cs231n assignment2 FullyConnectedNets
【待完成】
- 首先，线性向前传播
import time
import numpy as np
import matplotlib.pyplot as plt
from cs231n_2.classifiers.fc_net import *
from cs231n_2.data_utils import get_CIFAR10_data
from cs231n_2.gradient_check import eval_numerical_gradient, eval_numerical_gradient_array
from cs231n_2.solver import Solver
def rel_error(x, y):
return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))
# Affine layer: foward
num_inputs = 2
input_shape = (4, 5, 6)
output_dim = 3
input_size = num_inputs * np.prod(input_shape) # np.prod() 求乘积
weight_size = output_dim * np.prod(input_shape)
x = np.linspace(-0.1, 0.5, num=input_size).reshape(num_inputs, *input_shape) # (2,4,5,6) # np.linspace() 生成等差数列
w = np.linspace(-0.2, 0.3, num=weight_size).reshape(np.prod(input_shape), output_dim) # (120,3)
b = np.linspace(-0.3, 0.1, num=output_dim)
out, _ = affine_forward(x, w, b)
correct_out = np.array([[ 1.49834967, 1.70660132, 1.91485297],
[ 3.25553199, 3.5141327, 3.77273342]])
# Compare your output with ours. The error should be around e-9 or less.
print('Testing affine_forward function:')
print('difference: ', rel_error(out, correct_out))affine_forward 实现：
def affine_forward(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. #
###########################################################################
# x = x.reshape(x.shape[0], -1)
out = np.dot(x.reshape(x.shape[0], -1), w) + b
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = (x, w, b)
return out, cache- affine向后传播
# Test the affine_backward function
np.random.seed(231)
x = np.random.randn(10, 2, 3)
w = np.random.randn(6, 5)
b = np.random.randn(5)
dout = np.random.randn(10, 5)
dx_num = eval_numerical_gradient_array(lambda x: affine_forward(x, w, b)[0], x, dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_forward(x, w, b)[0], w, dout)
db_num = eval_numerical_gradient_array(lambda b: affine_forward(x, w, b)[0], b, dout)
_, cache = affine_forward(x, w, b)
dx, dw, db = affine_backward(dout, cache)
# The error should be around e-10 or less
print('Testing affine_backward function:')
print('dx error: ', rel_error(dx_num, dx))
print('dw error: ', rel_error(dw_num, dw))
print('db error: ', rel_error(db_num, db))affine_backward 实现：
def affine_backward(dout, cache):
x, w, b = cache
dx, dw, db = None, None, None
###########################################################################
# TODO: Implement the affine backward pass. #
###########################################################################
dx = np.dot(dout, w.T)
dw = np.dot(x.reshape(x.shape[0], -1).T, dout)
db = np.sum(dout, axis=0)
dx = dx.reshape(x.shape)
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx, dw, db
- ReLU
# Test the relu_forward function
x = np.linspace(-0.5, 0.5, num=12).reshape(3, 4)
out, _ = relu_forward(x)
correct_out = np.array([[ 0., 0., 0., 0., ],
[ 0., 0., 0.04545455, 0.13636364,],
[ 0.22727273, 0.31818182, 0.40909091, 0.5, ]])
# Compare your output with ours. The error should be on the order of e-8
print('Testing relu_forward function:')
print('difference: ', rel_error(out, correct_out))
np.random.seed(231)
x = np.random.randn(10, 10)
dout = np.random.randn(*x.shape)
dx_num = eval_numerical_gradient_array(lambda x: relu_forward(x)[0], x, dout)
_, cache = relu_forward(x)
dx = relu_backward(dout, cache)
# The error should be on the order of e-12
print('Testing relu_backward function:')
print('dx error: ', rel_error(dx_num, dx))relu_forward 实现：
def relu_forward(x):
out = None
###########################################################################
# TODO: Implement the ReLU forward pass. #
###########################################################################
out = np.maximum(0, x)
###########################################################################
# END OF YOUR CODE #
###########################################################################
cache = x
return out, cacherelu_backward 实现
def relu_backward(dout, cache):
dx, x = None, cache
###########################################################################
# TODO: Implement the ReLU backward pass. #
###########################################################################
dx = dout
dx[x <= 0] = 0
###########################################################################
# END OF YOUR CODE #
###########################################################################
return dx
- "Sandwich" layers
from cs231n.layer_utils import affine_relu_forward, affine_relu_backward
np.random.seed(231)
x = np.random.randn(2, 3, 4)
w = np.random.randn(12, 10)
b = np.random.randn(10)
dout = np.random.randn(2, 10)
out, cache = affine_relu_forward(x, w, b)
dx, dw, db = affine_relu_backward(dout, cache)
dx_num = eval_numerical_gradient_array(lambda x: affine_relu_forward(x, w, b)[0], x, dout)
dw_num = eval_numerical_gradient_array(lambda w: affine_relu_forward(x, w, b)[0], w, dout)
db_num = eval_numerical_gradient_array(lambda b: affine_relu_forward(x, w, b)[0], b, dout)
# Relative error should be around e-10 or less
print('Testing affine_relu_forward and affine_relu_backward:')
print('dx error: ', rel_error(dx_num, dx))
print('dw error: ', rel_error(dw_num, dw))
print('db error: ', rel_error(db_num, db))- Loss layers: Softmax and SVM
np.random.seed(231)
num_classes, num_inputs = 10, 50
x = 0.001 * np.random.randn(num_inputs, num_classes)
y = np.random.randint(num_classes, size=num_inputs)
dx_num = eval_numerical_gradient(lambda x: svm_loss(x, y)[0], x, verbose=False)
loss, dx = svm_loss(x, y)
# Test svm_loss function. Loss should be around 9 and dx error should be around the order of e-9
print('Testing svm_loss:')
print('loss: ', loss)
print('dx error: ', rel_error(dx_num, dx))
dx_num = eval_numerical_gradient(lambda x: softmax_loss(x, y)[0], x, verbose=False)
loss, dx = softmax_loss(x, y)
# Test softmax_loss function. Loss should be close to 2.3 and dx error should be around e-8
print('\nTesting softmax_loss:')
print('loss: ', loss)
print('dx error: ', rel_error(dx_num, dx))- Two-layer networkTwo-layer network
np.random.seed(231)
N, D, H, C = 3, 5, 50, 7
X = np.random.randn(N, D)
y = np.random.randint(C, size=N)
std = 1e-3
model = TwoLayerNet(input_dim=D, hidden_dim=H, num_classes=C, weight_scale=std)
print('Testing initialization ... ')
W1_std = abs(model.params['W1'].std() - std)
b1 = model.params['b1']
W2_std = abs(model.params['W2'].std() - std)
b2 = model.params['b2']
assert W1_std < std / 10, 'First layer weights do not seem right'
assert np.all(b1 == 0), 'First layer biases do not seem right'
assert W2_std < std / 10, 'Second layer weights do not seem right'
assert np.all(b2 == 0), 'Second layer biases do not seem right'
print('Testing test-time forward pass ... ')
model.params['W1'] = np.linspace(-0.7, 0.3, num=D*H).reshape(D, H)
model.params['b1'] = np.linspace(-0.1, 0.9, num=H)
model.params['W2'] = np.linspace(-0.3, 0.4, num=H*C).reshape(H, C)
model.params['b2'] = np.linspace(-0.9, 0.1, num=C)
X = np.linspace(-5.5, 4.5, num=N*D).reshape(D, N).T
scores = model.loss(X)
correct_scores = np.asarray(
[[11.53165108, 12.2917344, 13.05181771, 13.81190102, 14.57198434, 15.33206765, 16.09215096],
[12.05769098, 12.74614105, 13.43459113, 14.1230412, 14.81149128, 15.49994135, 16.18839143],
[12.58373087, 13.20054771, 13.81736455, 14.43418138, 15.05099822, 15.66781506, 16.2846319 ]])
scores_diff = np.abs(scores - correct_scores).sum()
assert scores_diff < 1e-6, 'Problem with test-time forward pass'
print('Testing training loss (no regularization)')
y = np.asarray([0, 5, 1])
loss, grads = model.loss(X, y)
correct_loss = 3.4702243556
assert abs(loss - correct_loss) < 1e-10, 'Problem with training-time loss'
model.reg = 1.0
loss, grads = model.loss(X, y)
correct_loss = 26.5948426952
assert abs(loss - correct_loss) < 1e-10, 'Problem with regularization loss'
# Errors should be around e-7 or less
for reg in [0.0, 0.7]:
print('Running numeric gradient check with reg = ', reg)
model.reg = reg
loss, grads = model.loss(X, y)
for name in sorted(grads):
f = lambda _: model.loss(X, y)[0]
grad_num = eval_numerical_gradient(f, model.params[name], verbose=False)
print('%s relative error: %.2e' % (name, rel_error(grad_num, grads[name])))model 实现
class TwoLayerNet(object):
def __init__(self, input_dim=3*32*32, hidden_dim=50, num_classes=10,
weight_scale=1e-3, reg=0.8):
self.params = {}
self.reg = reg
############################################################################
# TODO: Initialize the weights and biases of the two-layer net. Weights #
# should be initialized from a Gaussian centered at 0.0 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'] = weight_scale * np.random.randn(input_dim, hidden_dim)
self.params['b1'] = np.zeros(hidden_dim)
self.params['W2'] = weight_scale * np.random.randn(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. #
############################################################################
# Unpack variables from the params dictionary
W1, b1 = self.params['W1'], self.params['b1']
W2, b2 = self.params['W2'], self.params['b2']
X = X.reshape(X.shape[0], -1)
# 计算分值
h1_out,h1_cache = affine_relu_forward(X, W1, b1)
scores,out_cache = affine_forward(h1_out, W2, b2)
#############################################################################
# END OF YOUR CODE #
#############################################################################
# If the targets are not given then jump out, we're done
if y is None:
return scores
# Compute the loss
loss = None
#############################################################################
# TODO: Finish the forward pass, and compute the loss. This should include #
# both the data loss and L2 regularization for W1 and W2. Store the result #
# in the variable loss, which should be a scalar. Use the Softmax #
# classifier loss. #
#############################################################################
# 最后一层softmax
loss,dout = softmax_loss(scores,y)
loss += 0.5 * self.reg * (np.sum(W1 ** 2) + np.sum(W2 ** 2))
#############################################################################
# END OF YOUR CODE #
#############################################################################
# Backward pass: compute gradients
grads = {}
#############################################################################
# TODO: Compute the backward pass, computing the derivatives of the weights #
# and biases. Store the results in the grads dictionary. For example, #
# grads['W1'] should store the gradient on W1, and be a matrix of same size #
#############################################################################
# 计算梯度
dout, dw2, db2 = affine_backward(dout, out_cache)
dw2 += self.reg * W2
grads['W2'] = dw2
grads['b2'] = db2
_, dw1, db1 = affine_relu_backward(dout, h1_cache)
dw1 += self.reg * W1
grads['W1'] = dw1
grads['b1'] = db1
#############################################################################
# END OF YOUR CODE #
#############################################################################
return loss, grads- 模型实现后，开始导入真实数据并训练
data = get_CIFAR10_data()
for k, v in list(data.items()):
print(('%s: ' % k, v.shape))
model = TwoLayerNet()
solver = None
##############################################################################
# TODO: Use a Solver instance to train a TwoLayerNet that achieves at least #
# 50% accuracy on the validation set. #
##############################################################################
data_mini = {}
for k, v in data.items():
N = int(v.shape[0] / 5)
data_mini[k] = data[k][:N]
print(k, N)
solver = Solver(model, data,
num_train_samples=1000,
lr_decay=0.95,
num_epochs=20,
batch_size=200,
optim_config={
'learning_rate': 1e-3,
}
)
solver.train()
##############################################################################
# END OF YOUR CODE #
##############################################################################
- 画出 loss 和 acc
# Run this cell to visualize training loss and train / val accuracy
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()
多层网络的实现