MULTIPLE NUMERICAL REPRESENTATIONS WITHIN SINGLE UNITS OF DEEP NEURAL NETWORKS

Number sense is a fundamental cognitive function that is associated with selective neural responses to distinct numerical features, including absolute numerosity, numerical ratio, and difference. To examine their developmental origins, recent studies using deep neural network (DNN) models have shown that units selectively responsive to numerosity (Kim, 2021), ratio, or difference (Lee, 2023) can arise even in untrained DNNs, suggesting that statistical variation alone can generate numerical representations without learning. Intriguingly, cortical regions responsive to different numerical features show substantial overlap (Jacob, 2009), implying that a single circuit may support multiple numerical representations. However, it remains unclear whether a single neuron can simultaneously encode multiple numerical representations. Here, using AlexNet as an in silico model of a numerical circuit, we show that a single unit can exhibit selectivity to multiple numerical features. We constructed white and black dot arrays, enabling independent manipulation of numerosity (N=w+b), proportion (w/N), and difference (w−b). Using this stimulus set in an untrained network, we found that 2.82±0.50% and 1.06±0.12% of numerosity-selective units were also responsive to ratio and difference, which is 2.04±0.36 and 2.29±0.50 times chance level, respectively. For these overlapping units, selectivity to each feature was confirmed by a significant correlation between unit responses and the absolute distance between each image’s feature value and the unit’s preferred value (p < 0.05). These results suggest that feedforward connectivity alone can support multiple numerical selectivities within shared representations, supporting a hybrid view of the origin of number sense.