Learning may need only a few bits of synaptic precision
This addresses the challenge of designing efficient learning systems with low-precision synapses for biological modeling and hardware applications, though it is incremental as it extends prior binary synapse analysis.
The study investigated learning efficiency in neural networks with discretized synapses, finding that increasing synaptic precision beyond a few bits yields diminishing returns, with near-optimal performance achievable with only limited bits, consistent with biological evidence.
Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware implementation considerations as well. In this paper we extend a previous large deviations analysis which unveiled the existence of peculiar dense regions in the space of synaptic states which accounts for the possibility of learning efficiently in networks with binary synapses. We extend the analysis to synapses with multiple states and generally more plausible biological features. The results clearly indicate that the overall qualitative picture is unchanged with respect to the binary case, and very robust to variation of the details of the model. We also provide quantitative results which suggest that the advantages of increasing the synaptic precision (i.e.~the number of internal synaptic states) rapidly vanish after the first few bits, and therefore that, for practical applications, only few bits may be needed for near-optimal performance, consistently with recent biological findings. Finally, we demonstrate how the theoretical analysis can be exploited to design efficient algorithmic search strategies.