradigm for designing explainable neural operator frameworks.

Spiking Neural Networks (SNNs), inspired by biological neurons, are attractive for their event-driven energy efficiency but still fall short of Artificial Neural Networks (ANNs) in accuracy. Knowledge distillation (KD) has emerged as a promising approach to narrow this gap by transferring ANN knowledge into SNNs. Temporal-wise distillation (TWD) leverages the temporal dynamics of SNNs by providing supervision across timesteps, but it applies a constant teacher output to all timesteps, mismatching the inherently evolving temporal process of SNNs. Moreover, while TWD improves per-timestep accuracy, truncated inference still suffers from full-length temporal information loss due to the progressive accumulation process. We propose **MEOM** (**M**any **E**yes, **O**ne **M**ind), a unified KD framework that enriches supervision with diverse temporal perspectives through mask-weighted teacher features and progressively aligns truncated predictions with the full-length prediction, thereby enabling more reliable inference across all timesteps. Extensive experiments and theoretical analyses demonstrate that MEOM achieves state-of-the-art performance on multiple benchmarks. Code is available at https://github.com/KaiSUN1/MEOM.

Robotic manipulation policies often struggle to generalize to novel objects, limiting their real-world utility. In contrast, cognitive science suggests that children develop generalizable dexterous manipulation skills by mastering a small set of simple toys and then applying that knowledge to more complex items. Inspired by this, we study if similar generalization capabilities can also be achieved by robots. Our results indicate robots can learn generalizable grasping using randomly assembled objects that are composed from just four shape primitives: spheres, cuboids, cylinders, and rings. We show that training on these "toys" enables robust generalization to real-world objects, yielding strong zero-shot performance. Crucially, we find the key to this generalization is an object-centric visual representation induced by our proposed detection pooling mechanism. Evaluated in both simulation and on physical robots, our model achieves a 67% real-world grasping success rate on the YCB dataset, outperforming state-of-the-art approaches that rely on substantially more in-domain data. We further study how zero-shot generalization performance scales by varying the number and diversity of training toys and the demonstrations per toy. We believe this work offers a promising path to scalable and generalizable learning in robotic manipulation.

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing data-driven approaches. In this work, we propose a principled diffusion-based framework for learning physical systems from incomplete training samples. To this end, our method strategically partitions each such sample into observed context and unobserved query components through a carefully designed splitting strategy, then trains a conditional diffusion model to reconstruct the missing query portions given available contexts. This formulation enables accurate imputation across arbitrary observation patterns without requiring complete data supervision. Specifically, we provide theoretical analysis demonstrating that our diffusion training paradigm on incomplete data achieves asymptotic convergence to the true complete generative process under mild regularity conditions. Empirically, we show that our method significantly outperforms existing baselines on synthetic and real-world physical dynamics benchmarks, including fluid flows and weather systems, with particularly strong performance in limited and irregular observation regimes. These results demonstrate the effectiveness of our theoretically principled approach for learning and imputing partially observed dynamics.

Discovering the neural mechanisms underpinning cognition is one of the grand challenges of neuroscience. Addressing this challenge greatly benefits from specific hypotheses about the underlying neural network dynamics. However, previous approaches bridging neural network dynamics and cognitive behaviour required iterative refinement of network architectures and/or objectives for normative task optimization, resulting in a long, and mostly heuristic, human-in-the-loop design process. Here, we offer an alternative approach that automates this process by explicitly training recurrent neural networks (RNNs) to reproduce behaviour, including the same characteristic errors, that humans and animals produce in a cognitive task. Achieving this required two main innovations. First, as the amount of behavioural data that can be collected in experiments is often too limited to suffice for training RNNs, we use a non-parametric generative model of behavioural responses to produce surrogate data for training RNNs. Second, to capture all relevant statistical moments in the data, rather than a limited number of hand-picked low-order moments as in previous moment matching-based approaches, we developed a novel diffusion model-based approach for training RNNs. We chose a visual working memory (VWM) task as our test-bed, as behaviour in this task is well known to produce response distributions that are patently multimodal (due to so-called swap errors). The resulting network dynamics correctly predicted previously reported qualitative features of neural data recorded in macaques. Importantly, this was only the case when RNNs were trained using our approach, fitting the full richness of behavioural data -- and not when only a limited set of behavioural signatures were fitted, nor when RNNs were trained for task optimality instead of reproducing behaviour (as has been typical for RNNs used to generate dynamical hypotheses). Our model also makes novel predictions about the mechanism of swap errors, which can be readily tested in experiments. These results suggest that fitting rich patterns of behaviour provides a powerful way for the automatic discovery of neural network dynamics supporting important cognitive functions.

Transformers have demonstrated strong performance in time series forecasting, yet they often fail to capture the intrinsic structure of temporal data, making them susceptible to real-world noise and anomalies. Unlike in vision or language, the local geometry of temporal patterns is a critical feature in time series forecasting, but it is frequently disrupted by corruptions. In this work, we address this gap with two key contributions. First, we propose Local Geometry Attention (LGA), a novel attention mechanism theoretically grounded in local Gaussian process theory. LGA adapts to the intrinsic data geometry by learning query-specific distance metrics, enabling it to model complex temporal dependencies and enhance resilience to noise. Second, we introduce TSRBench, the first comprehensive benchmark for evaluating forecasting robustness under realistic, statistically-grounded corruptions. Experiments on TSRBench show that LGA significantly reduces performance degradation, consistently outperforming both Transformer and linear model. These results establish a foundation for developing robust time series models that can be deployed in real-world applications where data quality is not guaranteed. Our code is available at: https://anonymous.4open.science/r/LGA-5454.

Developing biologically plausible learning algorithms that can achieve performance comparable to error backpropagation remains a longstanding challenge. Existing approaches often compromise biological plausibility by entirely avoiding the use of spikes for error propagation or relying on both positive and negative learning signals, while the question of how spikes can represent negative values remains unresolved. To address these limitations, we introduce Bidirectional Spike-based Distillation (BSD), a novel learning algorithm that jointly trains a feedforward and a backward spiking network. We formulate learning as a transformation between two spiking representations (i.e., stimulus encoding and concept encoding) so that the feedforward network implements perception and decision-making by mapping stimuli to actions, while the backward network supports memory recall by reconstructing stimuli from concept representations. Extensive experiments on diverse benchmarks, including image recognition, image generation, and sequential regression, show that BSD achieves performance comparable to networks trained with classical error backpropagation. These findings represent a significant step toward biologically grounded, spike-driven learning in neural networks.

While brain-aligned large language models (LLMs) have garnered attention for their potential as cognitive models and for potential for enhanced safety and trustworthiness in AI, the role of this brain alignment for linguistic competence remains uncertain. In this work, we investigate the functional implications of brain alignment by introducing brain-misaligned models--LLMs intentionally trained to predict brain activity poorly while maintaining high language modeling performance. We evaluate these models on over 200 downstream tasks encompassing diverse linguistic domains, including semantics, syntax, discourse, reasoning, and morphology. By comparing brain-misaligned models with well-matched brain-aligned counterparts, we isolate the specific impact of brain alignment on language understanding. Our experiments reveal that brain misalignment substantially impairs downstream performance, highlighting the critical role of brain alignment in achieving robust linguistic competence. These findings underscore the importance of brain alignment in LLMs and offer novel insights into the relationship between neural representations and linguistic processing.

Modeling the temporal dynamics of the human brain remains a core challenge in computational neuroscience and artificial intelligence. Traditional methods often ignore the biological spike characteristics of brain activity and find it difficult to reveal the dynamic dependencies and causal interactions between brain regions, limiting their effectiveness in brain function research and clinical applications. To address this issue, we propose a Spike-based Digital Brain (Spike-DB), a novel fundamental model that introduces the spike computing paradigm into brain time series modeling. Spike-DB encodes fMRI signals as spike trains and learns the temporal driving relationships between anchor and target regions to achieve high-precision prediction of brain activity and reveal underlying causal dependencies and dynamic relationship characteristics. Based on Spike-DB, we further conducted downstream tasks including brain disease classification, abnormal brain region identification, and effective connectivity inference. Experimental results on real-world epilepsy datasets and the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset show that Spike-DB outperforms existing mainstream methods in both prediction accuracy and downstream tasks, demonstrating its broad potential in clinical applications and brain science research. Our code is available at https://github.com/UAIBC-Brain/Spike-DB.

Speech brain–computer interfaces (BCIs) aim to restore communication for people with paralysis by translating neural activity into text. Most systems use cascaded frameworks that decode phonemes before assembling sentences with an n-gram language model (LM), preventing joint optimization of all stages simultaneously. Here, we introduce an end-to-end BraIn-to-Text (BIT) framework that translates neural activity into coherent sentences using a single differentiable neural network. Central to our approach is a cross-task, cross-species pretrained neural encoder, whose representations transfer to both attempted and imagined speech. In a cascaded setting with an n-gram LM, the pretrained encoder establishes a new state-of-the-art (SOTA) on the Brain-to-Text ’24 and ’25 benchmarks. Integrated end-to-end with audio large language models (LLMs) and trained with contrastive learning for cross-modal alignment, BIT reduces the word error rate (WER) of the prior end-to-end method from 24.69% to 10.22%. Notably, we find that small-scale audio-LLMs markedly improve end-to-end decoding. Beyond record-setting performance, BIT aligns attempted and imagined speech embeddings to enable cross-task generalization. Altogether, our approach advances the integration of large, diverse neural datasets, paving the way for an end-to-end decoding framework that supports seamless, differentiable optimization.

Scientific discovery is increasingly constrained by costly experiments and limited budgets, making efficient optimization essential for AI for science. Bayesian Optimization (BO), while widely adopted for balancing exploration and exploitation, suffers from slow cold-start performance and poor scalability in high-dimensional settings, limiting its effectiveness in real-world scientific applications. To address these challenges, we propose LLM-Guided Bayesian Optimization (LGBO), the first LLM preference-guided BO framework that continuously integrates the semantic reasoning of large language models (LLMs) into the optimization loop. Unlike prior works that use LLMs only for warm-start initialization or candidate generation, LGBO introduces a region-lifted preference mechanism that embeds LLM-driven preferences into every iteration, shifting the surrogate mean in a stable and controllable way. Theoretically, we prove that LGBO is not perform significantly worse than standard BO in the worst case, while achieving significantly faster convergence when preferences align with the objective. Empirically, LGBO achieves consistent improvements across diverse dry benchmarks in physics, chemistry, biology, and materials science. Most notably, in a new wet-lab optimization of Fe–Cr battery electrolytes, LGBO reaches \textbf{90\% of the best observed value within 6 iterations}, whereas standard BO and existing LLM-augmented baselines require more than 10 iterations. Together, the results suggest that LGBO offers a promising direction for integrating LLMs into scientific optimization workflows.