# Fundamental bounds on learning performance in neural circuits

## TL;DR

This paper establishes fundamental limits on neural circuit size and learning performance, revealing an optimal network size for learning efficiency in noisy biological settings, with implications for brain evolution and neurological disorders.

## Contribution

It introduces a theoretical framework showing how synaptic noise creates an optimal network size for learning, balancing complexity and efficiency in neural circuits.

## Key findings

- Optimal network size depends on noise level and task complexity.
- Adding neurons beyond the optimal size impairs learning performance.
- Large neural circuits can either enhance behavior complexity or improve learning speed.

## Abstract

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.