视频里 Andrej Karpathy上课的时候说,这次的作业meaty but educational,确实很meaty,作业一般是由.ipynb文件和.py文件组成,这次因为每个.ipynb文件涉及到的.py文件较多,且互相之间有交叉,所以每篇博客只贴出一个.ipynb或者一个.py文件.(因为之前的作业由于是一个.ipynb文件对应一个.py文件,所以就整合到一篇博客里)
**还是那句话,有错误希望帮我指出来,多多指教,谢谢 **
optim.py内容：
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
#############################################################################
# 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']. #
#############################################################################
config['cache'] = config['decay_rate'] * config['cache'] + (1 - config['decay_rate']) * dx**2
next_x = 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
beta1 = config['beta1']
beta2 = config['beta2']
epsilon = config['epsilon']
learning_rate = config['learning_rate']
config['m'] = beta1 * config['m'] + (1-beta1) * dx
config['v'] = beta2 * config['v'] + (1-beta2) * dx**2
mb = config['m']/(1 - beta1**config['t'])
vb = config['v']/(1 - beta2**config['t'])
next_x = x - learning_rate * mb / (np.sqrt(vb)+epsilon)
#############################################################################
# END OF YOUR CODE #
#############################################################################
return next_x, config
