Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network

Abstract

Number sense, the ability to decipher quantity, forms the foundation for mathematical cognition. How number sense emerges with learning is, however, not known. Here we use a biologically-inspired neural architecture comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS) to investigate how neural representations change with numerosity training. Learning dramatically reorganized neuronal tuning properties at both the single unit and population levels, resulting in the emergence of sharply-tuned representations of numerosity in the IPS layer. Ablation analysis revealed that spontaneous number neurons observed prior to learning were not critical to formation of number representations post-learning. Crucially, multidimensional scaling of population responses revealed the emergence of absolute and relative magnitude representations of quantity, including mid-point anchoring. These learnt representations may underlie changes from logarithmic to cyclic and linear mental number lines that are characteristic of number sense development in humans. Our findings elucidate mechanisms by which learning builds novel representations supporting number sense.

Neural codes for visual numerosity independent of other quantities are present both in the dorsal and in the ventral stream of the human brain

“…Such bending of the “number line” imposed by the second dimension could represent the level of uncertainty that typically characterizes numerical or rank order judgements, whereby the extreme values are easier to evaluate and/or order compared to the middle ones. Interestingly, a recent CNN model specifically trained to perform a numerosity classification task developed an analogous curved structure in the last layer (Mistry et al, 2023), coherent with the idea that a curved manifold may be functionally relevant for comparative decision making. Indeed, a similar curved structure bending around a midpoint from the MDS on BOLD data originating from the posterior parietal cortex was observed in a recent study while subjects engaged in a rank-ordering task (Nelli et al, 2023), suggesting that a similar neuronal schema may underlie both order and magnitude representations.…”

Digital twins for understanding mechanisms of learning disabilities: Personalized deep neural networks reveal impact of neuronal hyperexcitability

“…We first developed a pDNN model for numerical problem-solving tasks involving addition and subtraction operations. Our pDNN models were constructed using a biologically inspired model of the dorsal visual pathway based on the network architecture and physiological parameters of CORnet-S 14,15 . This neural architecture, comprising cortical layers V1, V2, V3, and intraparietal sulcus (IPS), has been shown to characterize how neural representations can change with numerosity training, and how learning can reorganize neuronal tuning properties at both the single unit and population levels 14 .…”

“…We developed cognitive neuroscience-informed and biologically plausible pDNNs 14 to capture individual differences in arithmetic task performance among children with and without MLD. This model was designed to investigate the complex interplay between behavior, neural representations, and neurophysiology in children with learning disabilities.…”

“…Behavioral studies suggest that performance on tasks problems involving addition and subtraction operations is characterized by significant individual differences in problem-solving abilities in children, and that children with MLD are impaired on both 5,18,50,51 . By leveraging biologically plausible DNNs 14 , and integrating behavioral with neuroimaging data, we explored individual variability and the neural correlates of arithmetic learning, thereby contributing to a deeper understanding of the neural underpinnings of core numerical problem-solving skills essential for early cognitive development.…”

“…Harnessing artificial intelligence (AI) models that capture individual variability and can serve as digital twins [11][12][13] capturing critical components of a biophysical system while allowing for in silico experimentation -offers new promise. Here we introduce a novel approach by developing a biologically plausible 14,15 personalized deep neural network (pDNN). These personalized networks are tailored to mirror individual behavioral patterns and evaluated against neuroimaging data obtained from the same individuals, thus serving as digital twins on which further experimentation and analysis of neuronal mechanisms can be performed, which would be difficult to achieve non-invasively in children.…”