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Long before the invention of writing, the very first detectable graphic productions of prehistoric humans were highly regular non-pictorial geometric signs such as parallel lines, zig-zags, triangular, or checkered patterns (Henshilwood et al., 2018; Waerden, 2012). Human cultures throughout the world compose complex figures using simple geometrical regularities such as parallelism and symmetry in their drawings, decorative arts, tools, buildings, graphics, and maps (Tversky, 2011). Cognitive anthropological studies suggest that, even in the absence of formal western education, humans possess intuitions of foundational geometric concepts such as points and lines and how they combine to form regular shapes (Dehaene et al., 2006; Izard et al., 2011). The scarce data available to date suggests that other primates, including chimpanzees, may not share the same ability to perceive and produce regular geometric shapes (Close and Call, 2015; Dehaene et al., 2022; Sablé-Meyer et al., 2021; Saito et al., 2014; Tanaka, 2007), though unintentional-but-regular mark-marking behavior has been reported in macaques (Sueur, 2025). Thus, studying the brain mechanisms that support the perception of geometric regularities may shed light on the origins of human compositionality and, ultimately, the mental language of mathematics. Here, we provide a first approach through the recording of functional MRI and magneto-encephalography signals evoked by simple geometric shapes such as triangles or squares. Our goal is to probe whether, over and above the pathways for processing the shapes of images such as faces, places, or objects, the regularities of geometric shapes evoke additional activity.

The present brain-imaging research capitalizes on a series of studies of how humans perceive quadrilaterals (Sablé-Meyer et al., 2021). In that study, we created 11 tightly matched stimuli that were all simple, non-figurative, textureless four-sided shapes, yet varied in their geometric regularity. The most regular was the square, with four parallel sides of equal length and four identical right angles. By progressively removing some of these features (parallelism, right angles, equality of length, and equality of angles), we created a hierarchy of quadrilaterals ranging from highly regular to completely irregular (Figure 1A). In a variety of tasks, geometric regularity had a large effect on human behavior. For instance, for equal objective amounts of deviation, human adults and children detected a deviant shape more easily among shapes of high regularity, such as squares or rectangles (<5% errors), than among irregular quadrilaterals (>40% errors). The effect appeared as a human universal, present in preschoolers, first-graders, and adults without access to formal western math education (the Himba from Namibia), and thus seemingly independent of education and of the existence of linguistic labels for regular shapes. Strikingly, when baboons were trained to perform the same task, they showed no such geometric regularity effect.

Baboon behavior was accounted for by convolutional neural network (CNN) models of object recognition, but human behavior could only be explained by appealing to a representation of discrete geometric properties of parallelism, right angle, and symmetry, in this and other tasks. We sometimes refer to this model as ‘symbolic’ because it relies on discrete, exact, rule-based features rather than continuous representations (Sablé-Meyer et al., 2022). In this representational format, geometric shapes are postulated to be represented by symbolic expressions in a ‘language-of-thought’, for example ‘a square is a four-sided figure with four equal sides and four right angles’ or equivalently by a computer-like program from drawing them in a Logo-like language (Sablé-Meyer et al., 2022).

We therefore formulated the hypothesis that, in the domain of geometry, humans deploy an additional cognitive process specifically attuned to geometric regularities. On top of the circuits for object recognition, which are largely homologous in human and non-human primates (Bao et al., 2020; Kriegeskorte et al., 2008b; Tsao et al., 2008), the human code for geometric shapes would involve a distinct ‘language of thought’, an encoding of discrete mathematical regularities and their combinations (Cavanagh, 2021; Dehaene et al., 2022; Fodor, 1975; Leeuwenberg, 1971; Quilty-Dunn et al., 2022; Sablé-Meyer et al., 2022; Sablé-Meyer et al., 2021).

This hypothesis predicts that the most elementary geometric shapes, such as a square, are not solely processed within the ventral and dorsal visual pathways, but may also evoke a later stage of geometrical feature encoding in brain areas that were previously shown to encode arithmetic, geometric, and other mathematical properties, that is the bilateral intraparietal, inferotemporal, and dorsal prefrontal areas (Amalric and Dehaene, 2016; Amalric and Dehaene, 2019). We hypothesized that (1) such cognitive processes encode shapes according to their discrete geometric properties including parallelism, right angles, equal lengths, and equal angles; (2) the brain compresses this information when those properties are more regularly organized, and thus exhibit activity proportional to minimal description length (Chater and Vitányi, 2003; Dehaene et al., 2022; Feldman, 2003); and (3) these computations occur downstream of other visual processes, since they rely on the initial output of visual processing pathways.

Here, we assessed these spatiotemporal predictions using two complementary neuroimaging techniques (functional MRI and magnetoencephalography [MEG]). We presented the same 11 quadrilaterals as in our previous research and used representational similarity analysis (Kriegeskorte et al., 2008a) to contrast two models for their cerebral encoding, based either on classical CNN models or on exact geometric features. In the fMRI experiment, we also collected simpler images contrasting the category of geometric shapes to other classical categories such as faces, places, or tools. Furthermore, to evaluate how early the brain networks for geometric shape perception arise, we collected those fMRI data in two age groups: adults and children in first grade (6 years old, this year was selected as it marks the first year French students receive formal instruction in mathematics). If geometric shape perception involves elementary intuitions of geometric regularity common to all humans, then the corresponding brain networks should be detectable early on.

All cells within a multicellular organism have the same genetic sequence up to a minuscule number of somatic mutations. Yet, many cell types exist with diverse morphological and functional traits. Epigenetics is an important regulator and driver of this diversity by allowing differences in cellular state and gene expression despite having the same genotype (Taherian Fard and Ragan, 2019). Indeed, cells traversing the trajectory from pluripotency through terminal differentiation have essentially the same genotype.

Epigenetic modifications such as post-translational modifications (PTMs) to histone proteins are involved in many vital regulatory processes influencing genomic accessibility, nuclear compartmentalization, and transcription factor binding and recognition (Reik et al., 2001; Kouzarides, 2007; Gibney and Nolan, 2010; Klemm et al., 2019; Hafner and Boettiger, 2023; Zhang and Reinberg, 2001). The Histone Code Hypothesis suggests that combinations of different histone PTMs specify distinct chromatin states, thereby regulating gene expression (Strahl and Allis, 2000; Jenuwein and Allis, 2001).

The field of epigenome editing has produced new tools for understanding the outcomes of epigenetic perturbations that promise to be useful for therapeutics by enabling fine-tuned control of gene expression (Matharu and Ahituv, 2020; Thakore et al., 2016; Goell and Hilton, 2021; Stricker et al., 2017). Currently, small molecule drugs are used to potently interfere with epigenetic regulation of gene expression. For example, Vorinostat inhibits histone deacetylases, thereby impacting the epigenetic landscape (Estey, 2013; Yoon and Eom, 2016). However, small molecules globally disrupt the epigenome and transcriptome and therefore are not suitable for targeting individual dysregulated genes nor clarifying epigenetic regulatory mechanisms (Swaminathan et al., 2007). Meanwhile, numerous tools have been designed to harness catalytically dead Cas9 (dCas9) to target epigenetic modifiers to DNA sequences encoded in guide RNAs (gRNAs) (Jinek et al., 2012; Mali et al., 2013; Hilton et al., 2015; Stepper et al., 2017; Kwon et al., 2017; Li et al., 2021). CRISPR-Cas9-based epigenome editing strategies facilitate unprecedented, precise control of the epigenome and gene activation, providing a path to epigenetic-based therapeutics (Cheng et al., 2019).

A major challenge for epigenome editing is designing gRNAs that can achieve a desired level of transcriptional or epigenetic modulation. Finding effective gRNAs currently typically requires expensive and low-throughput experimental strategies (Mohr et al., 2016; Liu et al., 2020; Mahata et al., 2023). An alternative approach would be to computationally model how epigenome editing impacts histone PTMs as well as how perturbing these PTMs would consequently impact gene expression.

To understand how histone PTMs relate to gene expression, large epigenetic and transcriptomic datasets are required. Advancements in high-throughput sequencing have allowed quantification of gene expression and profiling of histone PTMs. Large consortia have performed an extensive number of assays across a wide variety of cell types (The ENCODE Project Consortium, 2012; Kundaje et al., 2015; Barrett et al., 2012).

These include measurements of histone PTMs, transcription factor binding, gene expression, and chromatin accessibility. These data have enhanced our understanding of how histone PTMs and other chromatin dynamics impact transcriptional regulation (Keung et al., 2015; Rao et al., 2014; Holoch and Moazed, 2015).

Studying the function of these histone PTMs, however, has been largely limited to statistical associations with gene expression, which may not capture causal relationships (Karlić et al., 2010; Stillman, 2018; Singh et al., 2016). For example, deep learning has been successful in predicting gene expression from epigenetic modifications, such as transcription factor binding (Schmidt et al., 2017), chromatin accessibility (Schmidt et al., 2020), histone PTMs (Singh et al., 2016; Sekhon et al., 2018; Frasca et al., 2022; Singh et al., 2017; Hamdy et al., 2022; Chen et al., 2022), and DNA methylation (Zhong et al., 2019). However, these studies predict gene expression as binary levels instead of a continuous quantity. Finally, as statistical associations can be driven by non-causal mechanisms, it is unclear whether such computational models learn mechanistic, causal relationships between various epigenetic modifications and gene expression. Beyond modeling the relationship between histone PTMs and gene expression, to fully describe how a particular gRNA would affect gene expression, a model of how epigenome editing affects histone PTMs is also required. To our knowledge, there currently are no computational models that can accurately model, in silico, the impact of epigenome editing on histone PTMs.

Motivated by these observations, we explored models for how epigenome editing impacts histone PTMs as well as how histone PTMs impact gene expression. We used data available through ENCODE (Schreiber et al., 2020a; The ENCODE Project Consortium, 2012) to train a model of how histone PTMs impact gene expression. Our model is highly predictive of endogenous expression and learns an understanding of chromatin biology which is consistent with known patterns of various histone PTMs (Kimura, 2013). To test this model in the context of epigenome editing, we generated perturbation data using the dCas9-p300 histone acetyltransferase system (Hilton et al., 2015). The dCas9-p300 system is thought to act primarily through local acetylation of histone lysine residues, particularly histone subunit H3 lysine residue 27 (H3K27ac). Therefore, we modeled the impact of dCas9-p300 on the epigenome as a local increase in the H3K27ac profile near the target site; since the precise effect of these perturbations is unknown, we tried a variety of potential modification patterns. We then applied our trained model to predict the impact of these putative H3K27ac modifications on gene expression (Figure 1). We found that our models, which are designed to predict gene expression values, were effective in ranking relative fold-changes among genes in response to the dCas9-p300 system, achieving a Spearman’s rank correlation of ∼0.8. However, their performance in ranking fold-changes within individual genes was less successful when compared to the prediction of gene expression across cell types from their native epigenetic signatures. We offer possible explanations in the discussion section.