第一课

参考资料 reference

什么是PyTorch?

PyTorch是一个基于Python的科学计算库，它有以下特点:

• 类似于NumPy，但是它可以使用GPU
• 可以用它定义深度学习模型，可以灵活地进行深度学习模型的训练和使用

Tensors

Tensor类似与NumPy的ndarray，唯一的区别是Tensor可以在GPU上加速运算。

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from __future__ import print_function
import torch

构造一个未初始化的5x3矩阵:

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x = torch.empty(5, 3)
print(x)

tensor([[0.0000e+00, 0.0000e+00, 0.0000e+00],
        [0.0000e+00, 0.0000e+00, 1.1704e-41],
        [0.0000e+00, 2.2369e+08, 0.0000e+00],
        [0.0000e+00, 0.0000e+00, 0.0000e+00],
        [       nan,        nan, 5.8024e-08]])

构建一个随机初始化的矩阵:

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x = torch.rand(5, 3)
print(x)

tensor([[0.8864, 0.0875, 0.5509],
        [0.8290, 0.4770, 0.5214],
        [0.4291, 0.8248, 0.7763],
        [0.8400, 0.4375, 0.8075],
        [0.4034, 0.8427, 0.6798]])

构建一个全部为0，类型为long的矩阵:

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x = torch.zeros(5, 3, dtype=torch.long)
print(x)

tensor([[0, 0, 0],
        [0, 0, 0],
        [0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]])

从数据直接直接构建tensor:

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x = torch.tensor([5.5, 3])
print(x)

tensor([5.5000, 3.0000])

也可以从一个已有的tensor构建一个tensor。这些方法会重用原来tensor的特征，例如，数据类型，除非提供新的数据。

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x = x.new_ones(5, 3, dtype=torch.double)      # new_* methods take in sizes
print(x)

x = torch.randn_like(x, dtype=torch.float)    # override dtype!
print(x)                                      # result has the same size

tensor([[1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.],
        [1., 1., 1.]], dtype=torch.float64)
tensor([[ 0.2173, -1.3224,  0.5543],
        [ 0.1450,  0.2199, -0.0678],
        [ 0.7979, -0.4419, -1.2025],
        [ 0.8140,  0.2363,  0.2310],
        [-1.7360,  1.9243,  1.5151]])

得到tensor的形状:

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print(x.size())

torch.Size([5, 3])

Operations

有很多种tensor运算。我们先介绍加法运算。

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y = torch.rand(5, 3)
print(x + y)

tensor([[ 0.6617, -0.9648,  1.4188],
        [ 0.4702,  0.6419,  0.6207],
        [ 1.5369,  0.2954, -0.7771],
        [ 1.4111,  0.9671,  1.0595],
        [-1.3126,  2.2809,  1.8937]])

另一种着加法的写法

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print(torch.add(x, y))

tensor([[ 0.6617, -0.9648,  1.4188],
        [ 0.4702,  0.6419,  0.6207],
        [ 1.5369,  0.2954, -0.7771],
        [ 1.4111,  0.9671,  1.0595],
        [-1.3126,  2.2809,  1.8937]])

加法：把输出作为一个变量

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result = torch.empty(5, 3)
torch.add(x, y, out=result)
print(result)

tensor([[ 0.6617, -0.9648,  1.4188],
        [ 0.4702,  0.6419,  0.6207],
        [ 1.5369,  0.2954, -0.7771],
        [ 1.4111,  0.9671,  1.0595],
        [-1.3126,  2.2809,  1.8937]])

in-place加法

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# adds x to y
y.add_(x)
print(y)

tensor([[ 0.6617, -0.9648,  1.4188],
        [ 0.4702,  0.6419,  0.6207],
        [ 1.5369,  0.2954, -0.7771],
        [ 1.4111,  0.9671,  1.0595],
        [-1.3126,  2.2809,  1.8937]])

各种类似NumPy的indexing都可以在PyTorch tensor上面使用。

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print(x[:, 1])

tensor([-1.3224,  0.2199, -0.4419,  0.2363,  1.9243])

Resizing: 如果你希望resize/reshape一个tensor，可以使用torch.view：

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x = torch.randn(4, 4)
y = x.view(16)
z = x.view(-1, 8)  # the size -1 is inferred from other dimensions
print(x.size(), y.size(), z.size())

torch.Size([4, 4]) torch.Size([16]) torch.Size([2, 8])

如果你有一个只有一个元素的tensor，使用.item()方法可以把里面的value变成Python数值。

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x = torch.randn(1)
print(x)
print(x.item())

tensor([0.5669])
0.5668683052062988

更多阅读

各种Tensor operations, 包括transposing, indexing, slicing,
mathematical operations, linear algebra, random numbers在
<https://pytorch.org/docs/torch>.

Numpy和Tensor之间的转化

在Torch Tensor和NumPy array之间相互转化非常容易。

Torch Tensor和NumPy array会共享内存，所以改变其中一项也会改变另一项。

把Torch Tensor转变成NumPy Array

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a = torch.ones(5)
print(a)

tensor([1., 1., 1., 1., 1.])

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b = a.numpy()
print(b)

[1. 1. 1. 1. 1.]

改变numpy array里面的值。

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a.add_(1)
print(a)
print(b)

tensor([2., 2., 2., 2., 2.])
[2. 2. 2. 2. 2.]

把NumPy ndarray转成Torch Tensor

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import numpy as np
a = np.ones(5)
b = torch.from_numpy(a)
np.add(a, 1, out=a)
print(a)
print(b)

[2. 2. 2. 2. 2.]
tensor([2., 2., 2., 2., 2.], dtype=torch.float64)

所有CPU上的Tensor都支持转成numpy或者从numpy转成Tensor。

CUDA Tensors

使用.to方法，Tensor可以被移动到别的device上。

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# let us run this cell only if CUDA is available
# We will use ``torch.device`` objects to move tensors in and out of GPU
if torch.cuda.is_available():
    device = torch.device("cuda")          # a CUDA device object
    y = torch.ones_like(x, device=device)  # directly create a tensor on GPU
    x = x.to(device)                       # or just use strings ``.to("cuda")``
    z = x + y
    print(z)
    print(z.to("cpu", torch.double))       # ``.to`` can also change dtype together!

热身: 用numpy实现两层神经网络

一个全连接ReLU神经网络，一个隐藏层，没有bias。用来从x预测y，使用L2 Loss。

这一实现完全使用numpy来计算前向神经网络，loss，和反向传播。

numpy ndarray是一个普通的n维array。它不知道任何关于深度学习或者梯度(gradient)的知识，也不知道计算图(computation graph)，只是一种用来计算数学运算的数据结构。

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import numpy as np

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random input and output data
x = np.random.randn(N, D_in)
y = np.random.randn(N, D_out)

# Randomly initialize weights
w1 = np.random.randn(D_in, H)
w2 = np.random.randn(H, D_out)

learning_rate = 1e-6
for t in range(500):
    # Forward pass: compute predicted y
    h = x.dot(w1)
    h_relu = np.maximum(h, 0)
    y_pred = h_relu.dot(w2)

    # Compute and print loss
    loss = np.square(y_pred - y).sum()
    print(t, loss)

    # Backprop to compute gradients of w1 and w2 with respect to loss

    # loss = (y_pred - y) ** 2
    grad_y_pred = 2.0 * (y_pred - y)
    #
    grad_w2 = h_relu.T.dot(grad_y_pred)
    grad_h_relu = grad_y_pred.dot(w2.T)
    grad_h = grad_h_relu.copy()
    grad_h[h < 0] = 0
    grad_w1 = x.T.dot(grad_h)

    # Update weights
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

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415 1.620126489878264e-05
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421 1.1832124847189769e-05
422 1.1228621028826248e-05
423 1.0656066913018655e-05
424 1.011273346058932e-05
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498 2.1341070029951215e-07
499 2.026117831426625e-07

PyTorch: Tensors

这次我们使用PyTorch tensors来创建前向神经网络，计算损失，以及反向传播。

一个PyTorch Tensor很像一个numpy的ndarray。但是它和numpy ndarray最大的区别是，PyTorch Tensor可以在CPU或者GPU上运算。如果想要在GPU上运算，就需要把Tensor换成cuda类型。

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import torch


dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random input and output data
x = torch.randn(N, D_in, device=device, dtype=dtype)
y = torch.randn(N, D_out, device=device, dtype=dtype)

# Randomly initialize weights
w1 = torch.randn(D_in, H, device=device, dtype=dtype)
w2 = torch.randn(H, D_out, device=device, dtype=dtype)

learning_rate = 1e-6
for t in range(500):
    # Forward pass: compute predicted y
    h = x.mm(w1)
    h_relu = h.clamp(min=0)
    y_pred = h_relu.mm(w2)

    # Compute and print loss
    loss = (y_pred - y).pow(2).sum().item()
    print(t, loss)

    # Backprop to compute gradients of w1 and w2 with respect to loss
    grad_y_pred = 2.0 * (y_pred - y)
    grad_w2 = h_relu.t().mm(grad_y_pred)
    grad_h_relu = grad_y_pred.mm(w2.t())
    grad_h = grad_h_relu.clone()
    grad_h[h < 0] = 0
    grad_w1 = x.t().mm(grad_h)

    # Update weights using gradient descent
    w1 -= learning_rate * grad_w1
    w2 -= learning_rate * grad_w2

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简单的autograd

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# Create tensors.
x = torch.tensor(1., requires_grad=True)
w = torch.tensor(2., requires_grad=True)
b = torch.tensor(3., requires_grad=True)

# Build a computational graph.
y = w * x + b    # y = 2 * x + 3

# Compute gradients.
y.backward()

# Print out the gradients.
print(x.grad)    # x.grad = 2
print(w.grad)    # w.grad = 1
print(b.grad)    # b.grad = 1

tensor(2.)
tensor(1.)
tensor(1.)

PyTorch: Tensor和autograd

PyTorch的一个重要功能就是autograd，也就是说只要定义了forward pass(前向神经网络)，计算了loss之后，PyTorch可以自动求导计算模型所有参数的梯度。

一个PyTorch的Tensor表示计算图中的一个节点。如果x是一个Tensor并且x.requires_grad=True那么x.grad是另一个储存着x当前梯度(相对于一个scalar，常常是loss)的向量。

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import torch

dtype = torch.float
device = torch.device("cpu")
# device = torch.device("cuda:0") # Uncomment this to run on GPU

# N 是 batch size; D_in 是 input dimension;
# H 是 hidden dimension; D_out 是 output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# 创建随机的Tensor来保存输入和输出
# 设定requires_grad=False表示在反向传播的时候我们不需要计算gradient
x = torch.randn(N, D_in, device=device, dtype=dtype)
y = torch.randn(N, D_out, device=device, dtype=dtype)

# 创建随机的Tensor和权重。
# 设置requires_grad=True表示我们希望反向传播的时候计算Tensor的gradient
w1 = torch.randn(D_in, H, device=device, dtype=dtype, requires_grad=True)
w2 = torch.randn(H, D_out, device=device, dtype=dtype, requires_grad=True)

learning_rate = 1e-6
for t in range(500):
    # 前向传播:通过Tensor预测y；这个和普通的神经网络的前向传播没有任何不同，
    # 但是我们不需要保存网络的中间运算结果，因为我们不需要手动计算反向传播。
    y_pred = x.mm(w1).clamp(min=0).mm(w2)

    # 通过前向传播计算loss
    # loss是一个形状为(1，)的Tensor
    # loss.item()可以给我们返回一个loss的scalar
    loss = (y_pred - y).pow(2).sum()
    print(t, loss.item())

    # PyTorch给我们提供了autograd的方法做反向传播。如果一个Tensor的requires_grad=True，
    # backward会自动计算loss相对于每个Tensor的gradient。在backward之后，
    # w1.grad和w2.grad会包含两个loss相对于两个Tensor的gradient信息。
    loss.backward()

    # 我们可以手动做gradient descent(后面我们会介绍自动的方法)。
    # 用torch.no_grad()包含以下statements，因为w1和w2都是requires_grad=True，
    # 但是在更新weights之后我们并不需要再做autograd。
    # 另一种方法是在weight.data和weight.grad.data上做操作，这样就不会对grad产生影响。
    # tensor.data会我们一个tensor，这个tensor和原来的tensor指向相同的内存空间，
    # 但是不会记录计算图的历史。
    with torch.no_grad():
        w1 -= learning_rate * w1.grad
        w2 -= learning_rate * w2.grad

        # Manually zero the gradients after updating weights
        w1.grad.zero_()
        w2.grad.zero_()

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PyTorch: nn

这次我们使用PyTorch中nn这个库来构建网络。
用PyTorch autograd来构建计算图和计算gradients，
然后PyTorch会帮我们自动计算gradient。

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import torch

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Use the nn package to define our model as a sequence of layers. nn.Sequential
# is a Module which contains other Modules, and applies them in sequence to
# produce its output. Each Linear Module computes output from input using a
# linear function, and holds internal Tensors for its weight and bias.
model = torch.nn.Sequential(
    torch.nn.Linear(D_in, H),
    torch.nn.ReLU(),
    torch.nn.Linear(H, D_out),
)

# The nn package also contains definitions of popular loss functions; in this
# case we will use Mean Squared Error (MSE) as our loss function.
loss_fn = torch.nn.MSELoss(reduction='sum')

learning_rate = 1e-4
for t in range(500):
    # Forward pass: compute predicted y by passing x to the model. Module objects
    # override the __call__ operator so you can call them like functions. When
    # doing so you pass a Tensor of input data to the Module and it produces
    # a Tensor of output data.
    y_pred = model(x)

    # Compute and print loss. We pass Tensors containing the predicted and true
    # values of y, and the loss function returns a Tensor containing the
    # loss.
    loss = loss_fn(y_pred, y)
    print(t, loss.item())

    # Zero the gradients before running the backward pass.
    model.zero_grad()

    # Backward pass: compute gradient of the loss with respect to all the learnable
    # parameters of the model. Internally, the parameters of each Module are stored
    # in Tensors with requires_grad=True, so this call will compute gradients for
    # all learnable parameters in the model.
    loss.backward()

    # Update the weights using gradient descent. Each parameter is a Tensor, so
    # we can access its gradients like we did before.
    with torch.no_grad():
        for param in model.parameters():
            param -= learning_rate * param.grad

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499 1.3836001926392782e-06

PyTorch: optim

这一次我们不再手动更新模型的weights,而是使用optim这个包来帮助我们更新参数。
optim这个package提供了各种不同的模型优化方法，包括SGD+momentum, RMSProp, Adam等等。

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import torch

# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Use the nn package to define our model and loss function.
model = torch.nn.Sequential(
    torch.nn.Linear(D_in, H),
    torch.nn.ReLU(),
    torch.nn.Linear(H, D_out),
)
loss_fn = torch.nn.MSELoss(reduction='sum')

# Use the optim package to define an Optimizer that will update the weights of
# the model for us. Here we will use Adam; the optim package contains many other
# optimization algoriths. The first argument to the Adam constructor tells the
# optimizer which Tensors it should update.
learning_rate = 1e-4
optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)
for t in range(500):
    # Forward pass: compute predicted y by passing x to the model.
    y_pred = model(x)

    # Compute and print loss.
    loss = loss_fn(y_pred, y)
    print(t, loss.item())

    # Before the backward pass, use the optimizer object to zero all of the
    # gradients for the variables it will update (which are the learnable
    # weights of the model). This is because by default, gradients are
    # accumulated in buffers( i.e, not overwritten) whenever .backward()
    # is called. Checkout docs of torch.autograd.backward for more details.
    optimizer.zero_grad()

    # Backward pass: compute gradient of the loss with respect to model
    # parameters
    loss.backward()

    # Calling the step function on an Optimizer makes an update to its
    # parameters
    optimizer.step()

0 689.9976806640625
1 673.0743408203125
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499 1.491649026519326e-09

PyTorch: 自定义 nn Modules

我们可以定义一个模型，这个模型继承自nn.Module类。如果需要定义一个比Sequential模型更加复杂的模型，就需要定义nn.Module模型。

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import torch


class TwoLayerNet(torch.nn.Module):
    def __init__(self, D_in, H, D_out):
        """
        In the constructor we instantiate two nn.Linear modules and assign them as
        member variables.
        """
        super(TwoLayerNet, self).__init__()
        self.linear1 = torch.nn.Linear(D_in, H)
        self.linear2 = torch.nn.Linear(H, D_out)

    def forward(self, x):
        """
        In the forward function we accept a Tensor of input data and we must return
        a Tensor of output data. We can use Modules defined in the constructor as
        well as arbitrary operators on Tensors.
        """
        h_relu = self.linear1(x).clamp(min=0)
        y_pred = self.linear2(h_relu)
        return y_pred


# N is batch size; D_in is input dimension;
# H is hidden dimension; D_out is output dimension.
N, D_in, H, D_out = 64, 1000, 100, 10

# Create random Tensors to hold inputs and outputs
x = torch.randn(N, D_in)
y = torch.randn(N, D_out)

# Construct our model by instantiating the class defined above
model = TwoLayerNet(D_in, H, D_out)

# Construct our loss function and an Optimizer. The call to model.parameters()
# in the SGD constructor will contain the learnable parameters of the two
# nn.Linear modules which are members of the model.
criterion = torch.nn.MSELoss(reduction='sum')
optimizer = torch.optim.SGD(model.parameters(), lr=1e-4)
for t in range(500):
    # Forward pass: Compute predicted y by passing x to the model
    y_pred = model(x)

    # Compute and print loss
    loss = criterion(y_pred, y)
    print(t, loss.item())

    # Zero gradients, perform a backward pass, and update the weights.
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

0 650.2210083007812
1 601.2785034179688
2 559.1675415039062
3 522.359130859375
4 489.7039489746094
5 460.2625732421875
6 433.5502624511719
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366 9.588249668013304e-05
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368 8.965901361079887e-05
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370 8.38430059957318e-05
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372 7.840731996111572e-05
373 7.582772377645597e-05
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498 1.3083595149510074e-06
499 1.267892798750836e-06

FizzBuzz

FizzBuzz是一个简单的小游戏。游戏规则如下：从1开始往上数数，当遇到3的倍数的时候，说fizz，当遇到5的倍数，说buzz，当遇到15的倍数，就说fizzbuzz，其他情况下则正常数数。

我们可以写一个简单的小程序来决定要返回正常数值还是fizz, buzz 或者 fizzbuzz。

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# One-hot encode the desired outputs: [number, "fizz", "buzz", "fizzbuzz"]
def fizz_buzz_encode(i):
    if   i % 15 == 0: return 3
    elif i % 5  == 0: return 2
    elif i % 3  == 0: return 1
    else:             return 0

def fizz_buzz_decode(i, prediction):
    return [str(i), "fizz", "buzz", "fizzbuzz"][prediction]

print(fizz_buzz_decode(1, fizz_buzz_encode(1)))
print(fizz_buzz_decode(2, fizz_buzz_encode(2)))
print(fizz_buzz_decode(5, fizz_buzz_encode(5)))
print(fizz_buzz_decode(12, fizz_buzz_encode(12)))
print(fizz_buzz_decode(15, fizz_buzz_encode(15)))

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buzz
fizz
fizzbuzz

我们首先定义模型的输入与输出(训练数据)

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import numpy as np
import torch

NUM_DIGITS = 10

# Represent each input by an array of its binary digits.
def binary_encode(i, num_digits):
    return np.array([i >> d & 1 for d in range(num_digits)])

trX = torch.Tensor([binary_encode(i, NUM_DIGITS) for i in range(101, 2 ** NUM_DIGITS)])
trY = torch.LongTensor([fizz_buzz_encode(i) for i in range(101, 2 ** NUM_DIGITS)])

然后我们用PyTorch定义模型

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# Define the model
NUM_HIDDEN = 100
model = torch.nn.Sequential(
    torch.nn.Linear(NUM_DIGITS, NUM_HIDDEN),
    torch.nn.ReLU(),
    torch.nn.Linear(NUM_HIDDEN, 4)
)

• 为了让我们的模型学会FizzBuzz这个游戏，我们需要定义一个损失函数，和一个优化算法。
• 这个优化算法会不断优化（降低）损失函数，使得模型的在该任务上取得尽可能低的损失值。
• 损失值低往往表示我们的模型表现好，损失值高表示我们的模型表现差。
• 由于FizzBuzz游戏本质上是一个分类问题，我们选用Cross Entropyy Loss函数。
• 优化函数我们选用Stochastic Gradient Descent。

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loss_fn = torch.nn.CrossEntropyLoss()
optimizer = torch.optim.SGD(model.parameters(), lr = 0.05)

以下是模型的训练代码

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# Start training it
BATCH_SIZE = 128
for epoch in range(10000):
    for start in range(0, len(trX), BATCH_SIZE):
        end = start + BATCH_SIZE
        batchX = trX[start:end]
        batchY = trY[start:end]

        y_pred = model(batchX)
        loss = loss_fn(y_pred, batchY)

        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

    # Find loss on training data
    loss = loss_fn(model(trX), trY).item()
    print('Epoch:', epoch, 'Loss:', loss)

Epoch: 0 Loss: 1.1985573768615723
Epoch: 1 Loss: 1.1627824306488037
Epoch: 2 Loss: 1.153425931930542
Epoch: 3 Loss: 1.1497533321380615
Epoch: 4 Loss: 1.1479018926620483
Epoch: 5 Loss: 1.1467877626419067
Epoch: 6 Loss: 1.1460249423980713
Epoch: 7 Loss: 1.1454517841339111
Epoch: 8 Loss: 1.1449863910675049
Epoch: 9 Loss: 1.1445919275283813
Epoch: 10 Loss: 1.1442433595657349
Epoch: 11 Loss: 1.1439307928085327
Epoch: 12 Loss: 1.1436454057693481
Epoch: 13 Loss: 1.14337956905365
Epoch: 14 Loss: 1.1431307792663574
Epoch: 15 Loss: 1.1428961753845215
Epoch: 16 Loss: 1.142675757408142
Epoch: 17 Loss: 1.1424572467803955
Epoch: 18 Loss: 1.1422516107559204
Epoch: 19 Loss: 1.1420538425445557
Epoch: 20 Loss: 1.1418650150299072
Epoch: 21 Loss: 1.141685962677002
Epoch: 22 Loss: 1.1415083408355713
Epoch: 23 Loss: 1.1413389444351196
Epoch: 24 Loss: 1.1411713361740112
Epoch: 25 Loss: 1.1410109996795654
Epoch: 26 Loss: 1.1408500671386719
Epoch: 27 Loss: 1.1406961679458618
Epoch: 28 Loss: 1.1405448913574219
Epoch: 29 Loss: 1.1403969526290894
Epoch: 30 Loss: 1.1402522325515747
Epoch: 31 Loss: 1.1401114463806152
Epoch: 32 Loss: 1.1399762630462646
Epoch: 33 Loss: 1.1398409605026245
Epoch: 34 Loss: 1.139709711074829
Epoch: 35 Loss: 1.1395775079727173
Epoch: 36 Loss: 1.139445185661316
Epoch: 37 Loss: 1.1393134593963623
Epoch: 38 Loss: 1.1391855478286743
Epoch: 39 Loss: 1.1390624046325684
Epoch: 40 Loss: 1.1389377117156982
Epoch: 41 Loss: 1.1388169527053833
Epoch: 42 Loss: 1.1386950016021729
Epoch: 43 Loss: 1.1385750770568848
Epoch: 44 Loss: 1.1384531259536743
Epoch: 45 Loss: 1.1383368968963623
Epoch: 46 Loss: 1.1382218599319458
Epoch: 47 Loss: 1.1381083726882935
Epoch: 48 Loss: 1.1379945278167725
Epoch: 49 Loss: 1.1378828287124634
Epoch: 50 Loss: 1.1377702951431274
Epoch: 51 Loss: 1.1376607418060303
Epoch: 52 Loss: 1.1375516653060913
Epoch: 53 Loss: 1.1374434232711792
Epoch: 54 Loss: 1.1373358964920044
Epoch: 55 Loss: 1.1372319459915161
Epoch: 56 Loss: 1.1371287107467651
Epoch: 57 Loss: 1.1370246410369873
Epoch: 58 Loss: 1.1369221210479736
Epoch: 59 Loss: 1.1368229389190674
Epoch: 60 Loss: 1.1367197036743164
Epoch: 61 Loss: 1.1366175413131714
Epoch: 62 Loss: 1.1365183591842651
Epoch: 63 Loss: 1.1364164352416992
Epoch: 64 Loss: 1.1363164186477661
Epoch: 65 Loss: 1.1362184286117554
Epoch: 66 Loss: 1.136118769645691
Epoch: 67 Loss: 1.1360193490982056
Epoch: 68 Loss: 1.135920524597168
Epoch: 69 Loss: 1.1358208656311035
Epoch: 70 Loss: 1.1357228755950928
Epoch: 71 Loss: 1.1356228590011597
Epoch: 72 Loss: 1.135527491569519
Epoch: 73 Loss: 1.1354278326034546
Epoch: 74 Loss: 1.1353328227996826
Epoch: 75 Loss: 1.1352288722991943
Epoch: 76 Loss: 1.135129451751709
Epoch: 77 Loss: 1.1350293159484863
Epoch: 78 Loss: 1.1349287033081055
Epoch: 79 Loss: 1.1348257064819336
Epoch: 80 Loss: 1.1347209215164185
Epoch: 81 Loss: 1.1346193552017212
Epoch: 82 Loss: 1.134515643119812
Epoch: 83 Loss: 1.13441002368927
Epoch: 84 Loss: 1.1343063116073608
Epoch: 85 Loss: 1.134202003479004
Epoch: 86 Loss: 1.1340950727462769
Epoch: 87 Loss: 1.1339876651763916
Epoch: 88 Loss: 1.1338807344436646
Epoch: 89 Loss: 1.1337720155715942
Epoch: 90 Loss: 1.1336610317230225
Epoch: 91 Loss: 1.1335523128509521
Epoch: 92 Loss: 1.1334378719329834
Epoch: 93 Loss: 1.1333235502243042
Epoch: 94 Loss: 1.1332066059112549
Epoch: 95 Loss: 1.1330877542495728
Epoch: 96 Loss: 1.1329704523086548
Epoch: 97 Loss: 1.1328511238098145
Epoch: 98 Loss: 1.1327301263809204
Epoch: 99 Loss: 1.1326102018356323
Epoch: 100 Loss: 1.1324888467788696
Epoch: 101 Loss: 1.132361650466919
Epoch: 102 Loss: 1.1322351694107056
Epoch: 103 Loss: 1.1321076154708862
Epoch: 104 Loss: 1.131980061531067
Epoch: 105 Loss: 1.1318477392196655
Epoch: 106 Loss: 1.1317113637924194
Epoch: 107 Loss: 1.131577968597412
Epoch: 108 Loss: 1.131436824798584
Epoch: 109 Loss: 1.131296992301941
Epoch: 110 Loss: 1.1311523914337158
Epoch: 111 Loss: 1.1310100555419922
Epoch: 112 Loss: 1.1308666467666626
Epoch: 113 Loss: 1.1307142972946167
Epoch: 114 Loss: 1.1305700540542603
Epoch: 115 Loss: 1.1304125785827637
Epoch: 116 Loss: 1.1302579641342163
Epoch: 117 Loss: 1.1300987005233765
Epoch: 118 Loss: 1.1299388408660889
Epoch: 119 Loss: 1.1297751665115356
Epoch: 120 Loss: 1.1296147108078003
Epoch: 121 Loss: 1.1294395923614502
Epoch: 122 Loss: 1.1292656660079956
Epoch: 123 Loss: 1.1290934085845947
Epoch: 124 Loss: 1.1289095878601074
Epoch: 125 Loss: 1.1287299394607544
Epoch: 126 Loss: 1.128541111946106
Epoch: 127 Loss: 1.1283516883850098
Epoch: 128 Loss: 1.1281630992889404
Epoch: 129 Loss: 1.1279628276824951
Epoch: 130 Loss: 1.1277685165405273
Epoch: 131 Loss: 1.1275688409805298
Epoch: 132 Loss: 1.1273595094680786
Epoch: 133 Loss: 1.1271624565124512
Epoch: 134 Loss: 1.1269479990005493
Epoch: 135 Loss: 1.126736044883728
Epoch: 136 Loss: 1.1265151500701904
Epoch: 137 Loss: 1.1262929439544678
Epoch: 138 Loss: 1.126067876815796
Epoch: 139 Loss: 1.1258388757705688
Epoch: 140 Loss: 1.1256027221679688
Epoch: 141 Loss: 1.1253615617752075
Epoch: 142 Loss: 1.1251219511032104
Epoch: 143 Loss: 1.1248878240585327
Epoch: 144 Loss: 1.1246533393859863
Epoch: 145 Loss: 1.1244161128997803
Epoch: 146 Loss: 1.124180555343628
Epoch: 147 Loss: 1.1239362955093384
Epoch: 148 Loss: 1.123681902885437
Epoch: 149 Loss: 1.123428463935852
Epoch: 150 Loss: 1.123167872428894
Epoch: 151 Loss: 1.122915267944336
Epoch: 152 Loss: 1.1226478815078735
Epoch: 153 Loss: 1.1223746538162231
Epoch: 154 Loss: 1.1220675706863403
Epoch: 155 Loss: 1.121840476989746
Epoch: 156 Loss: 1.121732234954834
Epoch: 157 Loss: 1.1213226318359375
Epoch: 158 Loss: 1.1212854385375977
Epoch: 159 Loss: 1.1210198402404785
Epoch: 160 Loss: 1.1205651760101318
Epoch: 161 Loss: 1.1203441619873047
Epoch: 162 Loss: 1.1200261116027832
Epoch: 163 Loss: 1.1197220087051392
Epoch: 164 Loss: 1.1194864511489868
Epoch: 165 Loss: 1.11925208568573
Epoch: 166 Loss: 1.11906099319458
Epoch: 167 Loss: 1.1189343929290771
Epoch: 168 Loss: 1.1183561086654663
Epoch: 169 Loss: 1.118335247039795
Epoch: 170 Loss: 1.117862582206726
Epoch: 171 Loss: 1.117429256439209
Epoch: 172 Loss: 1.117123007774353
Epoch: 173 Loss: 1.11692476272583
Epoch: 174 Loss: 1.116502046585083
Epoch: 175 Loss: 1.1162279844284058
Epoch: 176 Loss: 1.1158732175827026
Epoch: 177 Loss: 1.1155357360839844
Epoch: 178 Loss: 1.1152691841125488
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Epoch: 9970 Loss: 0.0066172960214316845
Epoch: 9971 Loss: 0.006616067606955767
Epoch: 9972 Loss: 0.006614924408495426
Epoch: 9973 Loss: 0.006615237332880497
Epoch: 9974 Loss: 0.00661293463781476
Epoch: 9975 Loss: 0.0066118729300796986
Epoch: 9976 Loss: 0.006611463613808155
Epoch: 9977 Loss: 0.006610286422073841
Epoch: 9978 Loss: 0.006609508767724037
Epoch: 9979 Loss: 0.006608613301068544
Epoch: 9980 Loss: 0.006607453338801861
Epoch: 9981 Loss: 0.006606157869100571
Epoch: 9982 Loss: 0.006605706177651882
Epoch: 9983 Loss: 0.006603860761970282
Epoch: 9984 Loss: 0.006602838169783354
Epoch: 9985 Loss: 0.006602330598980188
Epoch: 9986 Loss: 0.006601244676858187
Epoch: 9987 Loss: 0.006600590888410807
Epoch: 9988 Loss: 0.006599425803869963
Epoch: 9989 Loss: 0.0065981619991362095
Epoch: 9990 Loss: 0.00659700483083725
Epoch: 9991 Loss: 0.0065963477827608585
Epoch: 9992 Loss: 0.0065948013216257095
Epoch: 9993 Loss: 0.006593888625502586
Epoch: 9994 Loss: 0.006593203637748957
Epoch: 9995 Loss: 0.006592920050024986
Epoch: 9996 Loss: 0.006591069977730513
Epoch: 9997 Loss: 0.006590310949832201
Epoch: 9998 Loss: 0.0065892646089196205
Epoch: 9999 Loss: 0.006588027812540531

最后我们用训练好的模型尝试在1到100这些数字上玩FizzBuzz游戏

1
2
3
4
5
6
7

# Output now
testX = torch.Tensor([binary_encode(i, NUM_DIGITS) for i in range(1, 101)])
with torch.no_grad():
    testY = model(testX)
predictions = zip(range(1, 101), list(testY.max(1)[1].data.tolist()))

print([fizz_buzz_decode(i, x) for (i, x) in predictions])

['1', '2', 'fizz', '4', 'buzz', 'fizz', '7', '8', 'fizz', 'buzz', '11', 'fizz', '13', '14', 'fizzbuzz', '16', '17', 'fizz', '19', 'buzz', 'fizz', '22', '23', 'fizz', '25', '26', 'fizz', '28', '29', 'fizzbuzz', '31', '32', 'fizz', '34', 'buzz', 'fizz', '37', '38', 'fizz', 'buzz', '41', 'fizz', '43', '44', 'fizzbuzz', '46', '47', 'fizz', '49', 'buzz', 'fizz', '52', '53', 'fizz', 'buzz', '56', 'fizz', '58', '59', 'fizzbuzz', '61', '62', 'fizz', '64', 'buzz', 'fizz', '67', 'buzz', '69', 'buzz', '71', 'fizz', '73', '74', 'fizzbuzz', '76', '77', 'fizz', '79', 'buzz', 'fizz', '82', 'buzz', 'fizz', 'buzz', '86', 'fizz', '88', '89', 'fizzbuzz', '91', '92', 'fizz', '94', 'buzz', 'fizz', '97', '98', 'fizz', 'buzz']

1
2

print(np.sum(testY.max(1)[1].numpy() == np.array([fizz_buzz_encode(i) for i in range(1,101)])))
testY.max(1)[1].numpy() == np.array([fizz_buzz_encode(i) for i in range(1,101)])

96





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