cs231n作业：Assignment2-Fully-Connected Neural Nets
fc_net.py
from builtins import range
from builtins import object
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
- 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 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'. #
############################################################################
#w高斯分布，b初始化0
mu = 0
sigma = weight_scale
self.params['W1'] = mu + sigma * np.random.randn(input_dim,hidden_dim)
self.params['b1'] = np.zeros(hidden_dim)
self.params['W2'] = mu + sigma * np.random.randn(hidden_dim,num_classes)
self.params['b2'] = np.zeros(num_classes)
pass
############################################################################
# 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. #
############################################################################
N = X.shape[0]
D = np.prod(X.shape[1:])
x_in = X
x_in = x_in.reshape(N, D)
fc1 = x_in.dot(self.params['W1']) + self.params['b1']
relu = np.maximum(0, fc1)
fc2 = relu.dot(self.params['W2']) + self.params['b2']
scores = fc2
pass
############################################################################
# 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. #
############################################################################
W1, b1 = self.params['W1'], self.params['b1']
W2, b2 = self.params['W2'], self.params['b2']
loss, dout2 = softmax_loss(scores, y)
loss += 0.5 * self.reg * (np.sum(W1*W1)+np.sum(W2*W2))
cache2 = relu, W2, b2
dx2,dw2,db2 = affine_backward(dout2, cache2)
grads['W2'] = dw2 + self.reg * self.params['W2'] #注意不要忘记 loss 中W1, W2 的贡献 和正则化参数
grads['b2'] = db2
cache1 = fc1
dout1 = dx2
dout = relu_backward(dout1, cache1)
cache = X, W1, b1
dx1,dw1,db1 = affine_backward(dout, cache)
grads['W1'] = dw1 + self.reg * self.params['W1']
grads['b1'] = db1
pass
############################################################################
# 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/layer normalization as options. For a network with L layers,
the architecture will be
{affine - [batch/layer norm] - relu - [dropout]} x (L - 1) - affine - softmax
where batch/layer 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=1, normalization=None, 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=1 then
the network should not use dropout at all.
- normalization: What type of normalization the network should use. Valid values
are "batchnorm", "layernorm", or None for no normalization (the default).
- 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.normalization = normalization
self.use_dropout = dropout != 1
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 centered at 0 with standard #
# deviation equal to weight_scale. 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 ones and shift #
# parameters should be initialized to zeros. #
############################################################################
parameters = [input_dim] + hidden_dims + [num_classes]
lx = len(parameters)
for i in range(1,lx):
idw = 'W' + str(i)
idb = 'b' + str(i)
self.params[idw] = np.random.randn(parameters[i-1], parameters[i]) * weight_scale
self.params[idb] = np.zeros(parameters[i])
if self.normalization=='batchnorm':
for i in range(1,lx-1):
idga = 'gamma' + str(i)
idbe = 'beta' + str(i)
self.params[idga] = np.ones(parameters[i])
self.params[idbe] = np.zeros(parameters[i])
############################################################################
# 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.normalization=='batchnorm':
self.bn_params = [{'mode': 'train'} for i in range(self.num_layers - 1)]
if self.normalization=='layernorm':
self.bn_params = [{} for i in range(self.num_layers - 1)]
# Cast all parameters to the correct datatype
for k, v in self.params.items():
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.use_dropout:
self.dropout_param['mode'] = mode
if self.normalization=='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. #
############################################################################
N, D = X.shape[0], np.prod(X.shape[1:])
scores = X.reshape(N,D)
list_x_in = {}
list_x_in['x' + str(0)] = scores
for i in range(1,self.num_layers):
xa, wa, ba = scores, self.params['W' + str(i)], self.params['b' + str(i)]
if self.normalization == 'batchnorm' and self.use_dropout:
gamma, beta = self.params['gamma' + str(i)], self.params['beta' + str(i)]
scores, cache = affine_bn_relu_drop_forward(xa, wa, ba, gamma, beta, self.bn_params[i - 1],self.dropout_param)
elif self.normalization == 'batchnorm':
gamma, beta = self.params['gamma' + str(i)], self.params['beta' + str(i)]
scores, cache = affine_bn_relu_forward(xa, wa, ba, gamma, beta, self.bn_params[i-1])
elif self.use_dropout:
scores, cache = affine_relu_drop_forward(xa, wa, ba, self.dropout_param)
else:
scores, cache = affine_relu_forward(xa, wa, ba)
list_x_in['x'+str(i)] = cache
#注：最后一层没用relu
xa, wa, ba = scores, self.params['W' + str(self.num_layers)], self.params['b' + str(self.num_layers)]
scores, cache = affine_forward(xa, wa, ba)
list_x_in['x' + str(self.num_layers)] = cache
############################################################################
# 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/layer 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, dout = softmax_loss(scores, y)
for i in range(self.num_layers):
loss = loss + 0.5*self.reg*np.sum(np.square(self.params['W'+str(i+1)]))
cache = list_x_in['x' + str(self.num_layers)]
dout, dw, db = affine_backward(dout, cache)
grads['W' + str(self.num_layers)], grads['b' + str(self.num_layers)] = dw + self.reg * self.params['W' + str(self.num_layers)], db
for id in range(self.num_layers-1,0,-1):
cache = list_x_in['x'+str(id)]
if self.normalization == 'batchnorm' and self.use_dropout:
dout, dw, db, dgamma, dbeta = affine_bn_relu_drop_backward(dout, cache)
grads['gamma' + str(id)], grads['beta' + str(id)] = dgamma, dbeta
elif self.normalization == 'batchnorm':
dout, dw, db, dgamma, dbeta = affine_bn_relu_backward(dout, cache)
grads['gamma' + str(id)], grads['beta' + str(id)] = dgamma, dbeta
elif self.use_dropout:
# print("dout", dout.shape)
dout, dw, db = affine_relu_drop_backward(dout, cache)
# print("dout",dout.shape)
else:
dout, dw, db = affine_relu_backward(dout, cache)
grads['W'+str(id)], grads['b'+str(id)] = dw+self.reg * self.params['W'+str(id)], db
############################################################################
# END OF YOUR CODE #
############################################################################
return loss, grads
optic.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. #
###########################################################################
v = config['momentum'] * v - config['learning_rate']*dw
next_w = w + v
pass
###########################################################################
# END OF YOUR CODE #
###########################################################################
config['velocity'] = v
return next_w, config
def rmsprop(w, dw, 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(w))
next_w = None
###########################################################################
# TODO: Implement the RMSprop update formula, storing the next value of w #
# in the next_w variable. Don't forget to update cache value stored in #
# config['cache']. #
###########################################################################
cache = config['decay_rate']*config['cache']+(1-config['decay_rate'])*np.square(dw)
next_w = w - config['learning_rate'] * dw / np.sqrt(cache+config['epsilon'])
config['cache'] = cache
pass
###########################################################################
# END OF YOUR CODE #
###########################################################################
return next_w, config
def adam(w, dw, 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(w))
config.setdefault('v', np.zeros_like(w))
config.setdefault('t', 0)
next_w = None
###########################################################################
# TODO: Implement the Adam update formula, storing the next value of w in #
# the next_w variable. Don't forget to update the m, v, and t variables #
# stored in config. #
# #
# NOTE: In order to match the reference output, please modify t _before_ #
# using it in any calculations. #
###########################################################################
config['t'] = config['t'] + 1
first_moment = config['beta1']*config['m'] + (1-config['beta1'])*dw
second_moment = config['beta2']*config['v'] + (1-config['beta2'])*dw*dw
first_moment_bias = first_moment / (1 - config['beta1']**config['t'])
second_moment_bias = second_moment / (1 - config['beta2']**config['t'])
next_w = w - config['learning_rate'] * first_moment_bias / (np.sqrt(second_moment_bias)+config['epsilon'])
config['m'] = first_moment
config['v'] = second_moment
pass
###########################################################################
# END OF YOUR CODE #
###########################################################################
return next_w, config