def train_pytorch_ch7(optimizer_fn, optimizer_hyperparams, features, labels,
batch_size=10, num_epochs=2):
# 初始化模型
net = nn.Sequential(
nn.Linear(features.shape[-1], 1)
)
loss = nn.MSELoss()
optimizer = optimizer_fn(net.parameters(), **optimizer_hyperparams)
def eval_loss():
return loss(net(features).view(-1), labels).item() / 2
ls = [eval_loss()]
data_iter = torch.utils.data.DataLoader(
torch.utils.data.TensorDataset(features, labels), batch_size, shuffle=True)
for _ in range(num_epochs):
start = time.time()
for batch_i, (X, y) in enumerate(data_iter):
# 除以2是为了和train_ch7保持一致, 因为squared_loss中除了2
l = loss(net(X).view(-1), y) / 2
optimizer.zero_grad()
l.backward()
optimizer.step()
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss())
# 打印结果和作图
print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
d2l.set_figsize()
d2l.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
d2l.plt.xlabel('epoch')
d2l.plt.ylabel('loss')
def show_trace(res):
n = max(abs(min(res)), abs(max(res)))
f_line = np.arange(-n, n, 0.01)
d2l.set_figsize((3.5, 2.5))
d2l.plt.plot(f_line, [f(x) for x in f_line], '-')
d2l.plt.plot(res, [f(x) for x in res], '-o')
d2l.plt.xlabel('x')
d2l.plt.ylabel('f(x)')
def train_ch7(optimizer_fn,
states,
hyperparams,
features,
labels,
batch_size=10,
num_epochs=2):
# 初始化模型
net, loss = d2l.linreg, d2l.squared_loss
w = torch.nn.Parameter(torch.tensor(np.random.normal(
0, 0.01, size=(features.shape[1], 1)),
dtype=torch.float32),
requires_grad=True)
b = torch.nn.Parameter(torch.zeros(1, dtype=torch.float32),
requires_grad=True)
def eval_loss():
return loss(net(features, w, b), labels).mean().item()
ls = [eval_loss()]
data_iter = torch.utils.data.DataLoader(torch.utils.data.TensorDataset(
features, labels),
batch_size,
shuffle=True)
for _ in range(num_epochs):
start = time.time()
for batch_i, (X, y) in enumerate(data_iter):
l = loss(net(X, w, b), y).mean() # 使用平均损失
# 梯度清零
if w.grad is not None:
w.grad.data.zero_()
b.grad.data.zero_() #使用data表示对数据进行操作
l.backward()
optimizer_fn([w, b], states, hyperparams) # 迭代模型参数
if (batch_i + 1) * batch_size % 100 == 0:
ls.append(eval_loss()) # 每100个样本记录下当前训练误差
# 打印结果和作图
print('loss: %f, %f sec per epoch' % (ls[-1], time.time() - start))
d2l.set_figsize()
d2l.plt.plot(np.linspace(0, num_epochs, len(ls)), ls)
d2l.plt.xlabel('epoch')
d2l.plt.ylabel('loss')
from PIL import Image
file_path = ' '
assert file_path != ' ', 'Please set path'
#置当前使用的GPU设备仅为0号设备
os.environ["CUDA_VISIBLE_DEVICES"] = "0"
import d2lzh1981 as d2l
# 定义device，是否使用GPU，依据计算机配置自动会选择
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(torch.__version__)
print(device)
#原始图像展示
d2l.set_figsize()
img = Image.open(file_path)
d2l.plt.imshow(img)
#展示图像
def show_images(imgs, num_rows, num_cols, scale=2):
figsize = (num_cols * scale, num_rows * scale)
_, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
for i in range(num_rows):
for j in range(num_cols):
axes[i][j].imshow(imgs[i * num_cols + j])
axes[i][j].axes.get_xaxis().set_visible(False)
axes[i][j].axes.get_yaxis().set_visible(False)
return axes
def apply(img, aug, num_rows=2, num_cols=4, scale=1.5):
优化与深度学习
优化与估计
尽管优化方法可以最小化深度学习中的损失函数值，但本质上优化方法达到的目标与深度学习的目标并不相同。
优化方法目标：训练集损失函数值
深度学习目标：测试集损失函数值（泛化性）
%matplotlib inline
import sys
sys.path.append('/home/kesci/input')
import d2lzh1981 as d2l
from mpl_toolkits import mplot3d # 三维画图
import numpy as np
def f(x): return x * np.cos(np.pi * x)
def g(x): return f(x) + 0.2 * np.cos(5 * np.pi * x)
d2l.set_figsize((5, 3))
x = np.arange(0.5, 1.5, 0.01)
fig_f, = d2l.plt.plot(x, f(x),label="train error")
fig_g, = d2l.plt.plot(x, g(x),'--', c='purple', label="test error")
fig_f.axes.annotate('empirical risk', (1.0, -1.2), (0.5, -1.1),arrowprops=dict(arrowstyle='->'))
fig_g.axes.annotate('expected risk', (1.1, -1.05), (0.95, -0.5),arrowprops=dict(arrowstyle='->'))
d2l.plt.xlabel('x')
d2l.plt.ylabel('risk')
d2l.plt.legend(loc="upper right")
<matplotlib.legend.Legend at 0x7fc092436080>
优化在深度学习中的挑战
局部最小值
鞍点
梯度消失
局部最小值