arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.10435cs.LG
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低维流形支持循环神经网络中的多重积分

Low-Dimensional Manifolds Support Multiplexed Integrations in Recurrent Neural Networks

Laboratoire de Physique de l’Ecole Normale Supérieure(巴黎高等师范学院物理实验室);CNRS(法国国家科学研究中心);Sorbonne Université(索邦大学)

Arnaud Fanthomme, Rémi Monasson

摘要:

我们研究的学习动力学和表示出现在循环神经网络训练整合一个或多个时间信号。结合分析和数值研究,我们描述了具有n个神经元的RNN学习整合任意持续时间的D(n)标量信号的条件。我们表明,无论是线性和ReLU神经元,它的内部状态生活接近一个D维流形,其形状与激活函数。因此,每个神经元在不同程度上携带着关于所有积分值的信息。我们讨论了我们的结果和计算神经科学家解释皮层记录的混合选择性概念之间的深刻类比。

英文摘要:

We study the learning dynamics and the representations emerging in Recurrent Neural Networks trained to integrate one or multiple temporal signals. Combining analytical and numerical investigations, we characterize the conditions under which a RNN with n neurons learns to integrate D(n) scalar signals of arbitrary duration. We show, both for linear and ReLU neurons, that its internal state lives close to a D-dimensional manifold, whose shape is related to the activation function. Each neuron therefore carries, to various degrees, information about the value of all integrals. We discuss the deep analogy between our results and the concept of mixed selectivity forged by computational neuroscientists to interpret cortical recordings.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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