The stride length of the filters during the convolution over the input. “”" def init(self, n_filters, filter_shape, input_shape=None, padding=‘same’, stride=1): self.n_filters = n_filters self.filter_shape = filter_shape self.padding = padding self.stride = stride self.input_shape = input_shape self.trainable = True def initialize(self, optimizer):
Initialize the weights
filter_height, filter_width = self.filter_shape channels = self.input_shape[0] limit = 1 / math.sqrt(np.prod(self.filter_shape)) self.W = np.random.uniform(-limit, limit, size=(self.n_filters, channels, filter_height, filter_width)) self.w0 = np.zeros((self.n_filters, 1))
Weight optimizers
self.W_opt = copy.copy(optimizer) self.w0_opt = copy.copy(optimizer) def parameters(self): return np.prod(self.W.shape) + np.prod(self.w0.shape) def forward_pass(self, X, training=True): batch_size, channels, height, width = X.shape self.layer_input = X
Turn image shape into column shape
(enables dot product between input and weights)
self.X_col = image_to_column(X, self.filter_shape, stride=self.stride, output_shape=self.padding)
Turn weights into column shape
self.W_col = self.W.reshape((self.n_filters, -1))
Calculate output
output = self.W_col.dot(self.X_col) + self.w0
Reshape into (n_filters, out_height, out_width, batch_size)
output = output.reshape(self.output_shape() + (batch_size, ))
Redistribute axises so that batch size comes first
return output.transpose(3,0,1,2) def backward_pass(self, accum_grad):
Reshape accumulated gradient into column shape
accum_grad = accum_grad.transpose(1, 2, 3, 0).reshape(self.n_filters, -1) if self.trainable:
Take dot product between column shaped accum. gradient and column shape
layer input to determine the gradient at the layer with respect to layer weights
grad_w = accum_grad.dot(self.X_col.T).reshape(self.W.shape)
The gradient with respect to bias terms is the sum similarly to in Dense layer
grad_w0 = np.sum(accum_grad, axis=1, keepdims=True)
Update the layers weights
self.W = self.W_opt.update(self.W, grad_w) self.w0 = self.w0_opt.update(self.w0, grad_w0)
Recalculate the gradient which will be propogated back to prev. layer
accum_grad = self.W_col.T.dot(accum_grad)
Reshape from column shape to image shape
accum_grad = column_to_image(accum_grad, self.layer_input.shape, self.filter_shape, stride=self.stride, output_shape=self.padding)
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