【python實現卷積神經網路】卷積層Conv2D反向傳播過程

西西嘛呦發表於2020-04-16
Python卷積神經網路反向傳播

程式碼來源：https://github.com/eriklindernoren/ML-From-Scratch

卷積神經網路中卷積層Conv2D（帶stride、padding）的具體實現：https://www.cnblogs.com/xiximayou/p/12706576.html

啟用函式的實現（sigmoid、softmax、tanh、relu、leakyrelu、elu、selu、softplus）：https://www.cnblogs.com/xiximayou/p/12713081.html

損失函式定義（均方誤差、交叉熵損失）：https://www.cnblogs.com/xiximayou/p/12713198.html

優化器的實現（SGD、Nesterov、Adagrad、Adadelta、RMSprop、Adam）：https://www.cnblogs.com/xiximayou/p/12713594.html

 

本節將根據程式碼繼續學習卷積層的反向傳播過程。

這裡就只貼出Conv2D前向傳播和反向傳播的程式碼了：

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)

        return accum_grad

而在定義卷積神經網路中是在neural_network.py中　　

   def train_on_batch(self, X, y):
        """ Single gradient update over one batch of samples """
        y_pred = self._forward_pass(X)
        loss = np.mean(self.loss_function.loss(y, y_pred))
        acc = self.loss_function.acc(y, y_pred)
        # Calculate the gradient of the loss function wrt y_pred
        loss_grad = self.loss_function.gradient(y, y_pred)
        # Backpropagate. Update weights
        self._backward_pass(loss_grad=loss_grad)

        return loss, acc

還需要看一下self._forward_pas和self._backward_pass：

    def _forward_pass(self, X, training=True):
        """ Calculate the output of the NN """
        layer_output = X
        for layer in self.layers:
            layer_output = layer.forward_pass(layer_output, training)

        return layer_output

    def _backward_pass(self, loss_grad):
        """ Propagate the gradient 'backwards' and update the weights in each layer """
        for layer in reversed(self.layers):
            loss_grad = layer.backward_pass(loss_grad)

我們可以看到，在前向傳播中會計算出self.layers中每一層的輸出，把包括卷積、池化、啟用和歸一化等。然後在反向傳播中從後往前更新每一層的梯度。這裡我們以一個卷積層+全連線層+損失函式為例。網路前向傳播完之後，最先獲得的梯度是損失函式的梯度。然後將損失函式的梯度傳入到全連線層，然後獲得全連線層計算的梯度，傳入到卷積層中，此時呼叫卷積層的backward_pass()方法。在卷積層中的backward_pass()方法中，如果設定了self.trainable，那麼會計算出對權重W以及偏置項w0的梯度，然後使用優化器optmizer，也就是W_opt和w0_opt進行引數的更新，然後再計算對前一層的梯度。最後有一個colun_to_image()方法。

def column_to_image(cols, images_shape, filter_shape, stride, output_shape='same'):
    batch_size, channels, height, width = images_shape
    pad_h, pad_w = determine_padding(filter_shape, output_shape)
    height_padded = height + np.sum(pad_h)
    width_padded = width + np.sum(pad_w)
    images_padded = np.empty((batch_size, channels, height_padded, width_padded))

    # Calculate the indices where the dot products are applied between weights
    # and the image
    k, i, j = get_im2col_indices(images_shape, filter_shape, (pad_h, pad_w), stride)

    cols = cols.reshape(channels * np.prod(filter_shape), -1, batch_size)
    cols = cols.transpose(2, 0, 1)
    # Add column content to the images at the indices
    np.add.at(images_padded, (slice(None), k, i, j), cols)

    # Return image without padding
    return images_padded[:, :, pad_h[0]:height+pad_h[0], pad_w[0]:width+pad_w[0]]

該方法是將之間為了方便計算卷積進行的形狀改變image_to_column()重新恢復成images_padded的格式。

像這種計算期間的各種的形狀的變換就挺讓人頭疼的，還會碰到numpy中各式各樣的函式，需要去查閱相關的資料。只要弄懂其中大致過程就可以了，加深相關知識的理解。

 

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