Allostatic Control of Persistent States in Spiking Neural Networks for perception and computation

We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal physiology that orchestrates responses to maintain a dynamic equilibrium in bodily needs and internal states. In this paper, we focus on an application in numerical cognition, where a bump of activity in an attractor network is used as a spatial numerical representation. While existing neural networks can maintain persistent states, to date, there is no unified framework for dynamically controlling spatial changes in neuronal activity in response to environmental changes. To address this, we couple a well known allostatic microcircuit, the Hammel model, with a ring attractor, resulting in a Spiking Neural Network architecture that can modulate the location of the bump as a function of some reference input. This localized activity in turn is used as a perceptual belief in a simulated subitization task a quick enumeration process without counting. We provide a general procedure to fine-tune the model and demonstrate the successful control of the bump location. We also study the response time in the model with respect to changes in parameters and compare it with biological data. Finally, we analyze the dynamics of the network to understand the selectivity and specificity of different neurons to distinct categories present in the input. The results of this paper, particularly the mechanism for moving persistent states, are not limited to numerical cognition but can be applied to a wide range of tasks involving similar representations.