Computational constraints underlying shape and texture functional domain organization in macaque V4.

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Published in final edited form as: Cereb Cortex. 2026 Feb 9;36(2):bhaf345. doi: 10.1093/cercor/bhaf345 Search in PMC Search in PubMed View in NLM Catalog Add to search Computational constraints underlying shape and texture functional domain organization in macaque V4 Dunhan Jiang Dunhan Jiang 1 Ray and Stephanie Lane Computational Biology Department, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States Find articles by Dunhan Jiang 1 , Tianye Wang Tianye Wang 2 School of Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 3 Peking-Tsinghua Center for Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 4 IDG/McGovern Institute for Brain Research, Peking University, Yiheyuan Rd, 100871, Beijing, China 5 Key Laboratory of Machine Perception (Ministry of Education), Peking University, Yiheyuan Rd, 100871, Beijing, China Find articles by Tianye Wang 2, 3, 4, 5 , Yingjue Bian Yingjue Bian 6 College of Engineering, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States Find articles by Yingjue Bian 6 , Shiming Tang Shiming Tang 2 School of Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 3 Peking-Tsinghua Center for Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 4 IDG/McGovern Institute for Brain Research, Peking University, Yiheyuan Rd, 100871, Beijing, China 5 Key Laboratory of Machine Perception (Ministry of Education), Peking University, Yiheyuan Rd, 100871, Beijing, China Find articles by Shiming Tang 2, 3, 4, 5 , Tai Sing Lee Tai Sing Lee 7 Computer Science Department and Neuroscience Institute, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States Find articles by Tai Sing Lee 7, * Author information Copyright and License information 1 Ray and Stephanie Lane Computational Biology Department, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States 2 School of Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 3 Peking-Tsinghua Center for Life Sciences, Peking University, Yiheyuan Rd, 100871, Beijing, China 4 IDG/McGovern Institute for Brain Research, Peking University, Yiheyuan Rd, 100871, Beijing, China 5 Key Laboratory of Machine Perception (Ministry of Education), Peking University, Yiheyuan Rd, 100871, Beijing, China 6 College of Engineering, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States 7 Computer Science Department and Neuroscience Institute, Carnegie Mellon University, Forbes Avenue, 15213, Pennsylvania, United States * Tai Sing Lee. [email protected] Author contributions statement D.J., S.T. and T.S.L. conceived the experiment, D.J., T.W. and Y.B. conducted the experiment(s), D.J., T.W. and Y.B. analyzed the results. D.J. and T.S.L. wrote and reviewed the manuscript. All codes are available at: https://github.com/777dunhan/topoV4 . PMC Copyright notice PMCID: PMC13070204  NIHMSID: NIHMS2159362  PMID: 41701643 The publisher's version of this article is available at Cereb Cortex Abstract V4, an intermediate visual area in the ventral pathway of the primate visual system, is known to contain neurons selective to visual stimulus attributes of intermediate complexity. Recent studies have shown that macaque V4 is organized into neuronal columns, each tuned to specific natural image features, and topologically arranged across the cortical surface to form functionally specialized domains. Using digital twins of V4 constructed from a large-scale wide-field imaging dataset, we demonstrate that shape- and texture-preferring neurons — previously identified in single-unit studies — are spatially clustered into functional domains. The segregated spatial organization suggests the existence of parallel modules for surface and boundary processing. Unlike artificial neural networks trained for ImageNet classification, which exhibit a strong texture bias, we find that V4 cortical columns and functional domains are more evenly balanced between shape and texture preferences. Finally, we show that computational constraints of feature similarity and retinotopy constraints are necessary and sufficient to explain many observed properties of the organization of the V4 topological map of natural image feature preferences. Keywords: deep neural network, macaque V4 organization, retinotopic structure, self-organizing map, shape and texture tuning Introduction The ventral pathway of the hierarchical visual system in primates extracts a variety of visual attributes ( Kravitz et al., 2013 ) to support object recognition ( DiCarlo et al., 2012 ). Area V4, an intermediate stage in this hierarchical pathway, contains neurons selective for spatial frequency ( Lu et al., 2018 ; Zhang et al., 2023 ), color ( Liu et al., 2020 ), orientation ( Tanigawa et al., 2010 ), curvature ( Hu et al., 2020 ) and figure ground segregation ( Roe et al., 2012 ). Meanwhile, neuronal groups are independently tuned to object surface texture ( Cox et al., 2013 ; Okazawa et al., 2014 ; Kim et al., 2022 ) and boundary shape ( Pasupathy and Connor, 2001 , 2002 ; Nandy et al., 2013 ; Jiang et al., 2021 ), highlighting their distinct functionality ( Kim et al., 2019 ; Pasupathy et al., 2019 ). Recent advances utilizing deep learning methods show that V4 neurons are not confined to encoding simple visual attributes; instead, they respond to complex attributes arising from natural image statistics ( Abbasi-Asl et al., 2018 ). V4 neurons with multifaceted feature selectivity are spatially organized into cortical columns ( Willeke et al., 2023 ). Our earlier wide-field calcium imaging study ( Wang et al., 2024 ) obtained pixel wise cortical responses of a large superficial layer of V4, corresponding to part of the lower right visual field. Each pixel contains roughly a hundred neurons and covers a surface area of 90μm by 90μm, comparable to that of a canonical column, such as a V1 orientation column. Henceforth, we call each pixel a column. Each column exhibits distinct natural image selectivity. Similarly tuned columns cluster into functional domains ( Fig. 1A - D ), revealing a topological map of natural image feature preferences. In this paper, we aim to identify computational principles that explain the topographical organization of these functional domains of various natural image preferences. Fig. 1. Open in a new tab A. The V4 digital twin is a deep learning model that predicts monkey V4 neuronal column response to images obtained by calcium imaging. This image preference map shows 3048 V4 columns’ most preferred 9 images out of 50k color natural images. B. Panel A white box zoom-in. C. V4 digital twin shape and texture image preference map. Each V4 column shows its most preferred 9 images out of a set of 816 synthetic shape and texture images. D. Panel C white box zoom-in. E. V4 feature dispersity map and example natural images associated with different dispersity values. High dispersity columns prefer dispersed texture features. Low dispersity columns prefer localized shape features. F. RSOM simulated cortical map (60 by 60 units). Each unit learns a retinotopic position and responses to 50k images (tuning) whose most preferred nine images are shown. G. Panel F white box zoom-in. H. RSOM connects to V4 column image space. Each column consists of a 50k dimension tuning and a retinotopic position. There exists a spectrum of neuronal preferences for natural image features. Wang et al. ( Wang et al., 2024 ) introduced a measure termed dispersity to characterize this spectrum along a certain dimension (1E). Neurons with high dispersity prefer features that are broadly distributed across their receptive fields. Neurons with low dispersity prefer more localized features. Perceptually, high-dispersity neurons tend to prefer patterns associated with surface texture properties, whereas low-dispersity neurons tend to prefer patterns more related to shapes and forms such as curves and corners. However, a direct link between the dispersity measure and shape–texture preferences has not been established. Here, we establish this connection by performing in-silico neurophysiological experiments using shape and texture stimuli previously employed in V4 electrophysiological study ( Kim et al., 2019 ). We observe that neurons with similar dispersity cluster into domains, with regions processing surface texture properties interleaved with those encoding boundary shapes and object parts in the topological map ( Fig. 1C & D ). This raises the question: what computational constraints and key factors drive the emergence of this interleaved organization of high- and low-dispersity functional domains across the V4 cortical map? No computational models of V4 topological organization have been rigorously evaluated and accepted, largely because prior data on natural image preferences was lacking. A recent deep residual network coupled with a spatial loss constraint, called TDANN ( Margalit et al., 2024 ), does have a presumed V4 layer, though it has not been evaluated against empirical data. Models of topological organization in visual areas before and after V4 along the ventral visual pathway can provide insight into the key factor underlying topological organization in V4. In macaque V1, neurons with similar orientation-selectivity cluster together to form pinwheel structures on a continuous map, allowing processing modules known as hyper-columns to be organized under an innate retinotopic structure ( Arcaro and Livingstone, 2017a ). As visual processing advances along this hierarchy, receptive fields expand, and neuronal tuning evolves to encode increasingly global attributes. This progression results in a critical trade-off: some visual attributes attain higher invariance, while others specialize further. At the apex of this hierarchy, in the inferotemporal cortex (ITC), neurons encoding related attributes cluster into functional domains ( Downing et al., 2006 ; Bao et al., 2020 ; Doshi and Konkle, 2023 ), dedicated to categories such as object size ( Konkle and Oliva, 2012 ), animacy ( Konkle and Caramazza, 2013 ), scenes ( Arcaro and Livingstone, 2017b ), and faces ( McGugin et al., 2012 ; Janssens et al., 2014 ), with reduced retinotopic constraints ( Levy et al., 2001 ; Hasson et al., 2002 ; Arcaro et al., 2009 ). Area V4, with its unique position along this hierarchy and distinct tuning, must integrates its preferred attributes into a coherent topological map ( Fize et al., 2003 ). We investigate the computational constraints required to reproduce the V4 topological map using a self-organizing map ( Kohonen, 1990 ). Our results show that a balance between feature-tuning similarity and retinotopic constraints is essential for capturing key properties of the V4 map, including (1) the relative positioning of distinct functional domains, (2) the simultaneous accommodation of both a continuous feature map and a retinotopic map, and (3) the spatial clustering of neurons tuned to surface texture (high-dispersity) versus shape properties (low-dispersity). We further examine the TDANN ( Margalit et al., 2024 ) putative V4 map and find it diverging substantially from the observed V4 organization, likely due to the disproportionately strong texture bias displayed in neural networks, including TDANN. In contrast, macaque V4 exhibits a more balanced representation of shape and texture tuning. This discrepancy highlights the critical role of neuronal tuning preferences in shaping topological maps. Our work underscores the importance of natural image feature preferences, tuning similarity, and retinotopic constraints in shaping the V4 functional map. We establish a link between dispersity and shape–texture preferences, revealing the interleaved functional domains that support the processing of surface textures and boundary shapes in V4. Materials and Methods Self-organizing maps We implement the Kohonen Self-Organizing Map (SOM) in PyTorch to investigate the computational constraints governing the development of the Macaque V4 topological map of natural image preferences. We explored two variants, both of 60 x 60 units. The first map (SOM) learns its weight vector ( w x h x f : 60 x 60 x 50000 ) from 3048 V4 column responses to 50k images, constrained only by tuning similarity. Another RSOM (retinotopically constrained SOM) incorporates a retinotopic vector (weighted polar angle and eccentricity) concatenated with the 50k-dimensional image response vector (weight vector of 60 x 60 x 50002) to allow dual similarity constrains. SOM and RSOM training Each SOM/RSOM weight is randomly initialized. During each training forward pass, SOM unit that best matches the input vector (one V4 column response vector) is identified as the best matching unit (BMU, Equation 1 , W = 1 ). For the RSOM, the first 50k elements use W = 1 , while two retinotopic terms use W = 125 . All units then update their weights using a Gaussian neighborhood function ( Equation 2 ), such that units closer to the BMU are adjusted more strongly toward the input vector than distant units. The neighborhood width σ t starts large and gradually decays over training, while the learning rate remains constant ( Equation 3 ). Each simulated map is trained for 120 epochs, with each epoch iterating over all 3048 V4 columns. BMU = arg min w , h ∑ f = 0 f = 50000 W ∗ ( input f − weight ( w , h ) , f ) 2 (1) η t = e − Dist ( BMU ( w , h ) , Unit ( i , j ) ) 2 2 σ t 2 (2) (R)SOM w = (R)SOM w + ( input − (R)SOM w ) ∗ ( α ∗ η t ) (3) Shape and texture experiments To examine the relationship between shape–texture preference and feature dispersity, we replicate the neurophysiological experiment Kim et al. (2019) of 92 shape and 112 texture images to probe V4 column responses in the V4 digital twin. Rotation augmentation at 0°, 90°, 180°, and 270° yield 816 stimuli. Each resized image is centered within a V4 column’s estimated receptive field to obtain its activation. For each V4 column, the proportion of texture stimuli within its top 15% preferred images served as an index of texture-over-shape preference, which correlates with V4 column’s feature dispersity across the population (0.60 Pearson correlation). We obtain each TDANN layer3.1 (V4) and layer4.0 (ITC) unit’s activation to these 816 images by centering each resized image in the target unit’s theoretical receptive field (RF). This RF center is derived from the TDANN convolution structure. Its side length equals three times the mean of the target unit’s estimated receptive field fitted elliptical Gaussian Sigmas (see feature attribution below). We use the most preferred nine images of every map column / pixel to determine its texture / shape preference type, a surrogate for texture preference to be compared against dispersity results. Feature attribution and dispersity analysis To quantify image selectivity of V4 columns along the spectrum from shape to texture, we develop the feature dispersity measurement ( Wang et al., 2024 ). We perform feature attribution analysis on TDANN ( Margalit et al., 2024 ) target units using the SmoothGrad-Square ( Smilkov et al., 2017 ; Hooker et al., 2019 ) method that introduces random noise to augment an input image into a batch of 20 noisy images before back-propagating the target unit activation for a gradient heatmap. For a target unit, we compute an averaged gradient heatmap from its most preferred 1k images (out of 50k), with each image’s heatmap normalized and scaled to sum up to the unit activation. The aggregated heatmap is fitted with an elliptical Gaussian with x- and y-axis Sigmas. For a unit, its receptive field is defined as the area within the fitted Gaussian’s half-maximum contour. We conduct content removal test ( Wang et al., 2024 ) on each target unit’s 25 most preferred images. Each image has its key area, K pixels with the highest gradient heatmap values, preserved or occluded. As K increases, target unit responses to key area preserved images increase, while responses to key area occluded images decrease. The particular K that produces the same response is called the critical key area, which divided by the receptive field area is the feature dispersity, a measure that quantifies the level of dispersion of preferred features of a target unit within its receptive field. Because natural image stimuli are cropped to create round apertures at the center with soft fade-off, we only compute dispersity values for TDANN units at the center of every feature map for every layer, which shares its dispersity with all other units in the same channel. High-dispersity domain fragmentation We compute Fano factor to characterize the degree of high-dispersity domain fragmentation in the V4 and our simulated maps. For a feature dispersity map, all units are hierarchically clustered into high- or low-dispersity types. 1000000 square neighborhoods are randomly sampled within the map space, each recording the number of high-dispersity columns / units. The variance of these numbers over their mean is the Fano factor that characterizes how spatially fragmented or clustered are high-dispersity units organized in cortical maps. RSOM unit tuning decomposition There are 16 functional domains in the V4 and simulated maps. Each domain identifies 20 images that occur most frequently among all units’ top nine preferred images (from 50k images). For each domain, we then select an example unit—the unit exhibiting the strongest response to these 20 images—and extract its responses to its top 1000 preferred images. We train a LASSO model to fit this response vector as a weighted linear combination of responses from 3048 V4 columns to exactly these images ( Equation 4 ). The loss is a mean squared error plus another L1 punishment on all weights, multiplied by 0.01 to control this penalty. Each model is trained with a learning rate of 0.05 for 7500 epochs, giving a final loss of around 0.01. representative- unit top 1 k = ∑ i = 1 3048 w i ⋅ column- i top 1 k (4) Results Key characteristics of the V4 topological map In our earlier work ( Wang et al., 2024 ), we trained a deep convolution neural network from V4 responses to 19.9k natural images, obtained by wide field calcium imaging. This model, as a digital twin of the macaque V4, predicts 3048 V4 imaged pixel responses to 50k ImageNet color natural images ( Deng et al., 2009 ). Each imaged pixel corresponds to the superficial layer of 90μm x 90μm V4 cortical tissues, approximating the scale of a single cortical column. We hence refer to each V4 imaged pixel as a V4 column. These columns are arranged within a cortical map covering roughly 7 mm × 6 mm cortical surface, with receptive fields positioned in the lower right visual field, spanning 1°–2.2° eccentricities and polar angles up to 60° from the vertical meridian. In the experiment, images were presented in a 4 × 4° aperture centered at 1.5° eccentricity and 45° polar angle. While prior V4 studies focus on one domain specialized for elementary visual features such as color ( Liu et al., 2020 ) or spatial frequencies ( Zhang et al., 2023 ), our V4 map defines 16 distinct domains based on the neurons’ natural image feature preferences, encompassing a broad range of feature selectivity within a topological organization. Fig. 1A illustrates this large-scale organization, where each of 3048 V4 columns shows its top nine preferred images from its tuning, the digital twin’s responses to 50k natural images ( Wang et al., 2024 ). On a coarse scale, the map exhibits functional domains of color preference. A detailed examination of 40 columns within Fig. 1A white box reveals multifaceted neural preferences for complex image attributes, including intricate shapes, patterns, and surface texture combinations ( Fig. 1B ). Neuronal columns appear to exhibit a spectrum of pattern preferences, ranging from patterns with characteristics of surface textures at the left and patterns emphasizing boundary curvatures and shapes at the right, and even facial features at the lower right. However, many natural images often contain texture and shape features simultaneously. Preference for texture and shape exists in a continuum and can be ambiguous for perceptual classification. To systematically and objectively characterize these preferences, we introduced the concept of dispersity ( Wang et al., 2024 ), a quantitative metric that captures the degree to which neural columns prefer surface textures versus precise spatial patterns such as shapes ( Fig. 1E ). While high-dispersity columns typically respond to broadly distributed features reminiscent of surfaces and textures, low-dispersity columns show selectivity toward precisely localized shape features. The dispersity map ( Fig. 1E ) highlights that the high and low dispersity domains are spatially interleaved throughout the V4 cortical surface, balancing each other proportionally. This dispersity measure is related to shape and texture image preference established by Pasupathy et al. ( Pasupathy and Connor, 2001 ; Kim et al., 2022 ), who identified different neuronal populations that prefer shape or texture. Testing their set of shape and texture stimuli ( Kim et al., 2019 ) on our V4 digital twin, we generate another image preference map ( Fig. 1C & D ), which is correlated with the dispersity map (see Materials and Methods ), demonstrating that shape preference domains (low dispersity) interleave systematically with texture preference domains (high dispersity). Our findings support the notion that the complex topological arrangement of V4 functional domains arises naturally from neural tuning properties derived from natural image statistics, where shape and texture selective neurons form distinct yet interleaved functional domains, highlighting an organizational principle that balances the processing of detailed shape features and broader surface textures within the cortical map. Self-Organizing Map can account for the V4 map To understand the computational constraints underlying the V4 map topology, we first ask, given V4 columns each with its tuning curve (responses to 50k natural images) and an estimated retinotopic position using the SmoothGrad-Square feature attribution analysis ( Wang et al., 2024 ; Smilkov et al., 2017 ; Hooker et al., 2019 ), can we use the self-organizing algorithm to explain their topological organization? We train two variants of self-organizing maps (see Materials and Methods ) to examine the constraints necessary to organize V4 columns into the observed cortical map topologies. Our first self-organizing map (SOM) is a 2D network of 60 x 60 units, each receiving only the tuning curve from all V4 columns as input. This map enforces the continuity of stimulus tuning while ignoring column’s retinotopic position. The second map ( Fig. 1F & G ) takes into account the retintopic position of V4 columns in addition to the tuning curve, hence called the retinotopically constrained SOM (RSOM). With a similar network configuration, the RSOM enforces both the stimulus tuning continuity and the retinotopy continuity ( Fig. 1H ). To quantitatively assess the correspondence of our simulated maps with the V4 map, we label each SOM / RSOM unit to inherit the domain label, the retinotopic position, and the dispersity value of a V4 column that has the most similar tuning curve to it ( Fig. 2A & B ). This allows us to construct two quantitative comparison metrics: a Distance Matrix , recording average inter-domain distances between columns in one domain and columns in another domain, and an Adjacency Matrix , indicating the frequency of one domain boundary columns abutting another domain. Each matrix measured relationships among the 16 identified functional domains, resulting in two 16 x 16 matrices for each of the SOM, V4, and RSOM maps ( Fig. 2C & D ). The Pearson correlation between the matrices of these maps shows a higher alignment between V4 and RSOM compared to SOM ( Table 1 ), confirming the significant contribution of the retinotopic constraint to the cortical topology of the V4 map. Fig. 2. Open in a new tab The first, second, and third rows correspond to the SOM, monkey V4 digital twin, and the RSOM. Each column hosts a different metric / map for all simulations and the V4. A. Averaged correlations between pairwise unit responses to 50k images (tuning curve), as a function of distance between units. Spatially closed units have similar tuning. B. Domain color map. V4 has 16 domains labeled in 16 colors. Every SOM / RSOM unit gets assigned the most similar V4 column based on tuning curve to borrow its domain label, retinotopy, and dispersity. C. Domain distance matrix. Averaged domain-to-domain distance by sampling all pairwise units. D. Domain adjacency matrix. The number of each specific domain’s units being adjacent to another domain. E. Polar angle maps with contours. F. Eccentricity maps with contours. G. Feature dispersity maps. High-dispersity units that prefer texture features cluster to form many smaller domains in V4 and the RSOM, but more concentrated cluster of texture units in the SOM. Table 1. Simulated and V4 map comparison Maps SOM RSOM V4 Correlation / distance ( Fig. 2A ) 0.972 0.967 1.0 Domain distance ( Fig. 2C ) 0.37 0.87 1.0 Domain adjacency ( Fig. 2D ) 0.60 0.72 1.0 Fano factor ( Fig. 2G ) 0.13 0.03 0.06 Open in a new tab Evaluation metrics that compare simulated maps against V4. Each map shows its similarity score against the V4 in 1-3. Each map has a standalone index in 4. (1). Averaged pairwise units tuning correlations as a function of map distances. (2). Domain distance matrix. (3). Domain adjacency matrix. (4). Fano factor, high-dispersity units dispersion index. Incorporating retinotopic constraints into the RSOM produces a structured retinotopic map characterized by eccentricity contours approximately perpendicular to polar angle contours, closely matching the V4 retinotopic structure ( Fig. 2E & F , second and third rows). In contrast, the retinotopic map of the SOM, driven solely by tuning similarity, appears to be fragmented and lacks clear organization ( Fig. 2E & F , first row). Notably, the retinotopic constraint leads to a more fragmented spatial arrangement, dividing functional domains of high dispersity into multiple smaller clusters, particularly evident in dispersity maps ( Fig. 2G column, comparing the first row versus the second and third rows). We compute a Fano factor to quantitatively compare the degree of fragmentation of high-dispersity units in the dispersity map derived from our simulations with that of the V4 (see Materials and Methods ). A higher Fano factor reflects more spatial clustering. The dispersity pattern of the RSOM closely matches that of the empirical V4 map, again exceeding the SOM without retinotopic constraints ( Table 1 ). These results underscore the essential role of the retinotopic constraint in shaping the fragmented yet organized nature of functional domains in V4. Tuning discontinuities at domain boundaries The self-organizing map (SOM) groups neuronal columns based on tuning similarity, striving for smooth feature transitions across the cortical surface. However, due to the inherent statistical structure of natural scenes, certain visual features occur more frequently than others, leading to non-uniform transitions between feature tunings. This inherent non-uniformity can be further amplified by retinotopic constraints. We leveraged this non-uniformity to delineate 16 functional domains in the V4 cortical map ( Wang et al., 2024 ). Consequently, we hypothesize that feature-tuning transitions within functional domains should differ markedly from transitions across domain boundaries. Our analyses in Fig. 3A & E support this hypothesis. Three example domains are shown, one per row. Fig. 3B & D present example domains in the RSOM and V4 maps, respectively, each highlighting the target domain with a color-coded boundary (same color scheme as Fig. 2B ): the green-outlined, pink-outlined, and red-outlined domains in the first, second, and third row, respectively. For each target V4 domain, we extract all boundary columns and compute, for each boundary column, how its tuning correlates with the tuning of other columns within a local neighborhood around that boundary location. Fig. 3E shows the average of these tuning correlations as a function of the physical map distance between column pairs that fall either within the same domain (blue curves) or across different domains (yellow curves). We find that V4 column tuning varies more gradually within a functional domain but drops sharply across domain boundaries. This distinctive pattern is consistently observed across all domains in the RSOM and the V4 map, confirming that functional domain boundaries coincide with salient discontinuities in feature tuning. Fig. 3. Open in a new tab Tuning gradients within and across domain boundaries. Three example functional domains are shown and analyzed, one per row, outlined by green, pink, and red contours respectively. A. Correlations between the tuning (responses to 50k natural images) of a RSOM domain boundary unit and tunings of other units (both inside and outside the domain, all within a 11-by-11 neighborhood centered around the boundary unit), as a function of distance away from the boundary unit, averaged over an example domain’s all boundary units. B. Heatmap of RSOM averaged and normalized responses to each domain’s 20 most frequently preferred images, with color-coded contour overlaid to outline domain (also indicate domain’s boundary units). The black dot indicates each domain’s example unit. C. Example unit tuning is decomposed as a weighted linear combination of all V4 columns’ tunings with a LASSO linear model. Each bin represents one V4 column, whose color indicates its domain label. 15 columns with the largest linear regression model weights are shown. D. Heatmap of V4 responses to each domain’s 20 most frequently preferred images, with color-coded contour overlaid to outline domain. E. Correlations between V4 domain boundary column tuning and tunings of other columns, as similarly computed in A. While tuning discontinuities at V4 domain boundaries are preserved in the RSOM, we further examine RSOM units to explain this phenomenon from a connectivity perspective. Each RSOM domain identifies its top twenty most frequently preferred images and one example unit with the strongest response to these images (black dot in Fig. 3B ), whose tuning is decomposed as a weighted linear combination of all V4 column tunings (see Materials and Methods ). The example unit at the green-outlined domain center ( Fig. 3B , first row) aggregates V4 columns from the same domain ( Fig. 3C , first row), representing homogeneous connectivity. When the example unit lies near a domain boundary—as in the second and third rows of Fig. 3B —its tuning becomes an aggregation of V4 columns originating from both the same domain and neighboring domains. Fig. 3C visualizes this heterogeneous connection to V4 columns from different domains (orange, light / dark green bins in the second, third rows, respectively). We further randomly sample ten boundary and interior units from each RSOM domain to analyze their tunings as in Fig. 3C , which results in statistically distinct connections (p<1e-5). While boundary units on average exhibit 41% homogeneous connection (summative weights of homogeneous V4 columns in LASSO model), this rate increases to 74% for interior units. In general, RSOM units located near the center of domains aggregate V4 columns mostly from their home domain. RSOM units at domain peripheries integrate inputs from a more heterogeneous mixture of V4 domains. This heterogeneity at domain boundary contributes to the tuning discontinuities observed in our simulated maps. This finding aligns with our earlier empirical observations ( Wang et al., 2024 ), based on combined wide-field and two-photon calcium imaging data, showing that V4 neurons at domain boundaries often exhibit mixed feature tunings spanning multiple functional domains. Topological maps of artificial neural networks We have demonstrated that the self-organizing algorithm, when constrained by balanced retinotopic and feature continuity factors, captures critical features of the V4 map. Artificial neural networks ( Zhuang et al., 2021 ; Konkle and Alvarez, 2022 ) incorporating similar factors should also account for key V4 map features. Performance-optimized convolution neural networks have been shown to resemble the hierarchical organization of the primate ventral visual pathway. Early convolution layers exhibit stronger representational similarities to lower visual areas, while deeper layers align more closely with ITC responses ( Margalit et al., 2024 ). However, even the best model explains only about half of the variance in neuronal responses. Notable discrepancies have been observed between the population coding patterns in these models and the brain ( Linsley et al., 2023 ; Dyballa et al., 2024 ). TDANN, a recent topographic deep artificial neural network ( Margalit et al., 2024 ), essentially incorporates a similar feature continuity constraint, as well as the retinotopic constraint implicitly through its convolution architecture. TDANN is able to generate topological maps similar to those observed in primate V1 and ITC from its hierarchical convolution layers. TDANN’s ability to reproduce intermediate-level cortical areas, such as the V4, has not yet been evaluated. We compare our V4 map with the corresponding TDANN layer3.1 and layer4.0 that is supposed to match the V4 and ITC map, respectively. We compute the tuning curves of all units in these TDANN layers to 50k color natural images, and segregate every map into 60 x 60 pixels, with each pixel inheriting the averaged tuning curve from all units within a local region owned by that pixel. Fig. 4A & C show natural image preference maps for both TDANN layers and their white box region zoomedin details, with each pixel showing its nine most preferred images, illustrating clear functional domains tuned to color and object features. Notably absent in the TDANN V4 map are face-selective regions frequently observed in our empirical V4 data, although such regions are present in TDANN’s ITC map. We then use the same set of shape and texture image stimuli to test TDANN unit activations (see Materials and Methods ). From each pixel’s top nine preferred images, 71% of TDANN V4 map pixels ( Fig. 4B ) and 69% of TDANN ITC map pixels ( Fig. 4D ) prefer texture images, which number is below 45% in the macaque V4. While this shows a pronounced texture bias in TDANN, it is also well known to exist in ImageNet-trained convolution neural networks ( Geirhos et al., 2018 ). Fig. 4. Open in a new tab A. Top: TDANN purported V4 layer (ResNet18 block 3 second trunk) natural image preference map. Artificial units in layer3.1 are mapped to a 2D simulated cortical sheet, which is evenly segmented into 60 by 60 pixels. Within each pixel area, all individual units’ activation to 50k images get averaged to give a combined tuning, with the top nine images shown. Bottom: white box zoom-in. B. Top: TDANN V4 image preference map to 816 synthetic shape and texture images. Bottom: white box zoom-in. C. Top: TDANN purported ITC layer (ResNet18 block 4 first trunk, layer4.0) natural image preference map. Bottom: white box zoom-in. D. Top: TDANN ITC image preference map to 816 synthetic shape and texture images. Bottom: white box zoom-in. E. TDANN V4 polar angle (top) and eccentricity (bottom) maps. Unit feature map location determines retinotopic position, assuming the feature map center is the fovea. Values are scaled to [0, 1]. F. Distribution of TDANN V4 unit feature dispersity values. G. Distribution of unit dispersities of ResNet18 layer3.1 trained with a shape-prior. H. TDANN ITC layer polar angle (top) and eccentricity (bottom) maps. I. Distribution of TDANN ITC layer unit dispersities. J. Distribution of unit dispersities of ResNet18 layer4.0 trained with a shape-prior. As TDANN maps presumably cover the entire visual field, we consider the center of its feature map the fovea of the visual field and compute the polar angle and eccentricity maps for the TDANN V4 map ( Fig. 4E ) and the TDANN ITC map ( Fig. 4H ) for comparison. Consistent with biological expectations, retinotopy is stronger in the TDANN V4 map compared to its ITC map. It should be noted that our experimentally measured V4 map covers only part of the lower right visual field, corresponding approximately to one set of roughly 16 repeating macroscopic domains evident in Fig. 4A . The most significant difference between our measured V4 map and TDANN’s V4 map is evident in the dispersity analysis. Using SmoothGrad-Square feature attribution ( Wang et al., 2024 ), we estimate receptive fields of TDANN units in its V4 and ITC layers before computing their feature dispersities with the same analysis we used for our experimentally measured V4 map (see Materials and Methods ). Units in both TDANN layers exhibit higher dispersity values than monkey V4 neuronal columns ( Wang et al., 2024 ), as evident in their distributions shown in Fig. 4F & I , indicating a noticeable texture bias. On the other hand, the TDANN V4 map ( Fig. 4B ) does contain islands of low-dispersity shape-selective domains, as they are forced apart by the structured retinotopic constraint ( Fig. 4E ). In contrast, low dispersity units clump together to form one large cluster in the TDANN ITC map ( Fig. 4D ) where the retinotopic constraint is considerably weaker ( Fig. 4H ). These results again highlight the crucial role of the retinotopic constraint in the spatial organization of shape- and texture-selective domains, and hence the feature dispersity map topology. Discussion In this paper, we demonstrate that the recently observed macaque V4 topological map ( Wang et al., 2024 ) of natural image feature selectivity can be explained using Kohonen’s self-organizing map ( Kohonen, 1990 ). We analyze the V4 data and characterize the V4 map in order to evaluate the model. We find that natural image feature preferences, tuning similarity, and retinotopic constraints serve as three important constraints that are necessary and sufficient for generating a map that exhibits several key characteristics of our observed V4 map, including (1) the positional relationships (distance and adjacency) among functional domains, (2) the accommodation of a structured retinotopic map within a continuous feature tuning map, but with more abrupt tuning changes across domain boundary, and (3) the spatial organization of functional domains with distinct feature preferences. Our findings extend current models of map formation in the primary visual cortex, suggesting V4 maps might develop under similar computational constraints. Early theoretical works in V1 propose that the spatial layout of cortical maps arises from competing constraints: continuous mapping of multidimensional features, primarily retinal position and orientation, ( Obermayer et al., 1990 ) and coverage uniformity, which ensures all feature combinations are equally represented ( Swindale, 1991 ). Empirical evidence validates that V1 maps optimize this trade-off ( Swindale et al., 2000 ). Subsequent works utilizing self-organizing algorithms ( Swindale, 2004 ) and elastic net ( Carreira-Perpiñán et al., 2005 ) demonstrate that balancing feature continuity with uniform coverage is critical to embed high-dimensional feature spaces—comprising retinotopy alongside features like ocular dominance and spatial frequency—into two-dimensional cortical sheets. Issa et al. further integrate the spatiotemporal filtering model with optical imaging to predict V1 responses, emphasizing that feature maps like orientation and spatial frequency are shaped by smooth variations in tuning constrained by retinotopic layout ( Issa et al., 2008 ). Despite operating in a rich, high-dimensional feature space defined by natural image selectivity, V4 organization follows similar principles that couple feature similarity and retinotopic proximity to produce coherent topologies. Thus, our work demonstrates that these classical V1 map formation principles are relevant for understanding the topological organization at macaque V4. Pasupathy et al. ( Pasupathy et al., 2019 ) have discovered distinct sets of V4 neurons tuned to shape and texture using single-unit recording. However, the anatomical organization and distribution of these neurons in V4 are not known. Our V4 digital twin reveals how shape and texture preferences are organized within the V4 map. However, the preferred natural images of a V4 column, as shown in the preference map ( Fig. 1 A & B ), often contain shape, texture, and color elements simultaneously. We have earlier developed a dispersity measure to untangle shape and texture selectivity. Here, we show that the dispersity measure is indeed highly correlated with shape and texture preferences based on tested image stimuli ( Kim et al., 2019 ). Thus, our dispersity map reveals or reflects the possible segregation and clustering of shape and texture selective neurons, in roughly equal proportion, in the V4 topological map. It is plausible that high-dispersity (texture) clusters receive their primary input from V1 blobs and V2 thin stripes, while low-dispersity (shape) clusters originate from V1 inter-blobs and V2 thick stripes ( Livingstone and Hubel, 1984 ; Blasdel, 1992 ). This division aligns with the parallel processing of surface texture and shape form information in the ventral visual pathway. While Neilson and Connor ( Srinath et al., 2021 ) proposed a regional segregation of 2D and 3D processing in V4, how this division is integrated with the broader framework of surface and shape processing remains an open question. The natural image feature preferences and tuning similarity constraint would have driven the topological map with a gradient in dispersity. The addition of the retinotopic constraint fragments the map into smaller high-dispersity and low-dispersity clusters, interleaving them in a hypercolumn-like fashion. Consequently, the V4 topological map emerges as a compromise between the feature continuity constraint and the retinotopic constraint. Convolutional neural networks (CNNs) inherently embed the retinotopic constraint as nearby units in the feature map have closer retinotopic positions. By adding a loss function that encourages units with similar natural image selectivities to be spatially closed to one another within an initial retinotopic map, the topographic deep artificial neural network (TDANN, ( Margalit et al., 2024 )) offers an alternative algorithm to learn a cortical topological map, with a similar set of computational constraints. The discrepancy between the TDANN-generated V4 map and the empirically observed V4 map does not stem from differences in the feature continuity or retinotopy constraints that drive map formation but rather from the specific tuning properties learned by CNN units through ImageNet training, whether via supervised classification or contrastive learning. CNNs are known to exhibit a strong texture bias ( Geirhos et al., 2018 ). This is evident in the feature dispersity distribution of TDANN units relative to the more shape-texture balanced dispersity distribution of V4, as shown in Fig. 4F . Strategies aim at increasing shape bias in deep learning ( Li et al., 2019 ; Zhao et al., 2025 ) produce artificial unit representations and tuning properties with a reduced texture bias in the V4-corresponding layer of the ResNet18 trained with the shape-bias enhancing constraints, making its dispersity distribution more aligned with that of V4 ( Fig. 4G & J ), as compared to the TDANN. Integrating topological maps with CNNs has deepened our understanding of the brain ( Margalit et al., 2024 ), but the computational advantages of topographically constrained deep networks remain to be demonstrated. While natural image feature preferences, tuning similarity, and retinotopy constraints can account for many of the empirical observed characteristics of the V4 map, they might not be the whole story. Topological maps can serve to minimize neural connection lengths ( Blauch et al., 2022 ). Thus, features with semantic relationships or with strong statistical co-occurrence in natural scenes should also be closer together in a topological map, even though they might not be similar in terms of visual patterns. A more general and comprehensive framework for understanding cortical organization should consider the computations enabled and facilitated by topological maps. Acknowledgments The authors thank anonymous reviewers for their valuable suggestions and the Neuroscience Institute at Carnegie Mellon University for providing high-performance computing. Funding This work is supported by NSF CISE RI 2420348 and NIH R01 EY030226-01A1 awarded to Tai Sing Lee, and STI2030-Major Projects 2022ZD0204600, National Natural Science Foundation of China U1909205, and funds from the Peking-Tsinghua Center for Life Sciences awarded to Shiming Tang. Footnotes Competing interests No competing interest is declared. 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