学习可能只需要几位突触的精确度
Learning may need only a few bits of synaptic precision
摘要：
当使用离散而不是连续的突触状态时，神经网络的学习带来了特殊的挑战。离散突触的选择是由生物学推理和实验激发的，也可能是硬件实现考虑的结果。在本文中，我们扩展了以前的大偏差分析，揭示了存在特殊的密集区域的空间中的突触状态的可能性，有效地学习网络与二进制突触。我们将分析扩展到具有多个状态和一般更合理的生物学特征的突触。结果清楚地表明，相对于二进制情况，整体定性图片是不变的，并且对模型细节的变化非常鲁棒。我们还提供了定量的结果表明，增加突触精度的优势（即~内部突触状态的数量）在最初的几个比特之后迅速消失，因此，对于实际应用，可能只需要几个比特就可以获得接近最佳的性能，这与最近的生物学发现相一致。最后，我们展示了如何利用理论分析来设计有效的算法搜索策略。
英文摘要：
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.
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