revise opt and utils

chapter_optimization/adadelta-gluon.md

@@ -8,9 +8,8 @@
 %config InlineBackend.figure_format = 'retina'
 %matplotlib inline
 import mxnet as mx
-from mxnet import autograd, gluon, nd
+from mxnet import gluon, nd
 from mxnet.gluon import nn
-import numpy as np
 import sys
 sys.path.append('..')
 import utils
@@ -24,9 +23,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -39,7 +38,7 @@ net.add(nn.Dense(1))
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'adadelta', {'rho': 0.9999})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=None,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/adadelta-scratch.md

@@ -66,9 +66,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -89,24 +89,23 @@ def init_params():
 
 ```{.python .input  n=2}
 net = utils.linreg
-squared_loss = utils.squared_loss
+loss = utils.squared_loss
 
 def optimize(batch_size, rho, num_epochs, log_interval):
     [w, b], sqrs, deltas = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [loss(net(features, w, b), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1):
-        for batch_i, (features, label) in enumerate(
-            utils.data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            utils.data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             adadelta([w, b], sqrs, deltas, rho, batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 最终，优化所得的模型参数值与它们的真实值较接近。

chapter_optimization/adagrad-gluon.md

@@ -9,9 +9,8 @@
 %config InlineBackend.figure_format = 'retina'
 %matplotlib inline
 import mxnet as mx
-from mxnet import autograd, gluon, nd
+from mxnet import gluon, nd
 from mxnet.gluon import nn
-import numpy as np
 import sys
 sys.path.append('..')
 import utils
@@ -25,9 +24,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -41,7 +40,7 @@ net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'adagrad',
                         {'learning_rate': 0.9})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=None,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/adagrad-scratch.md

@@ -75,9 +75,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -96,24 +96,23 @@ def init_params():
 
 ```{.python .input  n=3}
 net = utils.linreg
-squared_loss = utils.squared_loss
+loss = utils.squared_loss
 
 def optimize(batch_size, lr, num_epochs, log_interval):
     [w, b], sqrs = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [loss(net(features, w, b), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1):
-        for batch_i, (features, label) in enumerate(
-            utils.data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            utils.data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             adagrad([w, b], sqrs, lr, batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 最终，优化所得的模型参数值与它们的真实值较接近。

chapter_optimization/adam-gluon.md

@@ -8,9 +8,8 @@
 %config InlineBackend.figure_format = 'retina'
 %matplotlib inline
 import mxnet as mx
-from mxnet import autograd, gluon, nd
+from mxnet import gluon, nd
 from mxnet.gluon import nn
-import numpy as np
 import sys
 sys.path.append('..')
 import utils
@@ -24,9 +23,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -39,7 +38,7 @@ net.add(nn.Dense(1))
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'adam', {'learning_rate': 0.1})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=None,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/adam-scratch.md

@@ -84,9 +84,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -107,27 +107,26 @@ def init_params():
 
 ```{.python .input  n=2}
 net = utils.linreg
-squared_loss = utils.squared_loss
+loss = utils.squared_loss
 
 def optimize(batch_size, lr, num_epochs, log_interval):
     [w, b], vs, sqrs = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [loss(net(features, w, b), labels).mean().asnumpy()]
     t = 0
     for epoch in range(1, num_epochs + 1):
-        for batch_i, (features, label) in enumerate(
-            utils.data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            utils.data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             # 必须在调用Adam前。
             t += 1
             adam([w, b], vs, sqrs, lr, batch_size, t)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 最终，优化所得的模型参数值与它们的真实值较接近。

chapter_optimization/gd-sgd-gluon.md

@@ -24,9 +24,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -37,28 +37,27 @@ net.add(nn.Dense(1))
 
 ```{.python .input  n=2}
 # 优化目标函数。
-def optimize(batch_size, trainer, num_epochs, decay_epoch, log_interval, X, y,
-             net):
-    dataset = gdata.ArrayDataset(X, y)
+def optimize(batch_size, trainer, num_epochs, decay_epoch, log_interval,
+             features, labels, net):
+    dataset = gdata.ArrayDataset(features, labels)
     data_iter = gdata.DataLoader(dataset, batch_size, shuffle=True)
-    square_loss = gloss.L2Loss()
-    y_vals = [square_loss(net(X), y).mean().asnumpy()]
+    loss = gloss.L2Loss()
+    ls = [loss(net(features), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1): 
         # 学习率自我衰减。
         if decay_epoch and epoch > decay_epoch:
             trainer.set_learning_rate(trainer.learning_rate * 0.1)
-        for batch_i, (features, label) in enumerate(data_iter):
+        for batch_i, (X, y) in enumerate(data_iter):
             with autograd.record():
-                output = net(features)
-                loss = square_loss(output, label)
-            loss.backward()
+                l = loss(net(X), y)
+            l.backward()
             trainer.step(batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(square_loss(net(X), y).mean().asnumpy())
+                ls.append(loss(net(features), labels).mean().asnumpy())
     # 为了便于打印，改变输出形状并转化成numpy数组。
     print('w:', net[0].weight.data(), '\nb:', net[0].bias.data(), '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 以下几组实验分别重现了["梯度下降和随机梯度下降——从零开始"](gd-sgd-scratch.md)一节中实验结果。
@@ -67,35 +66,35 @@ def optimize(batch_size, trainer, num_epochs, decay_epoch, log_interval, X, y,
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.2})
 optimize(batch_size=1, trainer=trainer, num_epochs=3, decay_epoch=2,
-         log_interval=10, X=X, y=y, net=net)
+         log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input  n=4}
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.999})
 optimize(batch_size=1000, trainer=trainer, num_epochs=3, decay_epoch=None,
-         log_interval=1000, X=X, y=y, net=net)
+         log_interval=1000, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input  n=5}
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.2})
 optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-         log_interval=10, X=X, y=y, net=net)
+         log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input  n=6}
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 5})
 optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-         log_interval=10, X=X, y=y, net=net)
+         log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input  n=7}
 net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.002})
 optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-         log_interval=10, X=X, y=y, net=net)
+         log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/gd-sgd-scratch.md

@@ -134,9 +134,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -152,16 +152,16 @@ def linreg(X, w, b):
     return nd.dot(X, w) + b 
 
 # 平方损失函数。
-def squared_loss(yhat, y): 
-    return (yhat - y.reshape(yhat.shape)) ** 2 / 2
+def squared_loss(y_hat, y): 
+    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2
 
 # 遍历数据集。
-def data_iter(batch_size, num_examples, X, y): 
-    idx = list(range(num_examples))
-    random.shuffle(idx)
+def data_iter(batch_size, num_examples, features, labels): 
+    indices = list(range(num_examples))
+    random.shuffle(indices)
     for i in range(0, num_examples, batch_size):
-        j = nd.array(idx[i: min(i + batch_size, num_examples)])
-        yield X.take(j), y.take(j)
+        j = nd.array(indices[i: min(i + batch_size, num_examples)])
+        yield features.take(j), labels.take(j)
 ```
 
 下面我们描述一下优化函数`optimize`。
@@ -172,26 +172,26 @@ def data_iter(batch_size, num_examples, X, y):
 
 ```{.python .input  n=3}
 net = linreg
+loss = squared_loss
 
 def optimize(batch_size, lr, num_epochs, log_interval, decay_epoch):
     w, b = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [squared_loss(net(features, w, b), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1):
         # 学习率自我衰减。
         if decay_epoch and epoch > decay_epoch:
             lr *= 0.1
-        for batch_i, (features, label) in enumerate(
-            data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             sgd([w, b], lr, batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 当批量大小为1时，优化使用的是随机梯度下降。在当前学习率下，损失函数值在早期快速下降后略有波动。这是由于随机梯度的方差在迭代过程中无法减小。当迭代周期大于2，学习率自我衰减后，损失函数值下降后较平稳。最终，优化所得的模型参数值`w`和`b`与它们的真实值[2, -3.4]和4.2较接近。

chapter_optimization/momentum-gluon.md

@@ -8,9 +8,8 @@
 %config InlineBackend.figure_format = 'retina'
 %matplotlib inline
 import mxnet as mx
-from mxnet import autograd, gluon, nd
+from mxnet import gluon, nd
 from mxnet.gluon import nn
-import numpy as np
 import sys
 sys.path.append('..')
 import utils
@@ -24,9 +23,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -40,7 +39,7 @@ net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd',
                         {'learning_rate': 0.2, 'momentum': 0.99})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input}
@@ -48,7 +47,7 @@ net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd',
                         {'learning_rate': 0.2, 'momentum': 0.9})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input}
@@ -56,7 +55,7 @@ net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'sgd',
                         {'learning_rate': 0.2, 'momentum': 0.5})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=2,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/momentum-scratch.md

@@ -101,9 +101,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -122,27 +122,26 @@ def init_params():
 
 ```{.python .input  n=3}
 net = utils.linreg
-squared_loss = utils.squared_loss
+loss = utils.squared_loss
 
 def optimize(batch_size, lr, mom, num_epochs, log_interval):
     [w, b], vs = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [loss(net(features, w, b), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1):
         # 学习率自我衰减。
         if epoch > 2:
             lr *= 0.1
-        for batch_i, (features, label) in enumerate(
-            utils.data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            utils.data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             sgd_momentum([w, b], vs, lr, mom, batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 我们先将动量超参数$\gamma$（`mom`）设0.99。此时，小梯度随机梯度下降可被看作使用了特殊梯度：这个特殊梯度是最近100个时刻的$100\nabla f_\mathcal{B}(\boldsymbol{x})$的加权平均。我们观察到，损失函数值在3个迭代周期后上升。这很可能是由于特殊梯度中较大的系数100造成的。

chapter_optimization/rmsprop-gluon.md

@@ -9,9 +9,8 @@
 %config InlineBackend.figure_format = 'retina'
 %matplotlib inline
 import mxnet as mx
-from mxnet import autograd, gluon, nd
+from mxnet import gluon, nd
 from mxnet.gluon import nn
-import numpy as np
 import sys
 sys.path.append('..')
 import utils
@@ -25,9 +24,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 线性回归模型。
 net = nn.Sequential()
@@ -41,7 +40,7 @@ net.initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'rmsprop',
                         {'learning_rate': 0.03, 'gamma1': 0.9})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=None,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ```{.python .input}
@@ -49,7 +48,7 @@ net.collect_params().initialize(mx.init.Normal(sigma=1), force_reinit=True)
 trainer = gluon.Trainer(net.collect_params(), 'rmsprop',
                         {'learning_rate': 0.03, 'gamma1': 0.999})
 utils.optimize(batch_size=10, trainer=trainer, num_epochs=3, decay_epoch=None,
-               log_interval=10, X=X, y=y, net=net)
+               log_interval=10, features=features, labels=labels, net=net)
 ```
 
 ## 小结

chapter_optimization/rmsprop-scratch.md

@@ -64,9 +64,9 @@ num_inputs = 2
 num_examples = 1000
 true_w = [2, -3.4]
 true_b = 4.2
-X = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
-y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
-y += nd.random.normal(scale=0.01, shape=y.shape)
+features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
+labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
+labels += nd.random.normal(scale=0.01, shape=labels.shape)
 
 # 初始化模型参数。
 def init_params():
@@ -85,24 +85,23 @@ def init_params():
 
 ```{.python .input  n=2}
 net = utils.linreg
-squared_loss = utils.squared_loss
+loss = utils.squared_loss
 
 def optimize(batch_size, lr, gamma, num_epochs, log_interval):
     [w, b], sqrs = init_params()
-    y_vals = [squared_loss(net(X, w, b), y).mean().asnumpy()]
+    ls = [loss(net(features, w, b), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1):
-        for batch_i, (features, label) in enumerate(
-            utils.data_iter(batch_size, num_examples, X, y)):
+        for batch_i, (X, y) in enumerate(
+            utils.data_iter(batch_size, num_examples, features, labels)):
             with autograd.record():
-                output = net(features, w, b)
-                loss = squared_loss(output, label)
-            loss.backward()
+                l = loss(net(X, w, b), y)
+            l.backward()
             rmsprop([w, b], sqrs, lr, gamma, batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(squared_loss(net(X, w, b), y).mean().asnumpy())
+                ls.append(loss(net(features, w, b), labels).mean().asnumpy())
     print('w:', w, '\nb:', b, '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    utils.semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    utils.semilogy(es, ls, 'epoch', 'loss')
 ```
 
 我们将初始学习率设为0.03，并将$\gamma$（`gamma`）设为0.9。此时，变量$\boldsymbol{s}$可看作是最近$1/(1-0.9) = 10$个时刻的平方项$\boldsymbol{g} \odot \boldsymbol{g}$的加权平均。我们观察到，损失函数在迭代后期较震荡。

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+      <g id="Graphic_7">
+        <text transform="translate(289.05273 141.8855)" fill="black">
+          <tspan font-family="Arial" font-size="9" font-style="italic" font-weight="400" fill="black" x=".3034668" y="8">x</tspan>
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+        <text transform="translate(12.5 10.385498)" fill="black">
+          <tspan font-family="Arial" font-size="9" font-style="italic" font-weight="400" fill="black" x=".3034668" y="8">x</tspan>
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+      <g id="Graphic_5">
+        <text transform="translate(268.8 32.752784)" fill="black">
+          <tspan font-family="Arial" font-size="9" font-style="italic" font-weight="400" fill="black" x=".1159668" y="8">f = 10</tspan>
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-          <tspan font-family="Arial" font-size="12" font-style="italic" font-weight="400" fill="black" x=".15820312" y="11">f = 1</tspan>
+      <g id="Graphic_4">
+        <text transform="translate(186.19602 60.94369)" fill="black">
+          <tspan font-family="Arial" font-size="9" font-style="italic" font-weight="400" fill="black" x=".11865234" y="8">f = 1</tspan>
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-          <tspan font-family="Arial" font-size="12" font-style="italic" font-weight="400" fill="black" x=".15820312" y="11">f = 5</tspan>
+      <g id="Graphic_3">
+        <text transform="translate(222.6 50.152784)" fill="black">
+          <tspan font-family="Arial" font-size="9" font-style="italic" font-weight="400" fill="black" x=".11865234" y="8">f = 5</tspan>
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utils.py

@@ -3,7 +3,7 @@ from mxnet import gluon
 from mxnet import autograd
 from mxnet import nd
 from mxnet import image
-from mxnet.gluon import nn
+from mxnet.gluon import nn, data as gdata, loss as gloss
 import mxnet as mx
 import numpy as np
 from time import time
@@ -357,13 +357,13 @@ def set_fig_size(mpl, figsize=(3.5, 2.5)):
     mpl.rcParams['figure.figsize'] = figsize
 
 
-def data_iter(batch_size, num_examples, X, y):
+def data_iter(batch_size, num_examples, features, labels): 
     """遍历数据集。"""
-    idx = list(range(num_examples))
-    random.shuffle(idx)
+    indices = list(range(num_examples))
+    random.shuffle(indices)
     for i in range(0, num_examples, batch_size):
-        j = nd.array(idx[i: min(i + batch_size, num_examples)])
-        yield X.take(j), y.take(j)
+        j = nd.array(indices[i: min(i + batch_size, num_examples)])
+        yield features.take(j), labels.take(j)
 
 
 def linreg(X, w, b):
@@ -371,33 +371,33 @@ def linreg(X, w, b):
     return nd.dot(X, w) + b
 
 
-def squared_loss(yhat, y):
+def squared_loss(y_hat, y):
     """平方损失函数。"""
-    return (yhat - y.reshape(yhat.shape)) ** 2 / 2
+    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2
 
 
-def optimize(batch_size, trainer, num_epochs, decay_epoch, log_interval, X, y,
-             net):
+def optimize(batch_size, trainer, num_epochs, decay_epoch, log_interval,
+             features, labels, net):
     """优化目标函数。"""
-    dataset = gluon.data.ArrayDataset(X, y)
-    data_iter = gluon.data.DataLoader(dataset, batch_size, shuffle=True)
-    square_loss = gluon.loss.L2Loss()
-    y_vals = [square_loss(net(X), y).mean().asnumpy()]
+    dataset = gdata.ArrayDataset(features, labels)
+    data_iter = gdata.DataLoader(dataset, batch_size, shuffle=True)
+    loss = gloss.L2Loss()
+    ls = [loss(net(features), labels).mean().asnumpy()]
     for epoch in range(1, num_epochs + 1): 
         # 学习率自我衰减。
         if decay_epoch and epoch > decay_epoch:
             trainer.set_learning_rate(trainer.learning_rate * 0.1)
-        for batch_i, (features, label) in enumerate(data_iter):
+        for batch_i, (X, y) in enumerate(data_iter):
             with autograd.record():
-                output = net(features)
-                loss = square_loss(output, label)
-            loss.backward()
+                l = loss(net(X), y)
+            l.backward()
             trainer.step(batch_size)
             if batch_i * batch_size % log_interval == 0:
-                y_vals.append(square_loss(net(X), y).mean().asnumpy())
+                ls.append(loss(net(features), labels).mean().asnumpy())
+    # 为了便于打印，改变输出形状并转化成numpy数组。
     print('w:', net[0].weight.data(), '\nb:', net[0].bias.data(), '\n')
-    x_vals = np.linspace(0, num_epochs, len(y_vals), endpoint=True)
-    semilogy(x_vals, y_vals, 'epoch', 'loss')
+    es = np.linspace(0, num_epochs, len(ls), endpoint=True)
+    semilogy(es, ls, 'epoch', 'loss')
 
 
 def semilogy(x_vals, y_vals, x_label, y_label, figsize=(3.5, 2.5)):