Fundamental bounds on learning performance in neural circuits

How does the size of a neural circuit influence its learning performance? Intuitively, we expect the learning capacity of a neural circuit to grow with the number of neurons and synapses. Larger brains tend to be found in species with higher cognitive function and learning ability. Similarly, adding connections and units to artificial neural networks can allow them to solve more complex tasks. However, we show that in a biologically relevant setting where synapses introduce an unavoidable amount of noise, there is an optimal size of network for a given task. Beneath this optimal size, our analysis shows how adding apparently redundant neurons and connections can make tasks more learnable. Therefore large neural circuits can either devote connectivity to generating complex behaviors, or exploit this connectivity to achieve faster and more precise learning of simpler behaviors. Above the optimal network size, the addition of neurons and synaptic connections starts to impede learning performance. This suggests that overall brain size may be constrained by the need to learn efficiently with unreliable synapses, and may explain why some neurological learning deficits are associated with hyperconnectivity. Our analysis is independent of specific learning rules and uncovers fundamental relationships between learning rate, task performance, network size and intrinsic noise in neural circuits.