Infinite width limits of deep neural networks often have tractable forms. They have been used to analyse the behaviour of finite networks, as well as being useful methods in their own right. When investigating infinitely wide convolutional neural networks (CNNs), it was observed that the correlations arising from spatial weight sharing disappear in the infinite limit. This is undesirable, as spatial correlation is the main motivation behind CNNs. We show that the loss of this property is not a consequence of the infinite limit, but rather of choosing an independent weight prior. Correlating the weights maintains the correlations in the activations. Varying the amount of correlation interpolates between independent-weight limits and mean-pooling. Empirical evaluation of the infinitely wide network shows that optimal performance is achieved between the extremes, indicating that correlations can be useful.

翻译：深神经网络的无限宽度限制往往具有可伸缩的形式。 它们被用来分析有限网络的行为, 并且本身是有用的方法。 在调查无限广泛的进化神经网络(CNNs)时, 发现空间重量共享产生的相关关系在无限限度内消失。 这是不可取的, 因为空间相关性是CNN背后的主要动力。 我们显示, 失去这一属性不是无限限度的结果, 而是在之前选择独立重量的结果。 校正重量维持了激活中的关联性。 区分独立重量限制和平均集合之间的关联性。 对无限宽的网络的经验性评估表明,极端之间实现了最佳性能, 表明关联性是有用的。