Tutorial 9 - PyTorch

This tutorial is adapted from a 2022 blog post on the website Made With ML, by Goku Mohandas.

In this notebook, we will learn the basics of PyTorch, which is a Machine Learning library used to build dynamic neural networks. We’ll learn about the basics, such as creating and using Tensors.

import numpy as np
import torch

SEED = 1234

# Set seed for reproducibility
np.random.seed(seed=SEED)
torch.manual_seed(SEED)

<torch._C.Generator at 0x7e1d7c9ebe10>

Basics

# Creating a random tensor
x = torch.randn((2, 3))  # (rand(2,3) -> normal distribution)
print(f"Type: {x.type()}")
print(f"Size: {x.shape}")
print(f"Values: \n{x}")

Type: torch.FloatTensor
Size: torch.Size([2, 3])
Values:
tensor([[ 0.0461,  0.4024, -1.0115],
        [ 0.2167, -0.6123,  0.5036]])

# Zeros and Ones tensor
x = torch.zeros(2, 3)
print (x)
x = torch.ones(2, 3)
print (x)

tensor([[0., 0., 0.],
        [0., 0., 0.]])
tensor([[1., 1., 1.],
        [1., 1., 1.]])

# List --> Tensor
x = torch.Tensor([[1, 2, 3],[4, 5, 6]])
print(f"Size: {x.shape}")
print(f"Values: \n{x}")

Size: torch.Size([2, 3])
Values:
tensor([[1., 2., 3.],
        [4., 5., 6.]])

# NumPy array --> Tensor
x = torch.Tensor(np.random.rand(2, 3))
print(f"Size: {x.shape}")
print(f"Values: \n{x}")

Size: torch.Size([2, 3])
Values:
tensor([[0.1915, 0.6221, 0.4377],
        [0.7854, 0.7800, 0.2726]])

# Changing tensor type
x = torch.Tensor(3, 4)
print(f"Type: {x.type()}")
x = x.long()
print(f"Type: {x.type()}")

Type: torch.FloatTensor
Type: torch.LongTensor

Operations

# Addition
x = torch.randn(2, 3)
y = torch.randn(2, 3)
z = x + y
print(f"Size: {z.shape}")
print(f"Values: \n{z}")

Size: torch.Size([2, 3])
Values:
tensor([[ 0.0761, -0.6775, -0.3988],
        [ 3.0633, -0.1589,  0.3514]])

# Dot product
x = torch.randn(2, 3)
y = torch.randn(3, 2)
z = torch.mm(x, y)
print(f"Size: {z.shape}")
print(f"Values: \n{z}")

Size: torch.Size([2, 2])
Values:
tensor([[ 1.0796, -0.0759],
        [ 1.2746, -0.5134]])

# Transpose
x = torch.randn(2, 3)
print(f"Size: {x.shape}")
print(f"Values: \n{x}")
y = torch.t(x)
print(f"Size: {y.shape}")
print(f"Values: \n{y}")

Size: torch.Size([2, 3])
Values:
tensor([[ 0.8042, -0.1383,  0.3196],
        [-1.0187, -1.3147,  2.5228]])
Size: torch.Size([3, 2])
Values:
tensor([[ 0.8042, -1.0187],
        [-0.1383, -1.3147],
        [ 0.3196,  2.5228]])

# Reshape
x = torch.randn(2, 3)
z = x.view(3, 2)
print(f"Size: {z.shape}")
print(f"Values: \n{z}")

Size: torch.Size([3, 2])
Values:
tensor([[ 0.4501,  0.2709],
        [-0.8087, -0.0217],
        [-1.0413,  0.0702]])

# Dangers of reshaping (unintended consequences)
x = torch.tensor([
    [[1,1,1,1], [2,2,2,2], [3,3,3,3]],
    [[10,10,10,10], [20,20,20,20], [30,30,30,30]]
])
print(f"Size: {x.shape}")
print(f"x: \n{x}\n")

a = x.view(x.size(1), -1)
print(f"\nSize: {a.shape}")
print(f"a: \n{a}\n")

b = x.transpose(0,1).contiguous()
print(f"\nSize: {b.shape}")
print(f"b: \n{b}\n")

c = b.view(b.size(0), -1)
print(f"\nSize: {c.shape}")
print(f"c: \n{c}")

Size: torch.Size([2, 3, 4])
x:
tensor([[[ 1,  1,  1,  1],
         [ 2,  2,  2,  2],
         [ 3,  3,  3,  3]],

        [[10, 10, 10, 10],
         [20, 20, 20, 20],
         [30, 30, 30, 30]]])


Size: torch.Size([3, 8])
a:
tensor([[ 1,  1,  1,  1,  2,  2,  2,  2],
        [ 3,  3,  3,  3, 10, 10, 10, 10],
        [20, 20, 20, 20, 30, 30, 30, 30]])


Size: torch.Size([3, 2, 4])
b:
tensor([[[ 1,  1,  1,  1],
         [10, 10, 10, 10]],

        [[ 2,  2,  2,  2],
         [20, 20, 20, 20]],

        [[ 3,  3,  3,  3],
         [30, 30, 30, 30]]])


Size: torch.Size([3, 8])
c:
tensor([[ 1,  1,  1,  1, 10, 10, 10, 10],
        [ 2,  2,  2,  2, 20, 20, 20, 20],
        [ 3,  3,  3,  3, 30, 30, 30, 30]])

# Dimensional operations
x = torch.randn(2, 3)
print(f"Values: \n{x}")
y = torch.sum(x, dim=0) # add each row's value for every column
print(f"Values: \n{y}")
z = torch.sum(x, dim=1) # add each column's value for every row
print(f"Values: \n{z}")

Values:
tensor([[ 0.5797, -0.0599,  0.1816],
        [-0.6797, -0.2567, -1.8189]])
Values:
tensor([-0.1000, -0.3166, -1.6373])
Values:
tensor([ 0.7013, -2.7553])

Indexing, Slicing, and Joining

x = torch.randn(3, 4)
print (f"x: \n{x}")
print (f"x[:1]: \n{x[:1]}")
print (f"x[:1, 1:3]: \n{x[:1, 1:3]}")

x:
tensor([[ 0.2111,  0.3372,  0.6638,  1.0397],
        [ 1.8434,  0.6588, -0.2349, -0.0306],
        [ 1.7462, -0.0722, -1.6794, -1.7010]])
x[:1]:
tensor([[0.2111, 0.3372, 0.6638, 1.0397]])
x[:1, 1:3]:
tensor([[0.3372, 0.6638]])

# Select with dimensional indices
x = torch.randn(2, 3)
print(f"Values: \n{x}")

col_indices = torch.LongTensor([0, 2])
chosen = torch.index_select(x, dim=1, index=col_indices) # values from column 0 & 2
print(f"Values: \n{chosen}")

row_indices = torch.LongTensor([0, 1])
col_indices = torch.LongTensor([0, 2])
chosen = x[row_indices, col_indices] # values from (0, 0) & (1, 2)
print(f"Values: \n{chosen}")

Values:
tensor([[ 0.6486,  1.7653,  1.0812],
        [ 1.2436,  0.8971, -0.0784]])
Values:
tensor([[ 0.6486,  1.0812],
        [ 1.2436, -0.0784]])
Values:
tensor([ 0.6486, -0.0784])

# Concatenation
x = torch.randn(2, 3)
print(f"Values: \n{x}")
y = torch.cat([x, x], dim=0) # stack by rows (dim=1 to stack by columns)
print(f"Values: \n{y}")

Values:
tensor([[ 0.5548, -0.0845,  0.5903],
        [-1.0032, -1.7873,  0.0538]])
Values:
tensor([[ 0.5548, -0.0845,  0.5903],
        [-1.0032, -1.7873,  0.0538],
        [ 0.5548, -0.0845,  0.5903],
        [-1.0032, -1.7873,  0.0538]])

Gradients

• \(y = 3x + 2\)

• \(z = \sum{y}/N\)

• \(\frac{\partial(z)}{\partial(x)} = \frac{\partial(z)}{\partial(y)} \frac{\partial(y)}{\partial(x)} = \frac{1}{N} * 3 = \frac{1}{12} * 3 = 0.25\)

# Tensors with gradient bookkeeping
x = torch.rand(3, 4, requires_grad=True)
y = 3*x + 2
z = y.mean()
z.backward() # z has to be scalar
print(f"x: \n{x}")
print(f"x.grad: \n{x.grad}")

x:
tensor([[0.7379, 0.0846, 0.4245, 0.9778],
        [0.6800, 0.3151, 0.3911, 0.8943],
        [0.6889, 0.8389, 0.1780, 0.6442]], requires_grad=True)
x.grad:
tensor([[0.2500, 0.2500, 0.2500, 0.2500],
        [0.2500, 0.2500, 0.2500, 0.2500],
        [0.2500, 0.2500, 0.2500, 0.2500]])

CUDA tensors

# Is CUDA available?
print (torch.cuda.is_available())

True

If False, CUDA is not available. In Google Colab, we can change it by Runtime > Change runtime type > Change Hardware accelerator to GPU > Click Save

# Is CUDA available now?
print (torch.cuda.is_available())

True

# Set device
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
print (device)

cuda

x = torch.rand(2,3)
print (x.is_cuda)
x = torch.rand(2,3).to(device) # Tensor is stored on the GPU
print (x.is_cuda)

False
True

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