話不多說，直接上程式碼：

Convolution: Naive forward pass

def conv_forward_naive(x, w, b, conv_param):
    """
    A naive implementation of the forward pass for a convolutional layer.

    The input consists of N data points, each with C channels, height H and
    width W. We convolve each input with F different filters, where each filter
    spans all C channels and has height HH and width WW.

    Input:
    - x: Input data of shape (N, C, H, W)
    - w: Filter weights of shape (F, C, HH, WW)
    - b: Biases, of shape (F,)
    - conv_param: A dictionary with the following keys:
      - 'stride': The number of pixels between adjacent receptive fields in the
        horizontal and vertical directions.
      - 'pad': The number of pixels that will be used to zero-pad the input. 
        

    During padding, 'pad' zeros should be placed symmetrically (i.e equally on both sides)
    along the height and width axes of the input. Be careful not to modfiy the original
    input x directly.

    Returns a tuple of:
    - out: Output data, of shape (N, F, H', W') where H' and W' are given by
      H' = 1 + (H + 2 * pad - HH) / stride
      W' = 1 + (W + 2 * pad - WW) / stride
    - cache: (x, w, b, conv_param)
    """
 

    out = None
    ###########################################################################
    # TODO: Implement the convolutional forward pass.                         #
    # Hint: you can use the function np.pad for padding.                      #
    ###########################################################################
 

    N, C, H, W = x.shape
    F, _, HH, WW = w.shape
    stride, pad = conv_param['stride'], conv_param['pad']
    H_out = int(1 + (H + 2 * pad - HH) / stride)
    W_out = int(1 + (W + 2 * pad - WW) / stride)
    out = np.zeros((N, F, H_out, W_out)) #預分配輸出out的記憶體

    x_pad = np.pad(x, ((0,), (0,), (pad,
 
), (pad,)), mode='constant', constant_values=0)
    for i in range(H_out):
        for j in range(W_out):
        	#逐一計算輸出值
            x_pad_mask = x_pad[:, :, stride * i:HH + stride * i, stride * j: stride * j + WW]
            for k in range(F):
                out[:, k, i, j] = np.sum(x_pad_mask * w[k, :, :, :], axis=(1,2,3))
    out += b[None, :, None, None] #加上偏置，這裡None添加了維度，使得能夠正確相加
    ###########################################################################
    #                             END OF YOUR CODE                            #
    ###########################################################################
    cache = (x, w, b, conv_param)
    return out, cache

Convolution: Naive backward pass

def conv_backward_naive(dout, cache):
    """
    A naive implementation of the backward pass for a convolutional layer.

    Inputs:
    - dout: Upstream derivatives.
    - cache: A tuple of (x, w, b, conv_param) as in conv_forward_naive

    Returns a tuple of:
    - dx: Gradient with respect to x
    - dw: Gradient with respect to w
    - db: Gradient with respect to b
    """
    dx, dw, db = None, None, None
    ###########################################################################
    # TODO: Implement the convolutional backward pass.                        #
    ###########################################################################
    x, w, b, conv_param = cache
    N, C, H, W = x.shape
    F, _, HH, WW = w.shape
    stride, pad = conv_param['stride'], conv_param['pad']
    H_out = int(1 + (H + 2 * pad - HH) / stride)
    W_out = int(1 + (W + 2 * pad - WW) / stride)

    x_pad = np.pad(x, ((0,), (0,), (pad,), (pad,)), mode='constant', constant_values=0)
    dx = np.zeros_like(x)
    dx_pad = np.zeros_like(x_pad)
    dw = np.zeros_like(w)

    db = np.sum(dout, axis=(0,2,3))
    for i in range(H_out):
      for j in range(W_out):
          x_pad_masked = x_pad[:, :, i*stride:i*stride+HH, j*stride:j*stride+WW]
          # 注意弄清輸出的每一位，有哪些輸入X和W參與，逐一計算梯度
          for k in range(F):
              dw[k ,: ,: ,:] += np.sum(x_pad_masked * (dout[:, k, i, j])[:, None, None, None], axis=0)
          for n in range(N):
              dx_pad[n, :, i*stride:i*stride+HH, j*stride:j*stride+WW] += np.sum((w[:, :, :, :] * 
                                                 (dout[n, :, i, j])[:,None ,None, None]), axis=0)
    dx = dx_pad[:,:,pad:-pad,pad:-pad]
    ###########################################################################
    #                             END OF YOUR CODE                            #
    ###########################################################################
    return dx, dw, db

測試結果

Testing conv_backward_naive function
dx error:  1.159803161159293e-08
dw error:  2.247109434939654e-10
db error:  3.37264006649648e-11

max_pool

def max_pool_forward_naive(x, pool_param):
    """
    A naive implementation of the forward pass for a max-pooling layer.

    Inputs:
    - x: Input data, of shape (N, C, H, W)
    - pool_param: dictionary with the following keys:
      - 'pool_height': The height of each pooling region
      - 'pool_width': The width of each pooling region
      - 'stride': The distance between adjacent pooling regions

    No padding is necessary here. Output size is given by 

    Returns a tuple of:
    - out: Output data, of shape (N, C, H', W') where H' and W' are given by
      H' = 1 + (H - pool_height) / stride
      W' = 1 + (W - pool_width) / stride
    - cache: (x, pool_param)
    """
    out = None
    ###########################################################################
    # TODO: Implement the max-pooling forward pass                            #
    ###########################################################################
    HH, WW, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
    N, C, H, W = x.shape
    H_out = int(1 + (H - HH) / stride)
    W_out = int(1 + (W - WW) / stride)

    out = np.zeros((N, C, H_out, W_out))
    for i in range(H_out):
        for j in range(W_out):
            x_mask = x[:, :, stride * i:stride * i + HH, stride * j:stride * j + WW]
            out[:, :, i, j] = np.max(x_mask, axis=(2, 3))
    ###########################################################################
    #                             END OF YOUR CODE                            #
    ###########################################################################
    cache = (x, pool_param)
    return out, cache


def max_pool_backward_naive(dout, cache):
    """
    A naive implementation of the backward pass for a max-pooling layer.

    Inputs:
    - dout: Upstream derivatives
    - cache: A tuple of (x, pool_param) as in the forward pass.

    Returns:
    - dx: Gradient with respect to x
    """
    dx = None
    ###########################################################################
    # TODO: Implement the max-pooling backward pass                           #
    ###########################################################################
    x, pool_param = cache
    N, C, H, W = x.shape
    HH, WW, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
    H_out = int((H-HH)/stride+1)
    W_out = int((W-WW)/stride+1)

    dx = np.zeros_like(x)
    for i in range(H_out):
        for j in range(W_out):
            x_masked = x[:,:,i*stride : i*stride+HH, j*stride : j*stride+WW]
            max_x_masked = np.max(x_masked,axis=(2,3))
            temp_binary_mask = (x_masked == (max_x_masked)[:,:,None,None])
            dx[:,:,i*stride : i*stride+HH, j*stride : j*stride+WW] += temp_binary_mask * (dout[:,:,i,j])[:,:,None,None]
    ###########################################################################
    #                             END OF YOUR CODE                            #
    ###########################################################################
    return dx

Three-layer ConvNet

class ThreeLayerConvNet(object):
    """
    A three-layer convolutional network with the following architecture:

    conv - relu - 2x2 max pool - affine - relu - affine - softmax

    The network operates on minibatches of data that have shape (N, C, H, W)
    consisting of N images, each with height H and width W and with C input
    channels.
    """

    def __init__(self, input_dim=(3, 32, 32), num_filters=32, filter_size=7,
                 hidden_dim=100, num_classes=10, weight_scale=1e-3, reg=0.0,
                 dtype=np.float32):
        """
        Initialize a new network.

        Inputs:
        - input_dim: Tuple (C, H, W) giving size of input data
        - num_filters: Number of filters to use in the convolutional layer
        - filter_size: Width/height of filters to use in the convolutional layer
        - hidden_dim: Number of units to use in the fully-connected hidden layer
        - num_classes: Number of scores to produce from the final affine layer.
        - weight_scale: Scalar giving standard deviation for random initialization
          of weights.
        - reg: Scalar giving L2 regularization strength
        - dtype: numpy datatype to use for computation.
        """
        self.params = {}
        self.reg = reg
        self.dtype = dtype

        ############################################################################
        # TODO: Initialize weights and biases for the three-layer convolutional    #
        # network. Weights should be initialized from a Gaussian centered at 0.0   #
        # with standard deviation equal to weight_scale; biases should be          #
        # initialized to zero. All weights and biases should be stored in the      #
        #  dictionary self.params. Store weights and biases for the convolutional  #
        # layer using the keys 'W1' and 'b1'; use keys 'W2' and 'b2' for the       #
        # weights and biases of the hidden affine layer, and keys 'W3' and 'b3'    #
        # for the weights and biases of the output affine layer.                   #
        #                                                                          #
        # IMPORTANT: For this assignment, you can assume that the padding          #
        # and stride of the first convolutional layer are chosen so that           #
        # **the width and height of the input are preserved**. Take a look at      #
        # the start of the loss() function to see how that happens.                #                           
        ############################################################################
        C, H, W = input_dim
        self.params['W1'] = np.random.normal(0, weight_scale, (num_filters, C, filter_size, filter_size))
        self.params['b1'] = np.zeros((num_filters))
        self.params['W2'] = np.random.normal(0, weight_scale, (int((H / 2) * (W / 2) * num_filters), hidden_dim))
        self.params['b2'] = np.zeros(hidden_dim)
        self.params['W3'] = np.random.normal(0, weight_scale, (hidden_dim, num_classes))
        self.params['b3'] = np.zeros(num_classes)
        ############################################################################
        #                             END OF YOUR CODE                             #
        ############################################################################

        for k, v in self.params.items():
            self.params[k] = v.astype(dtype)


    def loss(self, X, y=None):
        """
        Evaluate loss and gradient for the three-layer convolutional network.

        Input / output: Same API as TwoLayerNet in fc_net.py.
        """
        W1, b1 = self.params['W1'], self.params['b1']
        W2, b2 = self.params['W2'], self.params['b2']
        W3, b3 = self.params['W3'], self.params['b3']

        # pass conv_param to the forward pass for the convolutional layer
        # Padding and stride chosen to preserve the input spatial size
        filter_size = W1.shape[2]
        conv_param = {'stride': 1, 'pad': (filter_size - 1) // 2}

        # pass pool_param to the forward pass for the max-pooling layer
        pool_param = {'pool_height': 2, 'pool_width': 2, 'stride': 2}

        scores = None
        ############################################################################
        # TODO: Implement the forward pass for the three-layer convolutional net,  #
        # computing the class scores for X and storing them in the scores          #
        # variable.                                                                #
        #                                                                          #
        # Remember you can use the functions defined in cs231n/fast_layers.py and  #
        # cs231n/layer_utils.py in your implementation (already imported).         #
        ############################################################################
        out_conv, cache_conv = conv_relu_pool_forward(X, W1, b1, conv_param, pool_param)
        out_fc1, cache_fc1 = affine_relu_forward(out_conv, W2, b2)
        scores, cache_fc2 = affine_forward(out_fc1, W3, b3)
        ############################################################################
        #                             END OF YOUR CODE                             #
        ############################################################################

        if y is None:
            return scores

        loss, grads = 0, {}
        ############################################################################
        # TODO: Implement the backward pass for the three-layer convolutional net, #
        # storing the loss and gradients in the loss and grads variables. Compute  #
        # data loss using softmax, and make sure that grads[k] holds the gradients #
        # for self.params[k]. Don't forget to add L2 regularization!               #
        #                                                                          #
        # NOTE: To ensure that your implementation matches ours and you pass the   #
        # automated tests, make sure that your L2 regularization includes a factor #
        # of 0.5 to simplify the expression for the gradient.                      #
        ############################################################################
        loss, dout = softmax_loss(scores, y)
        loss += 0.5 * self.reg * (np.sum(W1**2) + np.sum(W2**2) + np.sum(W3**2))

        dx3, dw3, db3 = affine_backward(dout, cache_fc2)
        grads['W3'] = dw3 + self.reg * W3
        grads['b3'] = db3
        dx2, dw2, db2 = affine_relu_backward(dx3, cache_fc1)
        grads['W2'] = dw2 + self.reg * W2
        grads['b2'] = db2
        dx1, dw1, db1 = conv_relu_pool_backward(dx2, cache_conv)
        grads['W1'] = dw1 + self.reg * W1
        grads['b1'] = db1
        ############################################################################
        #                             END OF YOUR CODE                             #
        ############################################################################

        return loss, grads