CNNs

y=f(x) = g(x, params)

Besteht aus Verkettungen gN bis g1

g(x, params) = g1(x, W, b) = sigmoid(Wx +b)

Mulilayered: Verkettung

Single layer:

Specialized NN for data with grid like structure: Images, time series,….

Naive approach: vectorized image to FCN —> too many parameters, lack of translation invariance

Convolution is a mathematical operation on 2 functions f and g

Integral of the product of 2 functions after one of them is reveres and shifted

Convolution of Imahe and kernel

COnvolutions are commutative

Visually: moving kernel successively across the imge and perform a dot product at each location

Cross correlation if often implemented under the name of convolution

Performing convolution instead of matrix multiplication

Number of output channels: number of independent convolutions

Number of input channels: 3 in RGB images

Convolutions können auch auch multiple input channels angewandt werden —> 3D convlution

Kernel size

Weight matrix corresponding to convolutional layer is: Nin X k1 X k2 x Nout

Padding: same padding with zeros

Region in the input image that a pixel in the output feature map is affected by

As the network depth increases, the receptive field increases and more global information is encoded