I. Introduction to Convolution

In functional analysis, convolution, convolution or convolution is a mathematical operation that generates the third function from two functions F and G, and its essence is a special integral transformation, in which the product of the overlapping part of F and G is inverted and translated to represent the integral of the overlapping length. The function involved in convolution can be regarded as interval indicator function, and convolution can also be regarded as a generalization of "moving average".

Second, convolutional neural networks.

Convolutional neural network (CNN) is a kind of feedforward neural network with deep structure, which includes convolution calculation and is one of the representative algorithms of deep learning.

Convolutional neural network has the ability to express learning, and can classify the input information with translation invariance according to its hierarchical structure, so it is also called "Translation Invariant Artificial Neural Network (SIANN)".

Connectivity and biological similarity of convolutional neural networks;

1, connectivity

The connection between convolution layers in convolutional neural network is called sparse connection, that is, compared with the full connection in feedforward neural network, neurons in convolution layer are only connected with some of its adjacent layers, not all neurons. Specifically, any pixel (neuron) in the L-layer feature map of convolutional neural network is just a linear combination of pixels in the receptive field defined by l- 1 layer convolution kernel.

The sparse connection of convolutional neural network has regularization effect, which improves the stability and generalization ability of network structure and avoids over-fitting. At the same time, sparse connection reduces the total number of weight parameters, which is beneficial to the rapid learning of neural network and reduces the memory overhead in calculation.

2. Biological similarity

Inspired by the electrophysiological study of cat visual cortex, convolutional neural network constructs a model by imitating the biological visual perception mechanism. The setting of convolution kernel in convolution network corresponds to the organization of visual cortex in visual nervous system. Visual cortex cells receive signals from photoreceptors on the retina, but a single visual cortex cell does not receive all signals from photoreceptors.