Homeostatic synaptic scaling optimizes learning in network models of neural population codes

Studying and understanding the code of large neural populations hinges on learning accurate models of population activity. Statistical models that are based on sparse nonlinear Random Projections (RP) of the population proved to be highly accurate, efficient, and scalable. Interestingly, this class of models has a straightforward biologically-plausible implementation as a shallow neural circuit. Here we extend the RP models, and learn them by optimizing or ``reshaping" the random projections themselves. The reshaping of projections is akin to changing synaptic connections in the neural circuit implementation of RP models. Applied to recordings of tens of cortical neurons from behaving monkeys, we show that these Reshaped Random Projections models are more accurate and efficient than RP models and on par with backpropagation models. We explore the biological plausibility of RP models, by adding biological features to the circuit models. We find, surprisingly, that learning reshaped RP models with Homeostatic synaptic scaling results in even more efficient and accurate models. We further show that Homeostatic Reshaped RP models that rely on sparse and random connectivity are superior to fully connected network models. Our results therefore offer an accurate and highly efficient class of models for large populations codes. And, importantly, they suggest that beyond regulating network activity, homeostatic synaptic scaling may have a key computational role in neural circuits -- optimizing their performance and efficiency.