A visual sense of number emerges from divisive normalization in a simple center-surround convolutional network

Abstract

Many species of animals exhibit an intuitive sense of number, suggesting a fundamental neural mechanism for representing numerosity in a visual scene. Recent empirical studies demonstrate that early feedforward visual responses are sensitive to numerosity of a dot array but substantially less so to continuous dimensions orthogonal to numerosity, such as size and spacing of the dots. However, the mechanisms that extract numerosity are unknown. Here we identified the core neurocomputational principles underlying these effects: (1) center-surround contrast filters; (2) at different spatial scales; with (3) divisive normalization across network units. In an untrained computational model, these principles eliminated sensitivity to size and spacing, making numerosity the main determinant of the neuronal response magnitude. Moreover, a model implementation of these principles explained both well-known and relatively novel illusions of numerosity perception across space and time. This supports the conclusion that the neural structures and feedforward processes that encode numerosity naturally produce visual illusions of numerosity. Together, these results identify a set of neurocomputational properties that gives rise to the ubiquity of the number sense in the animal kingdom.

Emergence of number sense through the integration of multimodal information: developmental learning insights from neural network models

“…With regard to mathematical skills, the exact process by which the human brain grasps the concept of symbolic numbers remains unclear ( Diester and Nieder, 2007 ; Nieder and Dehaene, 2009 ; Testolin, 2020 ). Previous studies have reported the acquisition of number sense using computational models, for example, spatial filter ( Park and Huber, 2022 ; Paul et al, 2022 ), untrained neural networks ( Kim et al, 2021 ; Lee et al, 2023 ), neural networks trained on object recognition tasks not limited to number images ( Nasr et al, 2019 ; Nasr and Nieder, 2021 ), and neural networks trained with number images ( Stoianov and Zorzi, 2012 ; Testolin et al, 2020 ; Mistry et al, 2023 ). These studies commonly have indicated that acquiring number sense is possible using only single-modal information.…”

Contextual coherence increases perceived numerosity independent of semantic content.

“…An alternative possibility is that coherence influences perceived numerosity at later stages and can be driven by higher level features such as category membership or midlevel visual features, such as shape information. For example, Park & Huber (2022) suggested that the color coherence effect we observed might be caused by top-down semantic influences. Yet, a third possibility is that the coherence effect can emerge at multiple levels in the visual processing hierarchy.…”

Hierarchical representations of relative numerical magnitudes in the human frontoparietal cortex

“…This nding was supported by another study indicating that multivariate activity patterns before V3 mainly re ect non-numerical visual features 15 . In contrast, another line of research suggests that the monotonic response to numerosity observed in a visual-system-inspired convolutional neural network cannot be attributed to lower-level visual features of the stimuli, but rather to the concept of numerosity itself 45 .…”