Learning may need only a few bits of synaptic precision.
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, consistent with recent biological findings. Finally, we demonstrate how the theoretical analysis can be exploited to design efficient algorithmic search strategies.
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.|Human Genetics Foundation-Torino, Via Nizza 52, I-10126 Torino, Italy.
Carlo
C
Baldassi
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.|Human Genetics Foundation-Torino, Via Nizza 52, I-10126 Torino, Italy.
Federica
F
Gerace
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.|Human Genetics Foundation-Torino, Via Nizza 52, I-10126 Torino, Italy.
Carlo
C
Lucibello
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.|Human Genetics Foundation-Torino, Via Nizza 52, I-10126 Torino, Italy.
Luca
L
Saglietti
Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy.|Human Genetics Foundation-Torino, Via Nizza 52, I-10126 Torino, Italy.|Collegio Carlo Alberto, Via Real Collegio 30, I-10024 Moncalieri, Italy.
Riccardo
R
Zecchina
D007858:Learning / Q000502:physiology*; D008959:Models, Neurological; D016571:Neural Networks, Computer; D013569:Synapses / Q000502:physiology*