The most probable neural circuit exhibits low-dimensional sustained activity

Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons during a reaching task can be described by dynamics in low-dimensional space. These results suggest that the low-dimensional dynamics of a few types of neurons emerge in the cerebral cortex that is trained to perform a task. This study investigates a simple neural circuit emerges with a few types of neurons. Assuming an infinite number of neurons in the circuit with connection weights drawn from a Gaussian distribution, we model the dynamics of neurons by using a kernel function. Given that the system is infinitely large, almost all capable circuits approximate the most probable circuit for the task. We simulate two delayed response tasks and a motor-pattern generation task. The model network exhibits low-dimensional dynamics in all tasks. Considering that the connection weights are drawn from a Gaussian distribution, the most probable circuit is the circuit with the smallest connection weight; that is, the simplest circuit with the simplest dynamics. Finally, we relate the dynamics to algorithmic information theory.