Artificial neural networks achieve impressive success in many vision tasks. Nevertheless, previous work has suggested that their representation of geometric shapes only partially captures the representations found in humans, who additionally require a symbolic "language of geometry". In this study, we evaluate the progress in this area by systematically comparing human performance in three geometric shape perception tests, with the predictions of recent Convolutional Neural Networks (CNNs) and Vision Transformers, varying in size, training datasets and training methods, to recognize and process geometric shapes and compare these representations to the ones found in humans. In two tasks probing quadrilateral and geometric shape perception, introduced by Sable-Meyer et al. (2022, 2026), recent neural networks exhibit representations similar to humans and predict human performance better than a symbolic model. In a third task, involving geometric drawings, the networks still fell short of human performance. Across the three experiments, the main factor driving similarity between human and neural network representations was the size of the training dataset, rather than a specific architecture or the number of parameters of the model. Together, our results show that a massive scaling-up of the training data helps neural networks approximate human-like representations of geometric shapes, but that they still fall short of fully capturing the human representations of geometric shape.

Data graphs are central to scientific communication, educational material, and news content, yet the building blocks of graph comprehension remain only partially understood. Our work provides an initial assessment of three questions: (1) how can the conceptual knowledge underlying graph understanding be characterized? (2) how do these abilities develop from childhood to adulthood? and (3) how are they related to perceptual abilities and higher-level graph understanding? We propose a hierarchical model of graphicacy organized around a set of conceptual components ranging from basic numerical and geometric precursors to the understanding of functional relationships. To test the model, 146 adults completed a novel conceptual graphicacy task, and a subset of 58 also completed a perceptual trend judgment task. Accuracy patterns across items and conceptual categories revealed systematic differences in component difficulty, broadly consistent with the proposed conceptual progression. Conceptual graphicacy skills, understood as the knowledge participants possess about graph conventions and relationships, were significantly predicted by perceptual sensitivity in detecting the trend in a scatterplot and with self-reported mathematical skills. To probe the development of conceptual graphicacy skills, 191 primary school children completed a shortened version of the task. Performance improved with age, revealing how the hierarchy of conceptual knowledge develops across school years. Conceptual graphicacy also significantly predicted performance on a higher-level graphical reasoning task in children. Together, these findings provide initial evidence linking perceptual, conceptual, and higher-level components of graphicacy within a common framework.

How does the developing brain, initially equipped only with elementary mathematical intuitions, acquire higher mathematical concepts? Through a longitudinal functional MRI study of children from preschool through first and second grade, we tracked how neural responses to mathematical and non-mathematical statements change in the first two years of formal schooling and use the data to evaluate several theories of developmental change. Before school, when listening to math statements, children already engage an adult-like cortical network, with partial specialization for geometry. Over the first two years of school, we observe an overall increase in math-related activation, a small recruitment of additional neural territory, reduced activation for facts that get better known, and a small overall increase in the dimensionality of representational space. fMRI responses to individual sentences suggest that these mechanisms, particularly in left inferior frontal gyrus and bilateral intraparietal sulcus, all contribute to children′s growing mastery of mathematical concepts. ### Competing Interest Statement The authors have declared no competing interest.

When does conscious access occur relative to sensory stimulation? Although perceptual experience is often assumed to track the continuous presence of sensory input, recent neurophysiological findings challenge this assumption by showing that prefrontal activity does not scale with stimulus duration. Interpreting these findings has been difficult because prior studies did not directly probe the temporal profile of conscious access itself. Here, we address this gap using the psychological refractory period (PRP) effect as a report-free, time-resolved marker of central-stage processing associated with conscious access. Across two dual-task experiments, we measured delays in auditory responses induced by visual stimuli of varying duration and task relevance, with auditory probes time-locked to stimulus onset and offset. Visual stimulus onset reliably induced a PRP effect, even for task-irrelevant stimuli that did not elicit overt responses, indicating transient conscious access independent of stimulus duration. Task relevance prolonged this access, whereas stimulus disappearance elicited a markedly weaker and less consistent PRP effect, contingent on stimulus duration. Participants showed limited introspective awareness of these delays. Reanalysis of intracranial EEG data revealed that prefrontal decoding dynamics mirrored the behavioral modulation of the PRP. Together, these findings show that conscious access is transient and context-dependent, rather than a continuous reflection of sensory input, establishing the PRP as a precise, report-free chronometric tool for studying the timing of conscious access.

Abstract Although the brain areas for language processing are well delimited, whether lexical-semantic and syntactic processes are spatially segregated remains debated. To clarify this issue, we conducted two experiments using 7-Tesla functional MRI in 20 participants performing: a functional localizer involving reading sequences of words of increasing linguistic complexity; and a presentation of short, semantically impoverished three-word mini-sentences, flashed in a single glance (e.g., “he does it”), whose grammaticality and syntactic complexity was manipulated through syntactic movement. Our results reveal two functionally dissociable sets of cortical patches within the language system: one sensitive to syntactic structure even in the absence of meaning, and the other involved in semantic composition. This dual-network architecture was consistently observed in the majority of participants, although its precise anatomical localization varied. The two types of voxels coexisted even within a given brain region of the Glasser atlas. Results were confirmed using subject-specific analyses and region-by-condition interactions, as voxels in those two systems displayed markedly different responses to mini-sentences. Thus, high-resolution functional imaging reveals a division of labor between syntactic and semantic composition within the classical language network.

The ventrolateral prefrontal cortex (vlPFC) is well known for its involvement in high-level functions such as cognitive control and language. However, vlPFC's role in visual processing is less clear. Here, we investigated how neuronal ensembles in the vlPFC dynamically encode different types of visual information. Using chronic recording of spiking activity, we investigated vlPFC's representational geometry in a macaque monkey passively viewing a large set of naturalistic images, and compared this to representations in deep neural networks (DNNs). We found that the vlPFC processes visual information in two stages. First, an "early" response from 50 to 90 ms after stimulus onset encodes the low spatial frequency component of an image. It contains sufficient information to form a coarse estimate of the position and category of a salient object. Then, from 100 ms on, the representational geometry changes and contains much richer information. This late period contains non-categorical information typically present in conscious experiences such as the orientation of a face and natural scenes in the background. The late window also enables sub-category identification, which is boosted by the low spatial category prior. These results suggest that the vlPFC has a dual role in natural vision: first forming fast low-spatial-frequency-based priors shaping feed-forward visual processing, and subsequently maintaining a detailed and rich representation of a visual scene.

COURS -PAROLE, MUSIQUE, MATHÉMATIQUES : LES LANGAGES DU CERVEAUDans la suite logique du cours 2015-2016 consacré à la représentation cérébrale des structures linguistiques, le cours 2016-2017 s'est intéressé aux autres facultés cognitives apparentées et qui semblent caractéristiques de l'espèce humaine.Notre espèce est la seule non seulement à s'exprimer sous forme de mots mais également à créer de vastes systèmes mathématiques, informatiques, ou musicaux.Dans tous ces domaines, l'espèce humaine présente une capacité singulière de créer et de manipuler des structures symboliques enchâssées : ce sont des « langages » dans l'acception la plus large de ce mot.On peut, dès lors, s'interroger : un mécanisme cérébral unique sous-tend-il ces différents langages ?Ou bien, l'évolution a-t-elle doté le cerveau humain de mécanismes distincts de représentation des structures symboliques, propres à chaque domaine ?La question des « langages du cerveau » joue un rôle central dans la réflexion contemporaine sur les origines de la singularité de notre espèce.Marc Hauser, avec Tecumseh Fitch et Noam Chomsky, postule que l'apparition de la faculté humaine de langage trouve son origine dans l'émergence d'une opération unique : la récursion, c'est-à-dire la faculté de produire des représentations complexes en les enchâssant les unes dans les autres, à l'infini.Cependant, la récursion est-elle une adaptation à

The Individual Brain Charting project focuses on collecting functional Magnetic Resonance Imaging data across a large set of cognitive tasks from a fixed cohort of participants, within a standardized environment. This approach seeks to obtain refined cognitive phenotyping of individual brains, uncovering details of their functional organization. We present an extension to the dataset, integrating data from eleven participants obtained at 3T, from a fixed environment to minimize inter-site and inter-subject variability. This release further enriches the cumulative coverage of psychological domains, while introducing new concepts. It includes tasks on mathematical processing, spatial navigation, emotion recognition and memory, proactive control, oddball detection, reward processing, reaction time, biological motion perception, gambling, scene processing and working memory. In total, 18 tasks with 180 contrasts were added, and 54 cognitive components were included in the description of the ensuing contrasts. As the dataset becomes larger, the collection of the corresponding topographies becomes more comprehensive, leading to enhanced brain-atlasing frameworks. Aligned with open-access and data-sharing standards, this dataset emphasizes transparency and collaborative research.

Recent research suggests that humans use language-like mental representations for many stimuli, from auditory sequences to visual shapes. However, evidence has been largely indirect, relying on stimulus compression as a proxy for internal representation. Using constituency tests, we probed representational structure in the domain of geometry more directly. Across three preregistered experiments (n= 136), we find robust evidence for tree structure in human adults’ shape representations. First, the same shape can receive different structural representations depending on how a preceding animation organizes it. Second, subparts of shapes are easier to detect when they belong to the same subtree than when spanning different subtrees. Third, shape fragments are easier to reconfigure the higher in the tree they are split. Unlike humans, state-of-the-art deep networks show no syntactic effects whatsoever. Thus, humans—and so far only humans—encode geometric shapes in hierarchical structures, mirroring the representations used in natural language processing.

The neural mechanisms by which the developing brain acquires higher mathematical concepts from elementary intuitions remain poorly understood. Through a large-scale longitudinal functional MRI study of children from preschool through first and second grade, we tracked how neural responses to mathematical and nonmathematical statements change in the first 2 y of formal schooling, and we used these data to evaluate several theories of developmental change. Before school, when listening to math statements, children already engaged an adult-like cortical network, with partial specialization for geometry. Over the first 2 y of school, we observed an overall increase in math-related activation, a small recruitment of additional neural territory, reduced activation for facts that get better known, and a small overall increase in the dimensionality of representational space. fMRI responses to individual sentences suggest that these mechanisms, particularly in left inferior frontal gyrus and bilateral intraparietal sulcus, all contribute to children's growing mastery of mathematical concepts.

The perception and production of regular geometric shapes, a characteristic trait of human cultures since prehistory, has unknown neural mechanisms. Behavioral studies suggest that humans are attuned to discrete regularities such as symmetries and parallelism and rely on their combinations to encode regular geometric shapes in a compressed form. To identify the brain systems underlying this ability, as well as their dynamics, we collected functional MRI in both adults and 6-year-olds, and magnetoencephalography data in adults, during the perception of simple shapes such as hexagons, triangles, and quadrilaterals. The results revealed that geometric shapes, relative to other visual categories, induce a hypoactivation of ventral visual areas and an overactivation of the intraparietal and inferior temporal regions also involved in mathematical processing, whose activation is modulated by geometric regularity. While convolutional neural networks captured the early visual activity evoked by geometric shapes, they failed to account for subsequent dorsal parietal and prefrontal signals, which could only be captured by discrete geometric features or by bigger deep-learning models of vision. We propose that the perception of abstract geometric regularities engages an additional symbolic mode of visual perception.

As you read this sentence, you integrate meanings of individual words into complex, higher-order representations. In addition to the core language network (LN), this dynamic process recruits other domain-general networks such as the default mode network (DMN), with which it partially overlaps anatomically but segregates from functionally. To evaluate interactions between LN and DMN, we extracted instantaneous frequency, power, and phase (4-30 Hz) from intracranial electrodes in 32 participants who read sentences and wordlists. We isolated a complex low-frequency modulation, most reliably measured as a ramping of instantaneous frequency in the alpha band throughout sentences, greater than wordlists, occurring robustly across both the LN and DMN. Granger causal networks demonstrate this coincided with ramping increases in alpha-band connectivity between and within DMN and LN. We suggest that alpha-band modulations index dynamic interactions between core LN and broader domain-general networks and may be crucial for higher order semantic integration and the derivation of crossmodal knowledge from the language domain.

Plato's Republic, Einstein's Theory of relativity, Vivaldi's Four Seasons are all remarkable examples of humans' unique ability to create and manipulate complex abstract structures, whether in language, mathematics, or music. Yet the mechanisms by which children develop such abstract thinking, and the role of education and structured experiences such as musical practice in shaping these abilities remains unclear. To explore these questions, we conducted cross-sectional behavioral experiments with 528 children aged 4 to 8, spanning four educational grades, half of whom participated in a violin training program, from age four. Two experiments examined how children encode, process, and compress auditory sequences and visual patterns, while a third examined their sensitivity to geometric regularities. Our results reveal the emergence of symbolic reasoning as early as the start of formal schooling, with deeper abstraction as a function of grade. By first grade, children encoded complex auditory sequences within a Language of Thought (LoT) similar to adults. Additionally, when confronted with quadrilaterals, children showed increasing sensitivity to geometric regularities, suggesting a developmental transition from perceptual to symbolic reasoning. However, we did not observe significant impact of musical practice on abstraction abilities across any of the domains tested. We discuss whether and how the impact of education and extracurricular activities such as music could be enhanced.

How do humans store sequences that far exceed working memory capacity? Using visuo-spatial and binary auditory sequences, we previously showed that a Language of Thought (LoT) architecture, in which simple primitives are recursively combined into hierarchical programs, enables efficient storage of structured sequences. Here we ask whether this principle extends to purely ordinal structure: sequences defined by how items repeat and in what order, as in AABBCCAABBCC, independently of their spatial content. Across three experiments, participants reproduced 12-item sequences of spatial locations with various ordinal structures. The minimal description length derived from the LoT model predicted recall accuracy with remarkable precision (r = .96), substantially outperforming Shannon entropy, Lempel-Ziv complexity, chunking models and subjective complexity ratings. Critically, fine-grained analyses of participants' inter-click intervals during reproduction revealed systematic slowdowns at the hierarchical boundaries predicted by the LoT programs, providing a behavioral signature of the underlying mental syntax. These results identify a compact vocabulary of mental primitives, repetition, mirroring, and interleaving, whose composition accounts for the symbolic compression of ordinal structures. For ordinal regularities, human sequence memory operates as a form of program induction, leveraging a domain-general capacity for hierarchical compression to encode complex structured information.

Conscious access is thought to involve two main stages: transient linear encoding of the objective sensory stimulus, followed by nonlinear bifurcation towards a sustained state of activity (ignition) encoding the subjective percept. To test this hypothesis, we recorded thousands of neurons in the prefrontal cortex (PFC) of monkeys trained to perform a sequence working memory (WM) task with masked visual stimuli of variable contrast, thus modulating their subjective visibility. PFC responses revealed the predicted sequence of linear and nonlinear processing stages as a function of stimulus contrast. Crucially, both stages were instantiated by orthogonal neural subspaces within the same PFC neurons. A shared entry subspace transiently encoded objective sensory inputs, while rank-ordered WM subspaces exhibited all-or-none bifurcations towards sustained states. On error and stimulus-absent trials, endogenous neural signals competed with objective inputs within the entry subspace, and only rank subspace ignition predicted upcoming responses. Routing from the entry to the WM subspace was not automatic but involved an active gating process which vanished when the animal was distracted. Thus, within local PFC, multiple neural subspaces implement the successive neural processes underlying conscious access.

Abstract How the brain encodes abstract concepts remains poorly understood. Current theories propose that, in brains and computers alike, word meanings are represented by vectors of neural activation whose similarities reflect semantic relationships. Here, we tested whether this hypothesis also applies to abstract concepts of elementary mathematics. We collected behavioral, 7 Tesla functional MRI and magneto-encephalography (MEG) data and used representational similarity analysis to ask where, when and how fifteen concepts of integers, fractions, and geometric shapes are encoded in the adult brain. Behavioral similarity ratings revealed a rich conceptual structure characterized by both categorical distinctions (numbers vs shapes, integers vs fractions), a numerical distance effect for integers, and systematic correspondences between items involving the same number (e.g. three, third, triangle). Functional MRI identified a bilateral cortical network whose neural encodings of concepts correlated with their semantic similarity, overlapping with classic math-responsive regions and encompassing IPS and ITG as well as dorsolateral prefrontal cortex (dlPFC). A double dissociation was observed, with a preference for arithmetic in the right anterior intraparietal sulcus (IPS), and for geometry in left inferior temporal gyrus (ITG) and bilateral posterior IPS. MEG revealed that a semantic neural code common to written words and symbols is activated by about 230 ms, again primarily distinguishing integers, fractions and geometry concepts. Together, these findings suggest that mathematical concepts are organized in the brain along both categorical and numerical dimensions, with overlapping but partially distinct sites supporting arithmetic and geometry domains.

In various cultures, across history and at many different spatial scales, humans produce a rich variety of geometric shapes. Recent work has put forward a concrete proposition for a Language of Thought (LoT) underlying the mental representation of geometric shapes in contemporary humans. Initial experiments, based on a comparison of baboon and human performance in an intruder task, suggested that this ability could be unique to humans. Here, to deepen our understanding of the evolutionary origins of geometric representations, we compared humans and baboons (Papio papio) in a delayed geometric match-to-sample task with a broad array of shapes. Crucially, the presentation speed was manipulated so that, on slow-paced trials, animals were given more time to understand the shapes. The shapes were sampled from our proposed LoT and spanned a range of predicted geometric complexity under that model. Although the overall pattern of behavior was still strikingly different in humans and baboons, when presentations were slower, we did find a small contribution of the LoT representations in baboons, though weaker than in humans. In both species, longer looking time increased the effect of the LoT-based predictor. While humans used the ability to self-pace to modulate their looking time, thus benefiting from longer exposure times for more complex shapes and rendering this geometric complexity effect visible, baboons did not.

Sentences in natural language have a hierarchical structure, that can be described in terms of nested trees. To compose sentence meaning, the human brain needs to link successive words into complex syntactic structures. However, such hierarchical-structure processing could co-exist with a simpler, shallower, and perhaps evolutionarily older mechanism for local, word-by-word sequential processing. Indeed, classic work from psycholinguistics suggests the existence of such non-hierarchical processing, which can interfere with hierarchical processing and lead to sentence-processing errors in humans. However, such interference can arise from two, non mutually exclusive, reasons: interference between words in working memory, or interference between local versus long-distance word-prediction signals. Teasing apart these two possibilities is difficult based on behavioral data alone. Here, we conducted a magnetoen-cephalography experiment to study hierarchical vs. sequential computations during sentence processing in the human brain. We studied whether the two processes have distinct neural signatures and whether sequential interference observed behaviorally is due to memory-based interference or to competing word-prediction signals. Our results show (1) a large dominance of hierarchical processing in the human brain compared to sequential processing, and (2) neural evidence for interference between words in memory, but no evidence for competing prediction signals. Our study shows that once words enter the language system, computations are dominated by structure-based processing and largely robust to sequential effects; and that even when behavioral interference occurs, it need not indicate the existence of a shallow, local language prediction system.