CS231N Assignment 2 ConvolutionalNetworks

CS231N Assignment 2 ConvolutionalNetworks

1. 正向传播

def conv_forward_naive(x, w, b, conv_param):
    """
    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. 

    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)
    """
   N, C, H, W = x.shape
    F, _, HH, WW = w.shape
    pad, stride = conv_param['pad'], conv_param['stride']
    H_out = 1 + (H + 2 * pad - HH) // stride
    W_out = 1 + (W + 2 * pad - WW) // stride
    out = np.zeros((N, F, H_out, W_out))

    x_pad = np.pad(x, ((0,0), (0,0), (pad,pad), (pad,pad)), mode='constant', constant_values=0)
    for i in range(N):       # ith image    
        for f in range(F):   # fth filter        
            for j in range(H_out):            
                for k in range(W_out):                
                    out[i, f, j, k] = np.sum(x_pad[i, :, j*stride : HH+j*stride, k*stride : WW+k*stride ] * w[f]) + b[f]

    cache = (x, w, b, conv_param)
    return out, cache

技巧：
np.pad 的用法

2. 反向传播

此处bp算法，近似于linear的求法，注意矩阵运算的维度

def conv_backward_naive(dout, cache):
    """
    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
    """
    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 = 1 + (H + 2 * pad - HH) / stride
    W_out = 1 + (W + 2 * pad - WW) / stride

    x_pad = np.pad(x, ((0,0), (0,0), (pad,pad), (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.zeros_like(b)

    for i in range(N):       # ith image    
        for f in range(F):   # fth filter        
            for j in range(H_out):            
                for k in range(W_out):                
                    window = x_pad[i, :, j*stride :HH+j*stride , k*stride:WW+k*stride]
                    db[f] += dout[i, f, j, k]                
                    dw[f] += window * dout[i, f, j, k]                
                    dx_pad[i, :, j*stride :HH+j*stride , k*stride:WW+k*stride] += w[f] * dout[i, f, j, k]

    dx = dx_pad[:,:,pad:-pad,pad:-pad]
    return dx, dw, db

3. max-pool

def max_pool_forward_naive(x, pool_param):
    """
    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)
     """

    N, C, H, W = x.shape
    HH, WW, stride = pool_param['pool_height'], pool_param['pool_width'], pool_param['stride']
    H_out = (H-HH) / stride + 1
    W_out = (W-WW) / stride + 1
    out = np.zeros((N,C,H_out,W_out))

    for i in xrange(H_out):
        for j in xrange(W_out):
            x_masked = x[:,:,i*stride : i*stride+HH, j*stride : j*stride+WW]
            out[:,:,i,j] = np.max(x_masked, axis=(2,3)) 

    cache = (x, pool_param)
    return out, cache

4. max-pool bp

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

    Returns:
    - dx: Gradient with respect to x
    """
    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 = (H-HH) // stride + 1
    W_out = (W-WW) // stride + 1
    dx = np.zeros_like(x)

    for i in range(N):    
        for j in range(C):        
            for k in range(H_out):            
                for l in range(W_out):                
                    window = x[i, j, k*stride : HH+k*stride, l*stride : WW+l*stride]                
                    m = np.max(window)               
                    dx[i, j, k*stride : HH+k*stride, l*stride : WW+l*stride] = (window == m) * dout[i, j, k, l]
    return dx

three-layer CNN

class ThreeLayerConvNet(object):    
    """    
    A three-layer convolutional network with the following architecture:       
       conv - relu - 2x2 max pool - affine - relu - affine - softmax
    """

    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):
        self.params = {}
        self.reg = reg
        self.dtype = dtype

        # Initialize weights and biases
        C, H, W = input_dim
        self.params['W1'] = weight_scale * np.random.randn(num_filters, C, filter_size, filter_size)
        self.params['b1'] = np.zeros((1, num_filters))
        self.params['W2'] = weight_scale * np.random.randn(num_filters*H*W//4, hidden_dim)
        self.params['b2'] = np.zeros((1, hidden_dim))
        self.params['W3'] = weight_scale * np.random.randn(hidden_dim, num_classes)
        self.params['b3'] = np.zeros((1, num_classes))

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


    def loss(self, X, y=None):
        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
        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}

        # compute the forward pass
        a1, cache1 = conv_relu_pool_forward(X, W1, b1, conv_param, pool_param)
        a2, cache2 = affine_relu_forward(a1, W2, b2)
        scores, cache3 = affine_forward(a2, W3, b3)

        if y is None:    
            return scores

        # compute the backward pass
        data_loss, dscores = softmax_loss(scores, y)
        da2, dW3, db3 = affine_backward(dscores, cache3)
        da1, dW2, db2 = affine_relu_backward(da2, cache2)
        dX, dW1, db1 = conv_relu_pool_backward(da1, cache1)

        # Add regularization
        dW1 += self.reg * W1
        dW2 += self.reg * W2
        dW3 += self.reg * W3
        reg_loss = 0.5 * self.reg * sum(np.sum(W * W) for W in [W1, W2, W3])

        loss = data_loss + reg_loss
        grads = {'W1': dW1, 'b1': db1, 'W2': dW2, 'b2': db2, 'W3': dW3, 'b3': db3}

        return loss, grads

Sanity check loss
After you build a new network, one of the first things you should do is sanity check the loss. When we use the softmax loss, we expect the loss for random weights (and no regularization) to be about log(C) for C classes. When we add regularization this should go up.

Gradient check
After the loss looks reasonable, use numeric gradient checking to make sure that your backward pass is correct. When you use numeric gradient checking you should use a small amount of artifical data and a small number of neurons at each layer. Note: correct implementations may still have relative errors up to the order of e-2.

Overfit small data
A nice trick is to train your model with just a few training samples. You should be able to overfit small datasets, which will result in very high training accuracy and comparatively low validation accuracy.

---

Spatial Batch Normalization

def spatial_batchnorm_forward(x, gamma, beta, bn_param):
    N, C, H, W = x.shape
    x_new = x.transpose(0, 2, 3, 1).reshape(N*H*W, C)
    out, cache = batchnorm_forward(x_new, gamma, beta, bn_param)
    out = out.reshape(N, H, W, C).transpose(0, 3, 1, 2)

    return out, cache


def spatial_batchnorm_backward(dout, cache):
    N, C, H, W = dout.shape
    dout_new = dout.transpose(0, 2, 3, 1).reshape(N*H*W, C)
    dx, dgamma, dbeta = batchnorm_backward(dout_new, cache)
    dx = dx.reshape(N, H, W, C).transpose(0, 3, 1, 2)

    return dx, dgamma, dbeta

Group normalization
具体介绍可参考知乎，原论文未读

def spatial_groupnorm_forward(x, gamma, beta, G, gn_param):
    """
    Computes the forward pass for spatial group normalization.
    In contrast to layer normalization, group normalization splits each entry 
    in the data into G contiguous pieces, which it then normalizes independently.
    Per feature shifting and scaling are then applied to the data, in a manner identical to that of batch normalization and layer normalization.

    Inputs:
    - x: Input data of shape (N, C, H, W)
    - gamma: Scale parameter, of shape (C,)
    - beta: Shift parameter, of shape (C,)
    - G: Integer mumber of groups to split into, should be a divisor of C
    - gn_param: Dictionary with the following keys:
      - eps: Constant for numeric stability

    Returns a tuple of:
    - out: Output data, of shape (N, C, H, W)
    - cache: Values needed for the backward pass
    """
    out, cache = None, None
    eps = gn_param.get('eps',1e-5)

    N,C,H,W = x.shape
    x_group = np.reshape(x, (N, G, C//G, H, W)) #按G将C分组
    mean = np.mean(x_group, axis=(2,3,4), keepdims=True) #均值
    var = np.var(x_group, axis=(2,3,4), keepdims=True) #方差
    x_groupnorm = (x_group-mean)/np.sqrt(var+eps) #归一化
    x_norm = np.reshape(x_groupnorm, (N,C,H,W)) #还原维度
    out = x_norm*gamma+beta #还原C
    cache = (G, x, x_norm, mean, var, beta, gamma, eps)
    return out, cache


def spatial_groupnorm_backward(dout, cache):
    """
    Inputs:
    - dout: Upstream derivatives, of shape (N, C, H, W)
    - cache: Values from the forward pass

    Returns a tuple of:
    - dx: Gradient with respect to inputs, of shape (N, C, H, W)
    - dgamma: Gradient with respect to scale parameter, of shape (C,)
    - dbeta: Gradient with respect to shift parameter, of shape (C,)
    """
    dx, dgamma, dbeta = None, None, None

    N,C,H,W = dout.shape
    G, x, x_norm, mean, var, beta, gamma, eps = cache

    dbeta = np.sum(dout, axis=(0,2,3), keepdims=True)
    dgamma = np.sum(dout*x_norm, axis=(0,2,3), keepdims=True)

    dx_norm = dout * gamma
    dx_groupnorm = dx_norm.reshape((N, G, C // G, H, W))

    x_group = x.reshape((N, G, C // G, H, W))
    dvar = np.sum(dx_groupnorm * -1.0 / 2 * (x_group - mean) / (var + eps) ** (3.0 / 2), axis=(2,3,4), keepdims=True)

    N_GROUP = C//G*H*W
    dmean1 = np.sum(dx_groupnorm * -1.0 / np.sqrt(var + eps), axis=(2,3,4), keepdims=True)
    dmean2_var = dvar * -2.0 / N_GROUP * np.sum(x_group - mean, axis=(2,3,4), keepdims=True)
    dmean = dmean1 + dmean2_var

    dx_group1 = dx_groupnorm * 1.0 / np.sqrt(var + eps)
    dx_group2_mean = dmean * 1.0 / N_GROUP
    dx_group3_var = dvar * 2.0 / N_GROUP * (x_group - mean)
    dx_group = dx_group1 + dx_group2_mean + dx_group3_var

    dx = dx_group.reshape((N, C, H, W))
    return dx, dgamma, dbeta

这个作业多数是基于别人的代码

Charlie
杭州
8.11