Computational capacity as a function of network size

There is strong circumstantial evidence that organisms with larger nervous systems are capable of performing more complex computational tasks. Yet few studies have investigated this effect directly, instead typically treating network size as a fixed property of a simulation while exploring the effects of other parameters. Recent studies have found that network performance does increase modestly with network size, but larger networks also required longer training times to achieve a given performance. Here, we address the relationship between network size and computational capacity by using a spiking model of motor cortex to direct a virtual arm towards a target. The reaching task was performed by a two-joint virtual arm controlled by four muscles. These muscles were controlled by a neural model that consisted of Izhikevich neurons in three populations: a proprioceptive population, receiving input from the current arm position; a motor population, used to drive the arm muscles; and a sensory population, serving as the link between the proprioceptive and motor populations. The model was trained to reach the target using exploratory movements coupled with reinforcement learning and spike-timing dependent plasticity (STDP). The model was implemented using NEURON. A major challenge in scaling network size is that not all properties of the network can be held constant. While first-order properties (such as average firing rate) can be maintained, there are limitations in preserving second- and higher-order statistical properties. Thus, we explored different ways of scaling the connectivity of the network, including (a) preserving connection probability, scaling connection weight to be inversely proportional to model size, and increasing the variance of the external drive; and (b) reducing connection probability to preserve average node degree and leaving other parameters unchanged. In addition, we explored scaling each of the neuronal population groups versus only scaling the sensory (processing) population group. Large differences were observed in network dynamics and statistics based on different scaling choices. However, the relationship between network size and task performance was significant only for certain choices of model parameters. Task performance is highly sensitive to the network's metaparameters, such as STDP learning rates. These must be optimized specifically for different network sizes; otherwise, differences in suitability of these parameters overwhelm the advantages of larger networks. Thus, while network size does affect computational capacity, the relationship is dependent on the manner in which the scaling is implemented.