ICLR 2026 Papers

Canonicalization is a widely used strategy in equivariant machine learning, enforcing symmetry in neural networks by mapping each input to a standard form. Yet, it often introduces discontinuities that can affect stability during training, limit generalization, and complicate universal approximation theorems. In this paper, we address this by introducing *adaptive canonicalization*, a general framework in which the canonicalization depends both on the input and the network. Specifically, we present the adaptive canonicalization based on prior maximization, where the standard form of the input is chosen to maximize the predictive confidence of the network. We prove that this construction yields continuous and symmetry-respecting models that admit universal approximation properties. We propose two applications of our setting: (i) resolving eigenbasis ambiguities in spectral graph neural networks, and (ii) handling rotational symmetries in point clouds. We empirically validate our methods on molecular and protein classification, as well as point cloud classification tasks. Our adaptive canonicalization outperforms the three other common solutions to equivariant machine learning: data augmentation, standard canonicalization, and equivariant architectures.

Despite their impressive capabilities, LLMs exhibit a basic generalization failure known as the *Reversal Curse*, where they struggle to learn reversible factual associations. Understanding why this occurs could help identify weaknesses in current models and advance their generalization and robustness. In this paper, we conjecture that the Reversal Curse in LLMs is a manifestation of the long-standing *binding problem* in cognitive science, neuroscience and AI. Specifically, we hypothesize two primary causes of the Reversal Curse stemming from transformers' limitations in conceptual binding: the *inconsistency* and *entanglements* of concept representations. We perform a series of experiments that support these conjectures. Our exploration leads to a model design based on JEPA (Joint-Embedding Predictive Architecture) that for the first time breaks the Reversal Curse without side-stepping it with specialized data augmentation or non-causal masking, and moreover, generalization could be further improved by incorporating special memory layers that support disentangled concept representations. Our research opens up the broader fundamental challenge of designing models capable of learning systematic conceptual binding with less human scaffolding.

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are sensitive to the number of samples, i.e., the number of rows and columns of the sample matrix. We show that, in particular, the participation ratio of eigenvalues, a popular measure of global dimensionality, is highly biased with small sample sizes, and propose a bias-corrected estimator that is more accurate with finite samples and with noise. On synthetic data examples, we demonstrate that our estimator can recover the true known dimensionality. We apply our estimator to neural brain recordings, including calcium imaging, electrophysiological recordings, and fMRI data, and to the neural activations in a large language model and show our estimator is invariant to the sample size. Finally, our estimators can additionally be used to measure the local dimensionalities of curved neural manifolds by weighting the finite samples appropriately.

Sheaf Neural Networks (SNNs) are a powerful algebraic-topology generalization of Graph Neural Networks (GNNs), and have been shown to significantly improve our ability to model complex relational data. While the GNN literature proved that incorporating directionality can substantially boost performance in many real-world applications, no SNNs approaches are known with such a capability. To address this limitation, we introduce the Directed Cellular Sheaf, a generalized cellular sheaf designed to explicitly account for edge orientations. Building on it, we define a corresponding sheaf Laplacian, the Directed Sheaf Laplacian $L^{\widetilde{\mathcal{F}}}$, which exploits the sheaf's structure to capture both the graph’s topology and its directions. $L^{\widetilde{\mathcal{F}}}$ serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on twelve real-world benchmarks show that DSNN consistently outperforms many baseline methods.

Many AI models trained on natural images develop representations that resemble those of the human brain. However, the factors that drive this brain-model similarity remain poorly understood. To disentangle how the model, training and data independently lead a neural network to develop brain-like representations, we trained a family of self supervised vision transformers (DINOv3) that systematically varied these different factors. We compare their representations of images to those of the human brain recorded with both fMRI and MEG, providing high resolution in both spatial and temporal analyses. We assess the brain-model similarity with three complementary metrics focusing on overall representational similarity, topographical organization, and temporal dynamics. We show that all three factors - model size, training amount, and image type - independently and interactively impact each of these brain similarity metrics. In particular, the largest DINOv3 models trained with the most human-centric images reach the highest brain-similarity. This emergence of brain-like representations in AI models follows a specific chronology during training: models first align with the early representations of the sensory cortices, and only align with the late and prefrontal representations of the brain with considerably more training. Finally, this developmental trajectory is indexed by both structural and functional properties of the human cortex: the representations that are acquired last by the models specifically align with the cortical areas with the largest developmental expansion, thickness, least myelination, and slowest timescales. Overall, these findings disentangle the interplay between architecture and experience in shaping how artificial neural networks come to see the world as humans do, thus offering a promising framework to understand how the human brain comes to represent its visual world.

Transformers form the foundation of modern generative AI, yet their key–value memory lacks inherent spatial priors, constraining their capacity for spatial reasoning. In contrast, neuroscience points to the hippocampal–entorhinal system, where the medial entorhinal cortex provides structural codes and the hippocampus binds them with sensory codes to enable flexible spatial inference. However, existing hippocampus models such as the Tolman-Eichenbaum Machine (TEM) suffer from inefficiencies due to outer-product operations or context-length bottlenecks in self-attention, limiting their scalability and integration into modern deep learning frameworks. To bridge this gap, we propose mm-TEM, an efficient and scalable structural spatial memory model that leverages meta-MLP relational memory to improve training efficiency, form grid-like representations, and reveal an intriguing link between prediction horizon and grid scales. Extensive evaluation shows its good generalization on long sequences, large-scale environments, and multi-step prediction, with analyses confirming that its advantages stem from explicit understanding of spatial structures. Building on this, we introduce Hippoformer, which integrates mm-TEM with Transformer to combine structural spatial memory with precise working memory, achieving superior generalization in both 2D and 3D prediction tasks and highlighting the potential of hippocampal-inspired architectures for complex domains. Overall, Hippoformer represents a initial step toward seamlessly embedding structured spatial memory into foundation architectures, offering a potential scalable path to endow deep learning models with spatial intelligence.

In AI-assisted decision-making, human decision-makers finalize decisions by taking into account both their human confidence and AI confidence regarding specific outcomes. In practice, they often exhibit heterogeneous cognitive capacities, causing their confidence to deviate, sometimes significantly, from the actual label likelihood. We theoretically demonstrate that existing AI confidence adjustment objectives, such as *calibration* and *human-alignment*, are insufficient to ensure fair utility across groups of decision-makers with varying cognitive capacities. Such unfairness may raise concerns about social welfare and may erode human trust in AI systems. To address this issue, we introduce a new concept in AI confidence adjustment: *inter-group-alignment*. By theoretically bounding the utility disparity between human decision-maker groups as a function of *human-alignment* level and *inter-group-alignment* level, we establish an interpretable fairness-aware objective for AI confidence adjustment. Our analysis suggests that achieving utility fairness in AI-assisted decision-making requires both *human-alignment* and *inter-group-alignment*. Building on these objectives, we propose a multicalibration-based AI confidence adjustment approach tailored to scenarios involving human decision-makers with heterogeneous cognitive capacities. We further provide theoretical justification showing that our method constitutes a sufficient condition for achieving both *human-alignment* and *inter-group-alignment*. We validate our theoretical findings through extensive experiments on four real-world tasks. The results demonstrate that AI confidence adjusted toward both *human-alignment* and *inter-group-alignment* significantly improves utility fairness across human decision-maker groups, without sacrificing overall utility. *The implementation code is available at* https://anonymous.4open.science/r/FairHAI.

Synaptic plasticity is a fundamental substrate for learning and memory, where different synapse types exhibit distinct plasticity mechanisms. However, how functional behaviors emerge from heterogeneous synaptic plasticity mechanisms remains poorly understood. Here, we introduce a computational framework that harnesses Darwinian evolutionary principles to discover biologically plausible, heterogeneous synaptic plasticity rules within a biologically realistic model of the mouse primary visual cortex. Specifically, we parameterize several key factors related to synaptic plasticity, including presynaptic and postsynaptic spikes, their associated eligibility traces, and neuromodulatory signals. By integrating these factors via a truncated Taylor expansion, we construct a large-scale search space of candidate plasticity rules, with each rule containing over 2.6k optimizable parameters. Each rule is subsequently evaluated on both cross-domain visual task performance and biological validity. Leveraging a multi-objective evolutionary algorithm, we effectively navigate this high-dimensional search space to identify plasticity rules that are both biologically plausible and yield high task performance. We uncover diverse families of high-performing plasticity rules that achieve similar behavioral outcomes despite markedly different mathematical formulations, suggesting that real-world synaptic learning mechanisms may exhibit computational degeneracy. We further show that these biologically plausible rules are not only robust across network scales but also enable few-shot learning, offering a computational explanation for the emergence of innate ability.

Neuroscience has uncovered a fundamental mechanism of our social nature: human brain activity becomes synchronized with others in many social contexts involving interaction. Traditionally, social minds have been regarded as an exclusive property of living beings. Although large language models (LLMs) are widely accepted as powerful approximations of human behavior, with multi-LLM system being extensively explored to enhance their capabilities, it remains controversial whether they can be meaningfully compared to human social minds. In this work, we explore neural synchrony between socially interacting LLMs as an empirical evidence for this debate. Specifically, we introduce neural synchrony during social simulations as a novel proxy for analyzing the sociality of LLMs at the representational level. Through carefully designed experiments, we demonstrate that it reliably reflects both social engagement and temporal alignment in their interactions. Our findings indicate that neural synchrony between LLMs is strongly correlated with their social performance, highlighting an important link between neural synchrony and the social behaviors of LLMs. Our work offers a new perspective to examine the "social minds" of LLMs, highlighting surprising parallels in the internal dynamics that underlie human and LLM social interaction.

The brain interprets visual information through learned regularities, a computation formalized as performing probabilistic inference under a prior. The visual cortex establishes priors for this inference, some of which are delivered through widely established top-down connections that inform low-level cortices about statistics represented at higher levels in the cortical hierarchy. While evidence supports that adaptation leads to priors reflecting the structure of natural images, it remains unclear if similar priors can be flexibly acquired when learning a specific task. To investigate this, we built a generative model of V1 that we optimized for performing a simple discrimination task and analyzed it along with large scale recordings from mice performing an analogous task. In line with recent successful approaches, we assumed that neuronal activity in V1 can be identified with latent posteriors in the generative model, providing an opportunity to investigate the contributions of task-related priors to neuronal responses. To obtain a flexible test bed for this analysis, we extended the VAE formalism so that a task can be flexibly and data-efficiently acquired by reusing previously learned representations. Task-specific priors learned by this Task-Amortized VAE were used to investigate biases in mice and model when presenting stimuli that violated the trained task statistics. Mismatch between learned task statistics and incoming sensory evidence showed signatures of uncertainty in stimulus category in the posterior of TAVAE, reflecting properties of bimodal response profile in V1 recordings. The task-optimized generative model could account for various characteristics of V1 population activity, including within-day updates to the population responses. Our results confirm that flexible task-specific contextual priors can be learned on-demand by the visual system and can be deployed as early as the entry level of the visual cortex.

Alzheimer’s Disease (AD) is a progressive neurodegenerative disorder and a leading cause of dementia worldwide. Accurate diagnosis requires integrating diverse patient data modalities. With the rapid advancement of foundation models in neurobiology and medicine, integrating foundation models from various modalities has emerged as a promising yet underexplored direction for multi-modal AD diagnosis. A central challenge is enabling effective interaction among these models without disrupting the robust, modality-specific representations learned from large-scale pretraining. To address this, we propose a novel multi-modal framework for AD diagnosis that enables joint interaction among uni-modal foundation models through modality-anchored interaction. In this framework, one modality and its corresponding foundation model are designated as an anchor, while the remaining modalities serve as auxiliary sources of complementary information. To preserve the pre-trained representation space of the anchor model, we propose modality-aware Q-formers that selectively map auxiliary modality features into the anchor model’s feature space, enabling the anchor model to jointly process its own features together with the seamlessly integrated auxiliary features. We evaluate our method on AD diagnosis and progression prediction across four modalities: sMRI, fMRI, clinical records, and genetic data. Our framework consistently outperforms prior methods in two modality settings, and further demonstrates strong generalization to external datasets and other neurodegenerative diseases such as Parkinson’s disease.

The classical optimal transport such as Kantorovich's optimal transport and partial optimal transport could be too restrictive in applications due to the full-mass or fixed-mass preservation constraints. To remedy this limitation, we propose elastic optimal transport (ELOT) which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It aims to answer the problem of how to transport the probability mass adaptively between probability distributions, which is a fundamental topic in various areas of artificial intelligence. The strength of elastic optimal transport is its capability to transport adaptive-mass in the light of the geometry structure of the problem itself. As an application example in machine learning, we apply elastic optimal transport to both unsupervised domain adaptation and partial domain adaptation tasks. It adaptively transports masses from source domain to target domain by taking domain shift into consideration and respecting the ubiquity of noises or outliers in the data, in order to improve the generalization performance. The experiment results on the benchmarks show that ELOT significantly outperforms the state-of-the-art methods. As a powerful distribution matching tool, elastic optimal transport might be of interests to the broad areas such as artificial intelligence, healthcare, physics, operations research, urban science, etc. The source code is available in the supplementary material.

State-of-the-art machine learning often follows a two-stage process: $(i)$ pre-training on large, general-purpose datasets; $(ii)$ fine-tuning on task-specific data. In fine-tuning, selecting training examples that closely reflect the target distribution is crucial. However, it is often the case that only a few samples are available from the target distribution. Existing data selection methods treat these target samples as a validation set and estimate the effect of adding or removing a single sample from the training pool by performing inference on the validation set. We propose a simpler and faster alternative that inverts the usual role of train and validation: we perform inference on the training pool before and after fine-tuning on the validation set. We then select samples whose predictions change the most. Our key insight is that the training samples most affected by fine-tuning on a small validation set tend to be the most beneficial for reducing test loss on the target distribution. Experiments on instruction tuning and named entity recognition tasks show that, in most cases, our method achieves lower test log-loss than state-of-the-art approaches. We support our findings with theoretical analysis.

When reading, we often have specific information that interests us in a text. For example, you might be reading this paper because you are curious about LLMs for eye movements in reading, the experimental design, or perhaps you wonder ``This sounds like science fiction. Does it actually work?''. More broadly, in daily life, people approach texts with any number of text-specific goals that guide their reading behavior. In this work, we ask, for the first time, whether open-ended reading goals can be automatically decoded solely from eye movements in reading. To address this question, we introduce goal decoding tasks and evaluation frameworks using large-scale eye tracking for reading data in English with hundreds of text-specific information seeking tasks. We develop and compare several discriminative and generative multimodal text and eye movements LLMs for these tasks. Our experiments show considerable success on the task of selecting the correct goal among several options, and even progress towards free-form textual reconstruction of the precise goal formulation. These results open the door for further scientific investigation of goal driven reading, as well as the development of educational and assistive technologies that will rely on real-time decoding of reader goals from their eye movements.

Molecular dynamics (MD) simulations underpin modern computational drug discovery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need for repeated quantum-mechanical force calculations, enabling significant speedups over conventional pipelines. Yet many such methods typically enforce strict equivariance and rely on sequential rollouts, thus limiting their flexibility and simulation efficiency. They are also commonly single-task, trained on individual molecules and fixed time frames, which restricts generalization to unseen compounds and extended timesteps. To address these issues, we propose Atomistic Transformer Operator for Molecules (ATOM), a pretrained transformer neural operator for multi-task molecular dynamics. ATOM adopts a quasi-equivariant design that does not require an explicit molecular graph and employs a temporal attention mechanism to enable accurate, parallel decoding of multiple future states. To support operator pretraining across chemicals and timescales, we curate TG80, a large, diverse, and numerically stable MD dataset with over 2.5 million femtoseconds of trajectories across 80 compounds. ATOM achieves state-of-the-art performance on established single-task benchmarks, such as MD17, RMD17, and MD22. After multi-task pretraining on TG80, ATOM shows exceptional zero-shot and robust generalization to unseen molecules across varying time horizons. We believe ATOM represents a significant step toward accurate, efficient, and transferable molecular dynamics models.

Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student attains a low-rank structure in its first-layer weights when trained with stochastic gradient descent (SGD) and a strong regularizer. This structural property is known to reduce sample complexity of generalization. Indeed, in a second step, the same authors establish algorithm-specific learning guarantees under additional assumptions. In this paper, we focus exclusively on the structure discovery aspect and study it under weaker assumptions, more specifically: we allow (a) NNs of arbitrary size and depth, (b) with all parameters trainable, (c) under any smooth loss function, (d) tiny regularization, and (e) trained by any method that attains a second-order stationary point (SOSP), e.g. perturbed gradient descent (PGD). At the core of our approach is a key $\textit{derandomization}$ lemma, which states that optimizing the function $E_{x} \left[g_{\theta}(Wx + b)\right]$ converges to a point where $W = 0$, under mild conditions. The fundamental nature of this lemma directly explains structure discovery and has immediate applications in other domains including an end-to-end approximation for MAXCUT, and computing Johnson-Lindenstrauss embeddings.

The Bayesian brain hypothesis has been a leading theory in understanding perceptual decision-making under uncertainty. While extensive psychophysical evidence supports the notion of the brain performing Bayesian computations, how uncertainty information is encoded in sensory neural populations remains elusive. Specifically, two competing hypotheses propose that early sensory populations encode either the likelihood function (exemplified by probabilistic population codes) or the posterior distribution (exemplified by neural sampling codes) over the stimulus, with the key distinction lying in whether stimulus priors would modulate the neural responses. However, experimentally differentiating these two hypotheses has remained challenging, as it is unclear what task design would effectively distinguish the two. In this work, we present an information-theoretical framework for optimizing the task stimulus distribution that would maximally differentiate competing probabilistic neural codes. To quantify how distinguishable the two probabilistic coding hypotheses are under a given task design, we derive the *information gap*---the expected performance difference when likelihood versus posterior decoders are applied to neural populations---by evaluating the KL divergence between the true posterior and a task-marginalized surrogate posterior. Through extensive simulations, we demonstrate that the information gap accurately predicts decoder performance differences across diverse task settings. Critically, maximizing the information gap yields stimulus distributions that optimally differentiate likelihood and posterior coding hypotheses. Our framework enables principled, theory-driven experimental designs with maximal discriminative power to differentiate probabilistic neural codes, advancing our understanding of how neural populations represent and process sensory uncertainty.

Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries. The mathematical essence of this phenomenon is that a symmetric input, after being processed by an equivariant map, experiences an increase in symmetry. While prior research has documented symmetry increase in specific cases, a rigorous understanding of its underlying causes and general reduction strategies remains lacking. In this paper, we provide a detailed and in-depth characterization of symmetry increase together with a principled framework for its reduction: (i) For any given feature space and input symmetry group, we prove that the increased symmetry admits an infimum determined by the structure of the feature space; (ii) Building on this foundation, we develop a computable algorithm to derive this infimum, and propose practical guidelines for feature design to prevent harmful symmetry increases. (iii) Under standard regularity assumptions, we demonstrate that for most equivariant maps, our guidelines effectively reduce symmetry increase. To complement our theoretical findings, we provide visualizations and experiments on both synthetic datasets and the real-world QM9 dataset. The results validate our theoretical predictions.

Formulaic alpha factor mining (FAFM) is a central problem in quantitative investment, where interpretable formulas are designed to extract predictive signals from historical financial series. With the emergence of large language models (LLMs), recent studies have begun to explore their roles in FAFM, yet their capabilities across different tasks and configurations remain unclear. In this work, we introduce AlphaBench, the first systematic benchmark for evaluating LLMs in FAFM. AlphaBench covers three core tasks, including factor generation, factor evaluation, and factor searching, which are all popular tasks integrated in the workflow of quantitative researchers. Beyond task-level evaluation, we further analyze how different LLM settings, including model type, prompting paradigm, and reasoning strategy, influence performance. Our experiments on a range of open-source and closed-source models reveal that LLMs hold strong potential in automating factor mining, while also facing persistent challenges in robustness, search efficiency, and practical usability. The project is available at: https://alphabench.cc/