论文标题
关于深度全卷积神经网络的通用近似特性
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks
论文作者
论文摘要
我们从动力学系统的角度研究了通过深层完全卷积网络对移位不变或e象函数的近似。我们证明，深度残留的完全卷积网络及其连续层对应物可以在恒定通道宽度上实现这些对称函数的通用近似。此外，我们表明，在每个层中至少有2个通道的非残基变体可以实现同样的变体，至少为2个通道。此外，我们还表明，这些要求是必要的，从较少的通道或较小内核的网络无法成为通用近似群。
We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer counterpart can achieve universal approximation of these symmetric functions at constant channel width. Moreover, we show that the same can be achieved by non-residual variants with at least 2 channels in each layer and convolutional kernel size of at least 2. In addition, we show that these requirements are necessary, in the sense that networks with fewer channels or smaller kernels fail to be universal approximators.
