[CS231n@Stanford] Assignment2-Q1 (python) Fully-connected Neural Network实现

layer.py

import numpy as np


def affine_forward(x, w, b):
  """
  Computes the forward pass for an affine (fully-connected) layer.

  The input x has shape (N, d_1, ..., d_k) and contains a minibatch of N
  examples, where each example x[i] has shape (d_1, ..., d_k). We will
  reshape each input into a vector of dimension D = d_1 * ... * d_k, and
  then transform it to an output vector of dimension M.

  Inputs:
  - x: A numpy array containing input data, of shape (N, d_1, ..., d_k)
  - w: A numpy array of weights, of shape (D, M)
  - b: A numpy array of biases, of shape (M,)
  
  Returns a tuple of:
  - out: output, of shape (N, M)
  - cache: (x, w, b)
  """
  out = None
  #############################################################################
  # TODO: Implement the affine forward pass. Store the result in out. You     #
  # will need to reshape the input into rows.                                 #
  #############################################################################
  
  N = x.shape[0]
  x_temp = x.reshape(N,-1)
  out = x_temp.dot(w) + b
    
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  cache = (x, w, b)
  return out, cache


def affine_backward(dout, cache):
  """
  Computes the backward pass for an affine layer.

  Inputs:
  - dout: Upstream derivative, of shape (N, M)
  - cache: Tuple of:
    - x: Input data, of shape (N, d_1, ... d_k)
    - w: Weights, of shape (D, M)

  Returns a tuple of:
  - dx: Gradient with respect to x, of shape (N, d1, ..., d_k)
  - dw: Gradient with respect to w, of shape (D, M)
  - db: Gradient with respect to b, of shape (M,)
  """
  x, w, b = cache
  dx, dw, db = None, None, None
  #############################################################################
  # TODO: Implement the affine backward pass.                                 #
  #############################################################################
  
  db = np.sum(dout, axis = 0)
  x_temp = x.reshape(x.shape[0], -1)
  dw = x_temp.T.dot(dout)
  dx = dout.dot(w.T).reshape(x.shape)
  
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  return dx, dw, db


def relu_forward(x):
  """
  Computes the forward pass for a layer of rectified linear units (ReLUs).

  Input:
  - x: Inputs, of any shape

  Returns a tuple of:
  - out: Output, of the same shape as x
  - cache: x
  """
  out = None
  #############################################################################
  # TODO: Implement the ReLU forward pass.                                    #
  #############################################################################
  
  out = np.copy(x)
  out[out<0] = 0 

  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  cache = x
  return out, cache


def relu_backward(dout, cache):
  """
  Computes the backward pass for a layer of rectified linear units (ReLUs).

  Input:
  - dout: Upstream derivatives, of any shape
  - cache: Input x, of same shape as dout

  Returns:
  - dx: Gradient with respect to x
  """
  dx, x = None, cache
  #############################################################################
  # TODO: Implement the ReLU backward pass.                                   #
  #############################################################################
  
  dx = np.copy(dout)
  dx[x<0] = 0

  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  return dx


def batchnorm_forward(x, gamma, beta, bn_param):
  """
  Forward pass for batch normalization.
  
  During training the sample mean and (uncorrected) sample variance are
  computed from minibatch statistics and used to normalize the incoming data.
  During training we also keep an exponentially decaying running mean of the mean
  and variance of each feature, and these averages are used to normalize data
  at test-time.

  At each timestep we update the running averages for mean and variance using
  an exponential decay based on the momentum parameter:

  running_mean = momentum * running_mean + (1 - momentum) * sample_mean
  running_var = momentum * running_var + (1 - momentum) * sample_var

  Note that the batch normalization paper suggests a different test-time
  behavior: they compute sample mean and variance for each feature using a
  large number of training images rather than using a running average. For
  this implementation we have chosen to use running averages instead since
  they do not require an additional estimation step; the torch7 implementation
  of batch normalization also uses running averages.

  Input:
  - x: Data of shape (N, D)
  - gamma: Scale parameter of shape (D,)
  - beta: Shift paremeter of shape (D,)
  - bn_param: Dictionary with the following keys:
    - mode: 'train' or 'test'; required
    - eps: Constant for numeric stability
    - momentum: Constant for running mean / variance.
    - running_mean: Array of shape (D,) giving running mean of features
    - running_var Array of shape (D,) giving running variance of features

  Returns a tuple of:
  - out: of shape (N, D)
  - cache: A tuple of values needed in the backward pass
  """
  mode = bn_param['mode']
  eps = bn_param.get('eps', 1e-5)
  momentum = bn_param.get('momentum', 0.9)

  N, D = x.shape
  running_mean = bn_param.get('running_mean', np.zeros(D, dtype=x.dtype))
  running_var = bn_param.get('running_var', np.zeros(D, dtype=x.dtype))

  out, cache = None, None
  if mode == 'train':
    #############################################################################
    # TODO: Implement the training-time forward pass for batch normalization.   #
    # Use minibatch statistics to compute the mean and variance, use these      #
    # statistics to normalize the incoming data, and scale and shift the        #
    # normalized data using gamma and beta.                                     #
    #                                                                           #
    # You should store the output in the variable out. Any intermediates that   #
    # you need for the backward pass should be stored in the cache variable.    #
    #                                                                           #
    # You should also use your computed sample mean and variance together with  #
    # the momentum variable to update the running mean and running variance,    #
    # storing your result in the running_mean and running_var variables.        #
    #############################################################################
    sample_mean = np.mean(x, axis = 0) 
    sample_var = np.var(x, axis = 0)

    x_normalized = (x-sample_mean) / np.sqrt(sample_var + eps)
    out = gamma*x_normalized + beta


    running_mean = momentum * running_mean + (1 - momentum) * sample_mean
    running_var = momentum * running_var + (1 - momentum) * sample_var

    cache = (x, sample_mean, sample_var, x_normalized, beta, gamma, eps)
    #############################################################################
    #                             END OF YOUR CODE                              #
    #############################################################################
  elif mode == 'test':
    #############################################################################
    # TODO: Implement the test-time forward pass for batch normalization. Use   #
    # the running mean and variance to normalize the incoming data, then scale  #
    # and shift the normalized data using gamma and beta. Store the result in   #
    # the out variable.                                                         #
    #############################################################################
    
    x_normalized = (x - running_mean)/np.sqrt(running_var +eps)
    out = gamma*x_normalized + beta
    
    #############################################################################
    #                             END OF YOUR CODE                              #
    #############################################################################
  else:
    raise ValueError('Invalid forward batchnorm mode "%s"' % mode)

  # Store the updated running means back into bn_param
  bn_param['running_mean'] = running_mean
  bn_param['running_var'] = running_var

  return out, cache


def batchnorm_backward(dout, cache):
  """
  Backward pass for batch normalization.
  
  For this implementation, you should write out a computation graph for
  batch normalization on paper and propagate gradients backward through
  intermediate nodes.
  
  Inputs:
  - dout: Upstream derivatives, of shape (N, D)
  - cache: Variable of intermediates from batchnorm_forward.
  
  Returns a tuple of:
  - dx: Gradient with respect to inputs x, of shape (N, D)
  - dgamma: Gradient with respect to scale parameter gamma, of shape (D,)
  - dbeta: Gradient with respect to shift parameter beta, of shape (D,)
  """
  dx, dgamma, dbeta = None, None, None
  #############################################################################
  # TODO: Implement the backward pass for batch normalization. Store the      #
  # results in the dx, dgamma, and dbeta variables.                           #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################

  return dx, dgamma, dbeta


def batchnorm_backward_alt(dout, cache):
  """
  Alternative backward pass for batch normalization.
  
  For this implementation you should work out the derivatives for the batch
  normalizaton backward pass on paper and simplify as much as possible. You
  should be able to derive a simple expression for the backward pass.
  
  Note: This implementation should expect to receive the same cache variable
  as batchnorm_backward, but might not use all of the values in the cache.
  
  Inputs / outputs: Same as batchnorm_backward
  """
  dx, dgamma, dbeta = None, None, None
  #############################################################################
  # TODO: Implement the backward pass for batch normalization. Store the      #
  # results in the dx, dgamma, and dbeta variables.                           #
  #                                                                           #
  # After computing the gradient with respect to the centered inputs, you     #
  # should be able to compute gradients with respect to the inputs in a       #
  # single statement; our implementation fits on a single 80-character line.  #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  
  return dx, dgamma, dbeta


def dropout_forward(x, dropout_param):
  """
  Performs the forward pass for (inverted) dropout.

  Inputs:
  - x: Input data, of any shape
  - dropout_param: A dictionary with the following keys:
    - p: Dropout parameter. We drop each neuron output with probability p.
    - mode: 'test' or 'train'. If the mode is train, then perform dropout;
      if the mode is test, then just return the input.
    - seed: Seed for the random number generator. Passing seed makes this
      function deterministic, which is needed for gradient checking but not in
      real networks.

  Outputs:
  - out: Array of the same shape as x.
  - cache: A tuple (dropout_param, mask). In training mode, mask is the dropout
    mask that was used to multiply the input; in test mode, mask is None.
  """
  p, mode = dropout_param['p'], dropout_param['mode']
  if 'seed' in dropout_param:
    np.random.seed(dropout_param['seed'])

  mask = None
  out = None

  if mode == 'train':
    ###########################################################################
    # TODO: Implement the training phase forward pass for inverted dropout.   #
    # Store the dropout mask in the mask variable.                            #
    ###########################################################################
    pass
    ###########################################################################
    #                            END OF YOUR CODE                             #
    ###########################################################################
  elif mode == 'test':
    ###########################################################################
    # TODO: Implement the test phase forward pass for inverted dropout.       #
    ###########################################################################
    pass
    ###########################################################################
    #                            END OF YOUR CODE                             #
    ###########################################################################

  cache = (dropout_param, mask)
  out = out.astype(x.dtype, copy=False)

  return out, cache


def dropout_backward(dout, cache):
  """
  Perform the backward pass for (inverted) dropout.

  Inputs:
  - dout: Upstream derivatives, of any shape
  - cache: (dropout_param, mask) from dropout_forward.
  """
  dropout_param, mask = cache
  mode = dropout_param['mode']
  
  dx = None
  if mode == 'train':
    ###########################################################################
    # TODO: Implement the training phase backward pass for inverted dropout.  #
    ###########################################################################
    pass
    ###########################################################################
    #                            END OF YOUR CODE                             #
    ###########################################################################
  elif mode == 'test':
    dx = dout
  return dx


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 HH.

  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)
  """
  out = None
  #############################################################################
  # TODO: Implement the convolutional forward pass.                           #
  # Hint: you can use the function np.pad for padding.                        #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  cache = (x, w, b, conv_param)
  return out, cache


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.                          #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  return dx, dw, db


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

  Returns a tuple of:
  - out: Output data
  - cache: (x, pool_param)
  """
  out = None
  #############################################################################
  # TODO: Implement the max pooling forward pass                              #
  #############################################################################
  pass
  #############################################################################
  #                             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                             #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  return dx


def spatial_batchnorm_forward(x, gamma, beta, bn_param):
  """
  Computes the forward pass for spatial batch normalization.
  
  Inputs:
  - x: Input data of shape (N, C, H, W)
  - gamma: Scale parameter, of shape (C,)
  - beta: Shift parameter, of shape (C,)
  - bn_param: Dictionary with the following keys:
    - mode: 'train' or 'test'; required
    - eps: Constant for numeric stability
    - momentum: Constant for running mean / variance. momentum=0 means that
      old information is discarded completely at every time step, while
      momentum=1 means that new information is never incorporated. The
      default of momentum=0.9 should work well in most situations.
    - running_mean: Array of shape (D,) giving running mean of features
    - running_var Array of shape (D,) giving running variance of features
    
  Returns a tuple of:
  - out: Output data, of shape (N, C, H, W)
  - cache: Values needed for the backward pass
  """
  out, cache = None, None

  #############################################################################
  # TODO: Implement the forward pass for spatial batch normalization.         #
  #                                                                           #
  # HINT: You can implement spatial batch normalization using the vanilla     #
  # version of batch normalization defined above. Your implementation should  #
  # be very short; ours is less than five lines.                              #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################

  return out, cache


def spatial_batchnorm_backward(dout, cache):
  """
  Computes the backward pass for spatial batch normalization.
  
  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

  #############################################################################
  # TODO: Implement the backward pass for spatial batch normalization.        #
  #                                                                           #
  # HINT: You can implement spatial batch normalization using the vanilla     #
  # version of batch normalization defined above. Your implementation should  #
  # be very short; ours is less than five lines.                              #
  #############################################################################
  pass
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################

  return dx, dgamma, dbeta
  

def svm_loss(x, y):
  """
  Computes the loss and gradient using for multiclass SVM classification.

  Inputs:
  - x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
    for the ith input.
  - y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
    0 <= y[i] < C

  Returns a tuple of:
  - loss: Scalar giving the loss
  - dx: Gradient of the loss with respect to x
  """
  N = x.shape[0]
  correct_class_scores = x[np.arange(N), y]
  margins = np.maximum(0, x - correct_class_scores[:, np.newaxis] + 1.0)
  margins[np.arange(N), y] = 0
  loss = np.sum(margins) / N
  num_pos = np.sum(margins > 0, axis=1)
  dx = np.zeros_like(x)
  dx[margins > 0] = 1
  dx[np.arange(N), y] -= num_pos
  dx /= N
  return loss, dx


def softmax_loss(x, y):
  """
  Computes the loss and gradient for softmax classification.

  Inputs:
  - x: Input data, of shape (N, C) where x[i, j] is the score for the jth class
    for the ith input.
  - y: Vector of labels, of shape (N,) where y[i] is the label for x[i] and
    0 <= y[i] < C

  Returns a tuple of:
  - loss: Scalar giving the loss
  - dx: Gradient of the loss with respect to x
  """
  probs = np.exp(x - np.max(x, axis=1, keepdims=True))
  probs /= np.sum(probs, axis=1, keepdims=True)
  N = x.shape[0]
  loss = -np.sum(np.log(probs[np.arange(N), y])) / N
  dx = probs.copy()
  dx[np.arange(N), y] -= 1
  dx /= N
  return loss, dx

fc_net.py

import numpy as np

from cs231n.layers import *
from cs231n.layer_utils import *


class TwoLayerNet(object):
  """
  A two-layer fully-connected neural network with ReLU nonlinearity and
  softmax loss that uses a modular layer design. We assume an input dimension
  of D, a hidden dimension of H, and perform classification over C classes.
  
  The architecure should be affine - relu - affine - softmax.

  Note that this class does not implement gradient descent; instead, it
  will interact with a separate Solver object that is responsible for running
  optimization.

  The learnable parameters of the model are stored in the dictionary
  self.params that maps parameter names to numpy arrays.
  """
  
  def __init__(self, input_dim=3*32*32, hidden_dim=100, num_classes=10,
               weight_scale=1e-3, reg=0.0):
    """
    Initialize a new network.

    Inputs:
    - input_dim: An integer giving the size of the input
    - hidden_dim: An integer giving the size of the hidden layer
    - num_classes: An integer giving the number of classes to classify
    - dropout: Scalar between 0 and 1 giving dropout strength.
    - weight_scale: Scalar giving the standard deviation for random
      initialization of the weights.
    - reg: Scalar giving L2 regularization strength.
    """
    self.params = {}
    self.reg = reg
    
    ############################################################################
    # TODO: Initialize the weights and biases of the two-layer net. Weights    #
    # should be initialized from a Gaussian with standard deviation equal to   #
    # weight_scale, and biases should be initialized to zero. All weights and  #
    # biases should be stored in the dictionary self.params, with first layer  #
    # weights and biases using the keys 'W1' and 'b1' and second layer weights #
    # and biases using the keys 'W2' and 'b2'.                                 #
    ############################################################################
    
    self.params['W1'] = np.random.normal(0, weight_scale, (input_dim, hidden_dim))
    self.params['b1'] = np.zeros(hidden_dim)
    self.params['W2'] = np.random.normal(0, weight_scale, (hidden_dim, num_classes))
    self.params['b2'] = np.zeros(num_classes)

    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################


  def loss(self, X, y=None):
    """
    Compute loss and gradient for a minibatch of data.

    Inputs:
    - X: Array of input data of shape (N, d_1, ..., d_k)
    - y: Array of labels, of shape (N,). y[i] gives the label for X[i].

    Returns:
    If y is None, then run a test-time forward pass of the model and return:
    - scores: Array of shape (N, C) giving classification scores, where
      scores[i, c] is the classification score for X[i] and class c.

    If y is not None, then run a training-time forward and backward pass and
    return a tuple of:
    - loss: Scalar value giving the loss
    - grads: Dictionary with the same keys as self.params, mapping parameter
      names to gradients of the loss with respect to those parameters.
    """  
    scores = None
    ############################################################################
    # TODO: Implement the forward pass for the two-layer net, computing the    #
    # class scores for X and storing them in the scores variable.              #
    ############################################################################
    
    # affine_relu_out is the output of the ReLu layer
    # affine2_out is the output of the second Affine layer
    affine_relu_out, affine_relu_cache = affine_relu_forward(X, self.params['W1'], self.params['b1'])
    affine2_out, affine2_cache = affine_forward(affine_relu_out, self.params['W2'], self.params['b2']) 

    scores = affine2_out

    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################

    # If y is None then we are in test mode so just return scores
    if y is None:
      return scores
    
    loss, grads = 0, {}
    ############################################################################
    # TODO: Implement the backward pass for the two-layer net. Store the loss  #
    # in the loss variable and gradients in the grads dictionary. 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, dscores = softmax_loss(scores, y) 
    loss += 0.5 * self.reg*(np.sum(self.params['W1']* self.params['W1']) + np.sum(self.params['W2']* self.params['W2']))
    
    affine2_dx, affine2_dw, affine2_db = affine_backward(dscores, affine2_cache)
    grads['W2'] = affine2_dw + self.reg * self.params['W2']
    grads['b2'] = affine2_db

    affine1_dx, affine1_dw, affine1_db = affine_relu_backward(affine2_dx, affine_relu_cache)
    grads['W1'] = affine1_dw + self.reg * self.params['W1']
    grads['b1'] = affine1_db
    
    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################

    return loss, grads


class FullyConnectedNet(object):
  """
  A fully-connected neural network with an arbitrary number of hidden layers,
  ReLU nonlinearities, and a softmax loss function. This will also implement
  dropout and batch normalization as options. For a network with L layers,
  the architecture will be
  
  {affine - [batch norm] - relu - [dropout]} x (L - 1) - affine - softmax
  
  where batch normalization and dropout are optional, and the {...} block is
  repeated L - 1 times.
  
  Similar to the TwoLayerNet above, learnable parameters are stored in the
  self.params dictionary and will be learned using the Solver class.
  """

  def __init__(self, hidden_dims, input_dim=3*32*32, num_classes=10,
               dropout=0, use_batchnorm=False, reg=0.0,
               weight_scale=1e-2, dtype=np.float32, seed=None):
    """
    Initialize a new FullyConnectedNet.
    
    Inputs:
    - hidden_dims: A list of integers giving the size of each hidden layer.
    - input_dim: An integer giving the size of the input.
    - num_classes: An integer giving the number of classes to classify.
    - dropout: Scalar between 0 and 1 giving dropout strength. If dropout=0 then
      the network should not use dropout at all.
    - use_batchnorm: Whether or not the network should use batch normalization.
    - reg: Scalar giving L2 regularization strength.
    - weight_scale: Scalar giving the standard deviation for random
      initialization of the weights.
    - dtype: A numpy datatype object; all computations will be performed using
      this datatype. float32 is faster but less accurate, so you should use
      float64 for numeric gradient checking.
    - seed: If not None, then pass this random seed to the dropout layers. This
      will make the dropout layers deteriminstic so we can gradient check the
      model.
    """
    self.use_batchnorm = use_batchnorm
    self.use_dropout = dropout > 0
    self.reg = reg
    self.num_layers = 1 + len(hidden_dims)
    self.dtype = dtype
    self.params = {}

    ############################################################################
    # TODO: Initialize the parameters of the network, storing all values in    #
    # the self.params dictionary. Store weights and biases for the first layer #
    # in W1 and b1; for the second layer use W2 and b2, etc. Weights should be #
    # initialized from a normal distribution with standard deviation equal to  #
    # weight_scale and biases should be initialized to zero.                   #
    #                                                                          #
    # When using batch normalization, store scale and shift parameters for the #
    # first layer in gamma1 and beta1; for the second layer use gamma2 and     #
    # beta2, etc. Scale parameters should be initialized to one and shift      #
    # parameters should be initialized to zero.                                #
    ############################################################################
    for i in range(1, self.num_layers+1):

       layer_input_dim = input_dim if i == 1 else hidden_dims[i-2]
       layer_output_dim = num_classes if i==self.num_layers else hidden_dims[i-1]
      
       self.params['W' + str(i)] = np.random.normal(0, weight_scale, (layer_input_dim, layer_output_dim))
       self.params['b' + str(i)] = np.zeros(layer_output_dim)

       if use_batchnorm and i!=self.num_layers:
          self.params['beta'+str(i)]=np.zeros(layer_output_dim)
          self.params['gamma'+str(i)]=np.ones(layer_output_dim)
    
    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################

    # When using dropout we need to pass a dropout_param dictionary to each
    # dropout layer so that the layer knows the dropout probability and the mode
    # (train / test). You can pass the same dropout_param to each dropout layer.
    self.dropout_param = {}
    if self.use_dropout:
      self.dropout_param = {'mode': 'train', 'p': dropout}
      if seed is not None:
        self.dropout_param['seed'] = seed
    
    # With batch normalization we need to keep track of running means and
    # variances, so we need to pass a special bn_param object to each batch
    # normalization layer. You should pass self.bn_params[0] to the forward pass
    # of the first batch normalization layer, self.bn_params[1] to the forward
    # pass of the second batch normalization layer, etc.
    self.bn_params = []
    if self.use_batchnorm:
      self.bn_params = [{'mode': 'train'} for i in xrange(self.num_layers - 1)]
    
    # Cast all parameters to the correct datatype
    for k, v in self.params.iteritems():
      self.params[k] = v.astype(dtype)


  def loss(self, X, y=None):
    """
    Compute loss and gradient for the fully-connected net.

    Input / output: Same as TwoLayerNet above.
    """
    X = X.astype(self.dtype)
    mode = 'test' if y is None else 'train'

    # Set train/test mode for batchnorm params and dropout param since they
    # behave differently during training and testing.
    if self.dropout_param is not None:
      self.dropout_param['mode'] = mode   
    if self.use_batchnorm:
      for bn_param in self.bn_params:
        bn_param[mode] = mode

    scores = None
    ############################################################################
    # TODO: Implement the forward pass for the fully-connected net, computing  #
    # the class scores for X and storing them in the scores variable.          #
    #                                                                          #
    # When using dropout, you'll need to pass self.dropout_param to each       #
    # dropout forward pass.                                                    #
    #                                                                          #
    # When using batch normalization, you'll need to pass self.bn_params[0] to #
    # the forward pass for the first batch normalization layer, pass           #
    # self.bn_params[1] to the forward pass for the second batch normalization #
    # layer, etc.                                                              #
    ############################################################################
    current_input = X 
    affine_relu_cache={}
    affine_bn_relu_cache={}
    dropout_cache={}


    for i in range(1, self.num_layers):
        keyW = 'W' + str(i)
        keyb = 'b' + str(i)
        if not self.use_batchnorm:
            current_input, affine_relu_cache[i] = affine_relu_forward(current_input, self.params[keyW], self.params[keyb])

        else:  
            key_gamma = 'gamma'+str(i)
            key_beta = 'beta'+str(i)
            current_input, affine_bn_relu_cache[i] = affine_bn_relu_forward(current_input, self.params[keyW], self.params[keyb],
                                                                                    self.params[key_gamma], self.params[key_beta], self.bn_params[i-1] )

        if self.use_dropout:
            current_input, dropout_cache[i] = dropout_forward(current_input,self.dropout_param)  


    # Last affine layer:
    keyW = 'W' + str(self.num_layers)
    keyb = 'b' + str(self.num_layers)
    affine_out, affine_cache = affine_forward(current_input, self.params[keyW], self.params[keyb])
    scores = affine_out
    
    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################

    # If test mode return early
    if mode == 'test':
      return scores

    loss, grads = 0.0, {}
    ############################################################################
    # TODO: Implement the backward pass for the fully-connected net. Store the #
    # loss in the loss variable and gradients in the grads dictionary. 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!               #
    #                                                                          #
    # When using batch normalization, you don't need to regularize the scale   #
    # and shift parameters.                                                    #
    #                                                                          #
    # 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, dscores = softmax_loss(scores, y)

    #last layer:
    affine_dx, affine_dw, affine_db = affine_backward(dscores, affine_cache)
    grads['W'+str(self.num_layers)] = affine_dw + self.reg * self.params['W'+str(self.num_layers)]
    grads['b'+str(self.num_layers)] = affine_db
    loss += 0.5 * self.reg*(np.sum(self.params['W'+str(self.num_layers)]* self.params['W'+str(self.num_layers)]))


    for i in range(self.num_layers-1,0,-1):
        if self.use_dropout:
            affine_dx = dropout_backward(affine_dx, dropout_cache[i])

        if not self.use_batchnorm:       
            affine_dx, affine_dw, affine_db = affine_relu_backward(affine_dx, affine_relu_cache[i])

        else:       
            affine_dx, affine_dw, affine_db, dgamma, dbeta = affine_bn_relu_backward(affine_dx, affine_bn_relu_cache[i]) 
            grads['beta'+str(i)]=dbeta
            grads['gamma'+str(i)]=dgamma
        
        keyW = 'W' + str(i)
        keyb = 'b' + str(i)    
        loss += 0.5 * self.reg*(np.sum(self.params[keyW]* self.params[keyW])) 
        grads[keyW] = affine_dw + self.reg * self.params[keyW]
        grads[keyb] = affine_db

    ############################################################################
    #                             END OF YOUR CODE                             #
    ############################################################################

    return loss, grads



def affine_bn_relu_forward(x, w, b, gamma, beta, bn_param):
  """
  Convenience layer that perorms an affine transform followed by a ReLU

  Inputs:
  - x: Input to the affine layer
  - w, b: Weights for the affine layer

  Returns a tuple of:
  - out: Output from the ReLU
  - cache: Object to give to the backward pass
  """
  affine_out, fc_cache = affine_forward(x, w, b)
  bn_out, bn_cache = batchnorm_forward(affine_out, gamma, beta, bn_param)
  relu_out, relu_cache = relu_forward(bn_out)
  cache = (fc_cache, bn_cache, relu_cache)
  return relu_out, cache

def affine_bn_relu_backward(dout, cache):
  """
  Backward pass for the affine-relu convenience layer
  """
  fc_cache, bn_cache, relu_cache = cache
  drelu_out = relu_backward(dout, relu_cache)
  dbn_out, dgamma, dbeta = batchnorm_backward(drelu_out, bn_cache)
  dx, dw, db = affine_backward(dbn_out, fc_cache)
  return dx, dw, db, dgamma, dbeta

optim.py

import numpy as np

"""
This file implements various first-order update rules that are commonly used for
training neural networks. Each update rule accepts current weights and the
gradient of the loss with respect to those weights and produces the next set of
weights. Each update rule has the same interface:

def update(w, dw, config=None):

Inputs:
  - w: A numpy array giving the current weights.
  - dw: A numpy array of the same shape as w giving the gradient of the
    loss with respect to w.
  - config: A dictionary containing hyperparameter values such as learning rate,
    momentum, etc. If the update rule requires caching values over many
    iterations, then config will also hold these cached values.

Returns:
  - next_w: The next point after the update.
  - config: The config dictionary to be passed to the next iteration of the
    update rule.

NOTE: For most update rules, the default learning rate will probably not perform
well; however the default values of the other hyperparameters should work well
for a variety of different problems.

For efficiency, update rules may perform in-place updates, mutating w and
setting next_w equal to w.
"""


def sgd(w, dw, config=None):
  """
  Performs vanilla stochastic gradient descent.

  config format:
  - learning_rate: Scalar learning rate.
  """
  if config is None: config = {}
  config.setdefault('learning_rate', 1e-2)

  w -= config['learning_rate'] * dw
  return w, config


def sgd_momentum(w, dw, config=None):
  """
  Performs stochastic gradient descent with momentum.

  config format:
  - learning_rate: Scalar learning rate.
  - momentum: Scalar between 0 and 1 giving the momentum value.
    Setting momentum = 0 reduces to sgd.
  - velocity: A numpy array of the same shape as w and dw used to store a moving
    average of the gradients.
  """
  if config is None: config = {}
  config.setdefault('learning_rate', 1e-2)
  config.setdefault('momentum', 0.9)
  v = config.get('velocity', np.zeros_like(w))
  
  next_w = None
  #############################################################################
  # TODO: Implement the momentum update formula. Store the updated value in   #
  # the next_w variable. You should also use and update the velocity v.       #
  #############################################################################
 
  next_w = w
  v = config['momentum']* v - config['learning_rate']*dw
  next_w +=v
  
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  config['velocity'] = v

  return next_w, config



def rmsprop(x, dx, config=None):
  """
  Uses the RMSProp update rule, which uses a moving average of squared gradient
  values to set adaptive per-parameter learning rates.

  config format:
  - learning_rate: Scalar learning rate.
  - decay_rate: Scalar between 0 and 1 giving the decay rate for the squared
    gradient cache.
  - epsilon: Small scalar used for smoothing to avoid dividing by zero.
  - cache: Moving average of second moments of gradients.
  """
  if config is None: config = {}
  config.setdefault('learning_rate', 1e-2)
  config.setdefault('decay_rate', 0.99)
  config.setdefault('epsilon', 1e-8)
  config.setdefault('cache', np.zeros_like(x))

  next_x = None
  #############################################################################
  # TODO: Implement the RMSprop update formula, storing the next value of x   #
  # in the next_x variable. Don't forget to update cache value stored in      #  
  # config['cache'].                                                          #
  #############################################################################
  
  next_x = x
  config['cache'] = config['decay_rate']*config['cache']+(1-config['decay_rate'])*(dx*dx)
  x += -config['learning_rate']* dx / (np.sqrt(config['cache'])+config['epsilon'])
  
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################

  return next_x, config


def adam(x, dx, config=None):
  """
  Uses the Adam update rule, which incorporates moving averages of both the
  gradient and its square and a bias correction term.

  config format:
  - learning_rate: Scalar learning rate.
  - beta1: Decay rate for moving average of first moment of gradient.
  - beta2: Decay rate for moving average of second moment of gradient.
  - epsilon: Small scalar used for smoothing to avoid dividing by zero.
  - m: Moving average of gradient.
  - v: Moving average of squared gradient.
  - t: Iteration number.
  """
  if config is None: config = {}
  config.setdefault('learning_rate', 1e-3)
  config.setdefault('beta1', 0.9)
  config.setdefault('beta2', 0.999)
  config.setdefault('epsilon', 1e-8)
  config.setdefault('m', np.zeros_like(x))
  config.setdefault('v', np.zeros_like(x))
  config.setdefault('t', 0)
  
  next_x = None
  #############################################################################
  # TODO: Implement the Adam update formula, storing the next value of x in   #
  # the next_x variable. Don't forget to update the m, v, and t variables     #
  # stored in config.                                                         #
  #############################################################################
  
  config['t']+=1 
  config['m'] = config['beta1']*config['m'] + (1- config['beta1'])*dx
  config['v'] = config['beta2']*config['v'] + (1- config['beta2'])*(dx**2)   
  mb = config['m']/(1-config['beta1']**config['t'])
  vb = config['v']/(1-config['beta2']**config['t'])
  next_x = x -config['learning_rate']* mb / (np.sqrt(vb) + config['epsilon'])
  
  #############################################################################
  #                             END OF YOUR CODE                              #
  #############################################################################
  
  return next_x, config

FullyConnectedNets.ipynb的部分代码

model = TwoLayerNet()
solver = None

##############################################################################
# TODO: Use a Solver instance to train a TwoLayerNet that achieves at least  #
# 50% accuracy on the validation set.                                        #
##############################################################################
for k, v in data.iteritems():
  print '%s: ' % k, v.shape

model = TwoLayerNet(hidden_dim=100, reg= 8.598929e-03)
solver = Solver(model, data,
                update_rule='sgd',
                optim_config={
                  'learning_rate': 1.207591e-03,
                },
                lr_decay=0.95,
                num_epochs=10, batch_size=100,
                print_every=49000)
solver.train()
##############################################################################
#                             END OF YOUR CODE                               #
##############################################################################

best_model = None
################################################################################
# TODO: Train the best FullyConnectedNet that you can on CIFAR-10. You might   #
# batch normalization and dropout useful. Store your best model in the         #
# best_model variable.                                                         #
################################################################################
X_val= data['X_val']
y_val= data['y_val']
X_test= data['X_test']
y_test= data['y_test']

lr = 3.113669e-04 #[10] #[2.379994e-04] # 10**np.random.uniform(-7,1,20)
ws = 2.461858e-02

model = FullyConnectedNet([100, 100, 100, 100],
      weight_scale=ws, dtype=np.float64,use_batchnorm=False, reg= 1e-2)
solver = Solver(model, data,
        print_every=100, num_epochs=10, batch_size=25,
        update_rule='adam',
        optim_config={
          'learning_rate': lr,
        },
        lr_decay = 0.9,
        verbose = True
        )   

solver.train()

plt.subplot(2, 1, 1)
plt.plot(solver.loss_history)
plt.title('Loss history')
plt.xlabel('Iteration')
plt.ylabel('Loss')

plt.subplot(2, 1, 2)
plt.plot(solver.train_acc_history, label='train')
plt.plot(solver.val_acc_history, label='val')
plt.title('Classification accuracy history')
plt.xlabel('Epoch')
plt.ylabel('Clasification accuracy')
plt.show() 

best_model = model
################################################################################
#                              END OF YOUR CODE                                #
################################################################################

Solver的结果

Use a three-layer Net to overfit 50 training examples.

Use a five-layer Net to overfit 50 training examples.

RMSProp  Adam  SGD  Momentum 四种方法的对比

用adam方法训练的最好的模型

测试的结果：

Validation set accuracy:  0.54
Test set accuracy:  0.532