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神经网络cifar代码

神经网络cifar代码

作者: ForgetThatNight | 来源:发表于2018-07-06 20:23 被阅读46次

初识神经网络代码

drawData.py

import numpy as np
import matplotlib.pyplot as plt

#ubuntu 16.04 sudo pip instal matplotlib

plt.rcParams['figure.figsize'] = (10.0, 8.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

np.random.seed(0)
N = 100 # number of points per class
D = 2 # dimensionality
K = 3 # number of classes
X = np.zeros((N*K,D))
y = np.zeros(N*K, dtype='uint8')
for j in xrange(K):
  ix = range(N*j,N*(j+1))
  r = np.linspace(0.0,1,N) # radius
  t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
  X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
  y[ix] = j
fig = plt.figure()
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.xlim([-1,1])
plt.ylim([-1,1])
plt.show()
    

linerCla.py

#Train a Linear Classifier
import numpy as np
import matplotlib.pyplot as plt


np.random.seed(0)
N = 100 # number of points per class
D = 2 # dimensionality
K = 3 # number of classes
X = np.zeros((N*K,D))
y = np.zeros(N*K, dtype='uint8')
for j in xrange(K):
  ix = range(N*j,N*(j+1))
  r = np.linspace(0.0,1,N) # radius
  t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
  X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
  y[ix] = j



W = 0.01 * np.random.randn(D,K)
b = np.zeros((1,K))

# some hyperparameters
step_size = 1e-0
reg = 1e-3 # regularization strength

# gradient descent loop
num_examples = X.shape[0]
for i in xrange(1000):
  #print X.shape
  # evaluate class scores, [N x K]
  scores = np.dot(X, W) + b   #x:300*2 scores:300*3
  #print scores.shape 
  # compute the class probabilities
  exp_scores = np.exp(scores)
  probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K] probs:300*3
  print probs.shape 
  # compute the loss: average cross-entropy loss and regularization
  corect_logprobs = -np.log(probs[range(num_examples),y]) #corect_logprobs:300*1
  print corect_logprobs.shape
  data_loss = np.sum(corect_logprobs)/num_examples
  reg_loss = 0.5*reg*np.sum(W*W)
  loss = data_loss + reg_loss
  if i % 100 == 0:
    print "iteration %d: loss %f" % (i, loss)
  
  # compute the gradient on scores
  dscores = probs
  dscores[range(num_examples),y] -= 1
  dscores /= num_examples
  
  # backpropate the gradient to the parameters (W,b)
  dW = np.dot(X.T, dscores)
  db = np.sum(dscores, axis=0, keepdims=True)
  
  dW += reg*W # regularization gradient
  
  # perform a parameter update
  W += -step_size * dW
  b += -step_size * db
  scores = np.dot(X, W) + b
predicted_class = np.argmax(scores, axis=1)
print 'training accuracy: %.2f' % (np.mean(predicted_class == y))

h = 0.02
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                     np.arange(y_min, y_max, h))
Z = np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b
Z = np.argmax(Z, axis=1)
Z = Z.reshape(xx.shape)
fig = plt.figure()
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.show()

NNCla.py

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(0)
N = 100 # number of points per class
D = 2 # dimensionality
K = 3 # number of classes
X = np.zeros((N*K,D))
y = np.zeros(N*K, dtype='uint8')
for j in xrange(K):
  ix = range(N*j,N*(j+1))
  r = np.linspace(0.0,1,N) # radius
  t = np.linspace(j*4,(j+1)*4,N) + np.random.randn(N)*0.2 # theta
  X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
  y[ix] = j
  
h = 100 # size of hidden layer
W = 0.01 * np.random.randn(D,h)# x:300*2  2*100
b = np.zeros((1,h))
W2 = 0.01 * np.random.randn(h,K)
b2 = np.zeros((1,K))

# some hyperparameters
step_size = 1e-0
reg = 1e-3 # regularization strength

# gradient descent loop
num_examples = X.shape[0]
for i in xrange(2000):
  
  # evaluate class scores, [N x K]
  hidden_layer = np.maximum(0, np.dot(X, W) + b) # note, ReLU activation hidden_layer:300*100
  #print hidden_layer.shape
  scores = np.dot(hidden_layer, W2) + b2  #scores:300*3
  #print scores.shape
  # compute the class probabilities
  exp_scores = np.exp(scores)
  probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) # [N x K]
  #print probs.shape
  
  # compute the loss: average cross-entropy loss and regularization
  corect_logprobs = -np.log(probs[range(num_examples),y])
  data_loss = np.sum(corect_logprobs)/num_examples
  reg_loss = 0.5*reg*np.sum(W*W) + 0.5*reg*np.sum(W2*W2)
  loss = data_loss + reg_loss
  if i % 100 == 0:
    print "iteration %d: loss %f" % (i, loss)
  
  # compute the gradient on scores
  dscores = probs
  dscores[range(num_examples),y] -= 1
  dscores /= num_examples
  
  # backpropate the gradient to the parameters
  # first backprop into parameters W2 and b2
  dW2 = np.dot(hidden_layer.T, dscores)
  db2 = np.sum(dscores, axis=0, keepdims=True)
  # next backprop into hidden layer
  dhidden = np.dot(dscores, W2.T)
  # backprop the ReLU non-linearity
  dhidden[hidden_layer <= 0] = 0
  # finally into W,b
  dW = np.dot(X.T, dhidden)
  db = np.sum(dhidden, axis=0, keepdims=True)
  
  # add regularization gradient contribution
  dW2 += reg * W2
  dW += reg * W
  
  # perform a parameter update
  W += -step_size * dW
  b += -step_size * db
  W2 += -step_size * dW2
  b2 += -step_size * db2
hidden_layer = np.maximum(0, np.dot(X, W) + b)
scores = np.dot(hidden_layer, W2) + b2
predicted_class = np.argmax(scores, axis=1)
print 'training accuracy: %.2f' % (np.mean(predicted_class == y))


h = 0.02
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                     np.arange(y_min, y_max, h))
Z = np.dot(np.maximum(0, np.dot(np.c_[xx.ravel(), yy.ravel()], W) + b), W2) + b2
Z = np.argmax(Z, axis=1)
Z = Z.reshape(xx.shape)
fig = plt.figure()
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral, alpha=0.8)
plt.scatter(X[:, 0], X[:, 1], c=y, s=40, cmap=plt.cm.Spectral)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.show()

cifar代码

data_utils.py

import cPickle as pickle
import numpy as np
import os
#from scipy.misc import imread

def load_CIFAR_batch(filename):
  """ load single batch of cifar """
  with open(filename, 'rb') as f:
    datadict = pickle.load(f)
    X = datadict['data']
    Y = datadict['labels']
    X = X.reshape(10000, 3, 32, 32).transpose(0,2,3,1).astype("float")
    Y = np.array(Y)
    return X, Y

def load_CIFAR10(ROOT):
  """ load all of cifar """
  xs = []
  ys = []
  for b in range(1,2):
    f = os.path.join(ROOT, 'data_batch_%d' % (b, ))
    X, Y = load_CIFAR_batch(f)
    xs.append(X)
    ys.append(Y)    
  Xtr = np.concatenate(xs)
  Ytr = np.concatenate(ys)
  del X, Y
  Xte, Yte = load_CIFAR_batch(os.path.join(ROOT, 'test_batch'))
  return Xtr, Ytr, Xte, Yte


def get_CIFAR10_data(num_training=5000, num_validation=500, num_test=500):
    """
    Load the CIFAR-10 dataset from disk and perform preprocessing to prepare
    it for classifiers. These are the same steps as we used for the SVM, but
    condensed to a single function.
    """
    # Load the raw CIFAR-10 data

    cifar10_dir = 'C://download//cifar-10-python//cifar-10-batches-py//'
    X_train, y_train, X_test, y_test = load_CIFAR10(cifar10_dir)
    print X_train.shape
    # Subsample the data
    mask = range(num_training, num_training + num_validation)
    X_val = X_train[mask]
    y_val = y_train[mask]
    mask = range(num_training)
    X_train = X_train[mask]
    y_train = y_train[mask]
    mask = range(num_test)
    X_test = X_test[mask]
    y_test = y_test[mask]

    # Normalize the data: subtract the mean image
    mean_image = np.mean(X_train, axis=0)
    X_train -= mean_image
    X_val -= mean_image
    X_test -= mean_image
    
    # Transpose so that channels come first
    X_train = X_train.transpose(0, 3, 1, 2).copy()
    X_val = X_val.transpose(0, 3, 1, 2).copy()
    X_test = X_test.transpose(0, 3, 1, 2).copy()

    # Package data into a dictionary
    return {
      'X_train': X_train, 'y_train': y_train,
      'X_val': X_val, 'y_val': y_val,
      'X_test': X_test, 'y_test': y_test,
    }
    
"""
def load_tiny_imagenet(path, dtype=np.float32):
  
  Load TinyImageNet. Each of TinyImageNet-100-A, TinyImageNet-100-B, and
  TinyImageNet-200 have the same directory structure, so this can be used
  to load any of them.

  Inputs:
  - path: String giving path to the directory to load.
  - dtype: numpy datatype used to load the data.

  Returns: A tuple of
  - class_names: A list where class_names[i] is a list of strings giving the
    WordNet names for class i in the loaded dataset.
  - X_train: (N_tr, 3, 64, 64) array of training images
  - y_train: (N_tr,) array of training labels
  - X_val: (N_val, 3, 64, 64) array of validation images
  - y_val: (N_val,) array of validation labels
  - X_test: (N_test, 3, 64, 64) array of testing images.
  - y_test: (N_test,) array of test labels; if test labels are not available
    (such as in student code) then y_test will be None.
  
  # First load wnids
  with open(os.path.join(path, 'wnids.txt'), 'r') as f:
    wnids = [x.strip() for x in f]

  # Map wnids to integer labels
  wnid_to_label = {wnid: i for i, wnid in enumerate(wnids)}

  # Use words.txt to get names for each class
  with open(os.path.join(path, 'words.txt'), 'r') as f:
    wnid_to_words = dict(line.split('\t') for line in f)
    for wnid, words in wnid_to_words.iteritems():
      wnid_to_words[wnid] = [w.strip() for w in words.split(',')]
  class_names = [wnid_to_words[wnid] for wnid in wnids]

  # Next load training data.
  X_train = []
  y_train = []
  for i, wnid in enumerate(wnids):
    if (i + 1) % 20 == 0:
      print 'loading training data for synset %d / %d' % (i + 1, len(wnids))
    # To figure out the filenames we need to open the boxes file
    boxes_file = os.path.join(path, 'train', wnid, '%s_boxes.txt' % wnid)
    with open(boxes_file, 'r') as f:
      filenames = [x.split('\t')[0] for x in f]
    num_images = len(filenames)
    
    X_train_block = np.zeros((num_images, 3, 64, 64), dtype=dtype)
    y_train_block = wnid_to_label[wnid] * np.ones(num_images, dtype=np.int64)
    for j, img_file in enumerate(filenames):
      img_file = os.path.join(path, 'train', wnid, 'images', img_file)
      img = imread(img_file)
      if img.ndim == 2:
        ## grayscale file
        img.shape = (64, 64, 1)
      X_train_block[j] = img.transpose(2, 0, 1)
    X_train.append(X_train_block)
    y_train.append(y_train_block)
      
  # We need to concatenate all training data
  X_train = np.concatenate(X_train, axis=0)
  y_train = np.concatenate(y_train, axis=0)
  
  # Next load validation data
  with open(os.path.join(path, 'val', 'val_annotations.txt'), 'r') as f:
    img_files = []
    val_wnids = []
    for line in f:
      img_file, wnid = line.split('\t')[:2]
      img_files.append(img_file)
      val_wnids.append(wnid)
    num_val = len(img_files)
    y_val = np.array([wnid_to_label[wnid] for wnid in val_wnids])
    X_val = np.zeros((num_val, 3, 64, 64), dtype=dtype)
    for i, img_file in enumerate(img_files):
      img_file = os.path.join(path, 'val', 'images', img_file)
      img = imread(img_file)
      if img.ndim == 2:
        img.shape = (64, 64, 1)
      X_val[i] = img.transpose(2, 0, 1)

  # Next load test images
  # Students won't have test labels, so we need to iterate over files in the
  # images directory.
  img_files = os.listdir(os.path.join(path, 'test', 'images'))
  X_test = np.zeros((len(img_files), 3, 64, 64), dtype=dtype)
  for i, img_file in enumerate(img_files):
    img_file = os.path.join(path, 'test', 'images', img_file)
    img = imread(img_file)
    if img.ndim == 2:
      img.shape = (64, 64, 1)
    X_test[i] = img.transpose(2, 0, 1)

  y_test = None
  y_test_file = os.path.join(path, 'test', 'test_annotations.txt')
  if os.path.isfile(y_test_file):
    with open(y_test_file, 'r') as f:
      img_file_to_wnid = {}
      for line in f:
        line = line.split('\t')
        img_file_to_wnid[line[0]] = line[1]
    y_test = [wnid_to_label[img_file_to_wnid[img_file]] for img_file in img_files]
    y_test = np.array(y_test)
  
  return class_names, X_train, y_train, X_val, y_val, X_test, y_test

"""
def load_models(models_dir):
  """
  Load saved models from disk. This will attempt to unpickle all files in a
  directory; any files that give errors on unpickling (such as README.txt) will
  be skipped.

  Inputs:
  - models_dir: String giving the path to a directory containing model files.
    Each model file is a pickled dictionary with a 'model' field.

  Returns:
  A dictionary mapping model file names to models.
  """
  models = {}
  for model_file in os.listdir(models_dir):
    with open(os.path.join(models_dir, model_file), 'rb') as f:
      try:
        models[model_file] = pickle.load(f)['model']
      except pickle.UnpicklingError:
        continue
  return models

layer_utils.py

from layers import *



def affine_relu_forward(x, w, b):
  """
  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
  """
  a, fc_cache = affine_forward(x, w, b)
  out, relu_cache = relu_forward(a)
  cache = (fc_cache, relu_cache)
  return out, cache


def affine_relu_backward(dout, cache):
  """
  Backward pass for the affine-relu convenience layer
  """
  fc_cache, relu_cache = cache
  da = relu_backward(dout, relu_cache)
  dx, dw, db = affine_backward(da, fc_cache)
  return dx, dw, db


pass


def conv_relu_forward(x, w, b, conv_param):
  """
  A convenience layer that performs a convolution followed by a ReLU.

  Inputs:
  - x: Input to the convolutional layer
  - w, b, conv_param: Weights and parameters for the convolutional layer
  
  Returns a tuple of:
  - out: Output from the ReLU
  - cache: Object to give to the backward pass
  """
  a, conv_cache = conv_forward_fast(x, w, b, conv_param)
  out, relu_cache = relu_forward(a)
  cache = (conv_cache, relu_cache)
  return out, cache


def conv_relu_backward(dout, cache):
  """
  Backward pass for the conv-relu convenience layer.
  """
  conv_cache, relu_cache = cache
  da = relu_backward(dout, relu_cache)
  dx, dw, db = conv_backward_fast(da, conv_cache)
  return dx, dw, db


def conv_relu_pool_forward(x, w, b, conv_param, pool_param):
  """
  Convenience layer that performs a convolution, a ReLU, and a pool.

  Inputs:
  - x: Input to the convolutional layer
  - w, b, conv_param: Weights and parameters for the convolutional layer
  - pool_param: Parameters for the pooling layer

  Returns a tuple of:
  - out: Output from the pooling layer
  - cache: Object to give to the backward pass
  """
  a, conv_cache = conv_forward_fast(x, w, b, conv_param)
  s, relu_cache = relu_forward(a)
  out, pool_cache = max_pool_forward_fast(s, pool_param)
  cache = (conv_cache, relu_cache, pool_cache)
  return out, cache


def conv_relu_pool_backward(dout, cache):
  """
  Backward pass for the conv-relu-pool convenience layer
  """
  conv_cache, relu_cache, pool_cache = cache
  ds = max_pool_backward_fast(dout, pool_cache)
  da = relu_backward(ds, relu_cache)
  dx, dw, db = conv_backward_fast(da, conv_cache)
  return dx, dw, db

vis_utils.py

from math import sqrt, ceil
import numpy as np

def visualize_grid(Xs, ubound=255.0, padding=1):
  """
  Reshape a 4D tensor of image data to a grid for easy visualization.

  Inputs:
  - Xs: Data of shape (N, H, W, C)
  - ubound: Output grid will have values scaled to the range [0, ubound]
  - padding: The number of blank pixels between elements of the grid
  """
  (N, H, W, C) = Xs.shape
  grid_size = int(ceil(sqrt(N)))
  grid_height = H * grid_size + padding * (grid_size - 1)
  grid_width = W * grid_size + padding * (grid_size - 1)
  grid = np.zeros((grid_height, grid_width, C))
  next_idx = 0
  y0, y1 = 0, H
  for y in xrange(grid_size):
    x0, x1 = 0, W
    for x in xrange(grid_size):
      if next_idx < N:
        img = Xs[next_idx]
        low, high = np.min(img), np.max(img)
        grid[y0:y1, x0:x1] = ubound * (img - low) / (high - low)
        # grid[y0:y1, x0:x1] = Xs[next_idx]
        next_idx += 1
      x0 += W + padding
      x1 += W + padding
    y0 += H + padding
    y1 += H + padding
  # grid_max = np.max(grid)
  # grid_min = np.min(grid)
  # grid = ubound * (grid - grid_min) / (grid_max - grid_min)
  return grid

def vis_grid(Xs):
  """ visualize a grid of images """
  (N, H, W, C) = Xs.shape
  A = int(ceil(sqrt(N)))
  G = np.ones((A*H+A, A*W+A, C), Xs.dtype)
  G *= np.min(Xs)
  n = 0
  for y in range(A):
    for x in range(A):
      if n < N:
        G[y*H+y:(y+1)*H+y, x*W+x:(x+1)*W+x, :] = Xs[n,:,:,:]
        n += 1
  # normalize to [0,1]
  maxg = G.max()
  ming = G.min()
  G = (G - ming)/(maxg-ming)
  return G
  
def vis_nn(rows):
  """ visualize array of arrays of images """
  N = len(rows)
  D = len(rows[0])
  H,W,C = rows[0][0].shape
  Xs = rows[0][0]
  G = np.ones((N*H+N, D*W+D, C), Xs.dtype)
  for y in range(N):
    for x in range(D):
      G[y*H+y:(y+1)*H+y, x*W+x:(x+1)*W+x, :] = rows[y][x]
  # normalize to [0,1]
  maxg = G.max()
  ming = G.min()
  G = (G - ming)/(maxg-ming)
  return G

fc_net.py

from layer_utils import *
import numpy as np
class TwoLayerNet(object):   
    
    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   
        self.params['W1'] = weight_scale * np.random.randn(input_dim, hidden_dim)     
        self.params['b1'] = np.zeros((1, hidden_dim))    
        self.params['W2'] = weight_scale * np.random.randn(hidden_dim, num_classes)  
        self.params['b2'] = np.zeros((1, num_classes))

    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
        N = X.shape[0]
        # Unpack variables from the params dictionary
        W1, b1 = self.params['W1'], self.params['b1']
        W2, b2 = self.params['W2'], self.params['b2']
        h1, cache1 = affine_relu_forward(X, W1, b1)
        out, cache2 = affine_forward(h1, W2, b2)
        scores = out              # (N,C)
        # If y is None then we are in test mode so just return scores
        if y is None:   
            return scores

        loss, grads = 0, {}
        data_loss, dscores = softmax_loss(scores, y)
        reg_loss = 0.5 * self.reg * np.sum(W1*W1) + 0.5 * self.reg * np.sum(W2*W2)
        loss = data_loss + reg_loss

        # Backward pass: compute gradients
        dh1, dW2, db2 = affine_backward(dscores, cache2)
        dX, dW1, db1 = affine_relu_backward(dh1, cache1)
        # Add the regularization gradient contribution
        dW2 += self.reg * W2
        dW1 += self.reg * W1
        grads['W1'] = dW1
        grads['b1'] = db1
        grads['W2'] = dW2
        grads['b2'] = db2

        return loss, grads

layers.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
    # Reshape x into rows
    N = x.shape[0]
    x_row = x.reshape(N, -1)         # (N,D)
    out = np.dot(x_row, w) + b       # (N,M)
    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   
    dx = np.dot(dout, w.T)                       # (N,D)    
    dx = np.reshape(dx, x.shape)                 # (N,d1,...,d_k)   
    x_row = x.reshape(x.shape[0], -1)            # (N,D)    
    dw = np.dot(x_row.T, dout)                   # (D,M)    
    db = np.sum(dout, axis=0, keepdims=True)     # (1,M)    

    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    
    out = ReLU(x)    
    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    
    dx = dout    
    dx[x <= 0] = 0    

    return dx

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

def ReLU(x):    
    """ReLU non-linearity."""    
    return np.maximum(0, x)

optim.py

import numpy as np

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    
    v = config['momentum'] * v - config['learning_rate'] * dw    
    next_w = w + v    
    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    
    cache = config['cache']    
    decay_rate = config['decay_rate']    
    learning_rate = config['learning_rate']    
    epsilon = config['epsilon']    
    cache = decay_rate * cache + (1 - decay_rate) * (dx**2)    
    x += - learning_rate * dx / (np.sqrt(cache) + epsilon)  
    config['cache'] = cache    
    next_x = x    

    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    
    m = config['m']    
    v = config['v']    
    beta1 = config['beta1']    
    beta2 = config['beta2']    
    learning_rate = config['learning_rate']    
    epsilon = config['epsilon']   
    t = config['t']    
    t += 1    
    m = beta1 * m + (1 - beta1) * dx    
    v = beta2 * v + (1 - beta2) * (dx**2)    
    m_bias = m / (1 - beta1**t)    
    v_bias = v / (1 - beta2**t)    
    x += - learning_rate * m_bias / (np.sqrt(v_bias) + epsilon)    
    next_x = x    
    config['m'] = m    
    config['v'] = v    
    config['t'] = t    

    return next_x, config

solver.py

import numpy as np

import optim


class Solver(object):
  """
  A Solver encapsulates all the logic necessary for training classification
  models. The Solver performs stochastic gradient descent using different
  update rules defined in optim.py.

  The solver accepts both training and validataion data and labels so it can
  periodically check classification accuracy on both training and validation
  data to watch out for overfitting.

  To train a model, you will first construct a Solver instance, passing the
  model, dataset, and various optoins (learning rate, batch size, etc) to the
  constructor. You will then call the train() method to run the optimization
  procedure and train the model.
  
  After the train() method returns, model.params will contain the parameters
  that performed best on the validation set over the course of training.
  In addition, the instance variable solver.loss_history will contain a list
  of all losses encountered during training and the instance variables
  solver.train_acc_history and solver.val_acc_history will be lists containing
  the accuracies of the model on the training and validation set at each epoch.
  
  Example usage might look something like this:
  
  data = {
    'X_train': # training data
    'y_train': # training labels
    'X_val': # validation data
    'X_train': # validation labels
  }
  model = MyAwesomeModel(hidden_size=100, reg=10)
  solver = Solver(model, data,
                  update_rule='sgd',
                  optim_config={
                    'learning_rate': 1e-3,
                  },
                  lr_decay=0.95,
                  num_epochs=10, batch_size=100,
                  print_every=100)
  solver.train()


  A Solver works on a model object that must conform to the following API:

  - model.params must be a dictionary mapping string parameter names to numpy
    arrays containing parameter values.

  - model.loss(X, y) must be a function that computes training-time loss and
    gradients, and test-time classification scores, with the following inputs
    and outputs:

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

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

    If y is not None, run a training time forward and backward pass and return
    a tuple of:
    - loss: Scalar 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.
  """

  def __init__(self, model, data, **kwargs):
    """
    Construct a new Solver instance.
    
    Required arguments:
    - model: A model object conforming to the API described above
    - data: A dictionary of training and validation data with the following:
      'X_train': Array of shape (N_train, d_1, ..., d_k) giving training images
      'X_val': Array of shape (N_val, d_1, ..., d_k) giving validation images
      'y_train': Array of shape (N_train,) giving labels for training images
      'y_val': Array of shape (N_val,) giving labels for validation images
      
    Optional arguments:
    - update_rule: A string giving the name of an update rule in optim.py.
      Default is 'sgd'.
    - optim_config: A dictionary containing hyperparameters that will be
      passed to the chosen update rule. Each update rule requires different
      hyperparameters (see optim.py) but all update rules require a
      'learning_rate' parameter so that should always be present.
    - lr_decay: A scalar for learning rate decay; after each epoch the learning
      rate is multiplied by this value.
    - batch_size: Size of minibatches used to compute loss and gradient during
      training.
    - num_epochs: The number of epochs to run for during training.
    - print_every: Integer; training losses will be printed every print_every
      iterations.
    - verbose: Boolean; if set to false then no output will be printed during
      training.
    """
    self.model = model
    self.X_train = data['X_train']
    self.y_train = data['y_train']
    self.X_val = data['X_val']
    self.y_val = data['y_val']
    
    # Unpack keyword arguments
    self.update_rule = kwargs.pop('update_rule', 'sgd')
    self.optim_config = kwargs.pop('optim_config', {})
    self.lr_decay = kwargs.pop('lr_decay', 1.0)
    self.batch_size = kwargs.pop('batch_size', 100)
    self.num_epochs = kwargs.pop('num_epochs', 10)

    self.print_every = kwargs.pop('print_every', 10)
    self.verbose = kwargs.pop('verbose', True)

    # Throw an error if there are extra keyword arguments
    if len(kwargs) > 0:
      extra = ', '.join('"%s"' % k for k in kwargs.keys())
      raise ValueError('Unrecognized arguments %s' % extra)

    # Make sure the update rule exists, then replace the string
    # name with the actual function
    if not hasattr(optim, self.update_rule):
      raise ValueError('Invalid update_rule "%s"' % self.update_rule)
    self.update_rule = getattr(optim, self.update_rule)

    self._reset()


  def _reset(self):
    """
    Set up some book-keeping variables for optimization. Don't call this
    manually.
    """
    # Set up some variables for book-keeping
    self.epoch = 0
    self.best_val_acc = 0
    self.best_params = {}
    self.loss_history = []
    self.train_acc_history = []
    self.val_acc_history = []

    # Make a deep copy of the optim_config for each parameter
    self.optim_configs = {}
    for p in self.model.params:
      d = {k: v for k, v in self.optim_config.iteritems()}
      self.optim_configs[p] = d


  def _step(self):
    """
    Make a single gradient update. This is called by train() and should not
    be called manually.
    """
    # Make a minibatch of training data
    num_train = self.X_train.shape[0]
    batch_mask = np.random.choice(num_train, self.batch_size)
    X_batch = self.X_train[batch_mask]
    y_batch = self.y_train[batch_mask]

    # Compute loss and gradient
    loss, grads = self.model.loss(X_batch, y_batch)
    self.loss_history.append(loss)

    # Perform a parameter update
    for p, w in self.model.params.iteritems():
      dw = grads[p]
      config = self.optim_configs[p]
      next_w, next_config = self.update_rule(w, dw, config)
      self.model.params[p] = next_w
      self.optim_configs[p] = next_config


  def check_accuracy(self, X, y, num_samples=None, batch_size=100):
    """
    Check accuracy of the model on the provided data.
    
    Inputs:
    - X: Array of data, of shape (N, d_1, ..., d_k)
    - y: Array of labels, of shape (N,)
    - num_samples: If not None, subsample the data and only test the model
      on num_samples datapoints.
    - batch_size: Split X and y into batches of this size to avoid using too
      much memory.
      
    Returns:
    - acc: Scalar giving the fraction of instances that were correctly
      classified by the model.
    """
    
    # Maybe subsample the data
    N = X.shape[0]
    if num_samples is not None and N > num_samples:
      mask = np.random.choice(N, num_samples)
      N = num_samples
      X = X[mask]
      y = y[mask]

    # Compute predictions in batches
    num_batches = N / batch_size
    if N % batch_size != 0:
      num_batches += 1
    y_pred = []
    for i in xrange(num_batches):
      start = i * batch_size
      end = (i + 1) * batch_size
      scores = self.model.loss(X[start:end])
      y_pred.append(np.argmax(scores, axis=1))
    y_pred = np.hstack(y_pred)
    acc = np.mean(y_pred == y)

    return acc


  def train(self):
    """
    Run optimization to train the model.
    """
    num_train = self.X_train.shape[0]
    iterations_per_epoch = max(num_train / self.batch_size, 1)
    num_iterations = self.num_epochs * iterations_per_epoch

    for t in xrange(num_iterations):
      self._step()

      # Maybe print training loss
      if self.verbose and t % self.print_every == 0:
        print '(Iteration %d / %d) loss: %f' % (
               t + 1, num_iterations, self.loss_history[-1])

      # At the end of every epoch, increment the epoch counter and decay the
      # learning rate.
      epoch_end = (t + 1) % iterations_per_epoch == 0
      if epoch_end:
        self.epoch += 1
        for k in self.optim_configs:
          self.optim_configs[k]['learning_rate'] *= self.lr_decay

      # Check train and val accuracy on the first iteration, the last
      # iteration, and at the end of each epoch.
      first_it = (t == 0)
      last_it = (t == num_iterations + 1)
      if first_it or last_it or epoch_end:
        train_acc = self.check_accuracy(self.X_train, self.y_train,
                                        num_samples=1000)
        val_acc = self.check_accuracy(self.X_val, self.y_val)
        self.train_acc_history.append(train_acc)
        self.val_acc_history.append(val_acc)

        if self.verbose:
          print '(Epoch %d / %d) train acc: %f; val_acc: %f' % (
                 self.epoch, self.num_epochs, train_acc, val_acc)

        # Keep track of the best model
        if val_acc > self.best_val_acc:
          self.best_val_acc = val_acc
          self.best_params = {}
          for k, v in self.model.params.iteritems():
            self.best_params[k] = v.copy()

    # At the end of training swap the best params into the model
    self.model.params = self.best_params


two_layer_fc_net_start.py

import matplotlib.pyplot as plt
from fc_net import *
from data_utils import get_CIFAR10_data
from solver import Solver

data = get_CIFAR10_data()
model = TwoLayerNet(reg=0.9)
solver = Solver(model, data,                
                lr_decay=0.95,                
                print_every=100, num_epochs=40, batch_size=400, 
                update_rule='sgd_momentum',                
                optim_config={'learning_rate': 5e-4, 'momentum': 0.9})

solver.train()                 

plt.subplot(2, 1, 1) 
plt.title('Training loss')
plt.plot(solver.loss_history, 'o')
plt.xlabel('Iteration')

plt.subplot(2, 1, 2)
plt.title('Accuracy')
plt.plot(solver.train_acc_history, '-o', label='train')
plt.plot(solver.val_acc_history, '-o', label='val')
plt.plot([0.5] * len(solver.val_acc_history), 'k--')
plt.xlabel('Epoch')
plt.legend(loc='lower right')
plt.gcf().set_size_inches(15, 12)
plt.show()


best_model = model
y_test_pred = np.argmax(best_model.loss(data['X_test']), axis=1)
y_val_pred = np.argmax(best_model.loss(data['X_val']), axis=1)
print 'Validation set accuracy: ', (y_val_pred == data['y_val']).mean()
print 'Test set accuracy: ', (y_test_pred == data['y_test']).mean()
# Validation set accuracy:  about 52.9%
# Test set accuracy:  about 54.7%


# Visualize the weights of the best network
"""
from vis_utils import visualize_grid

def show_net_weights(net):    
    W1 = net.params['W1']    
    W1 = W1.reshape(3, 32, 32, -1).transpose(3, 1, 2, 0)    
    plt.imshow(visualize_grid(W1, padding=3).astype('uint8'))   
    plt.gca().axis('off')    
show_net_weights(best_model)
plt.show()
"""

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