16. PyTorch Fundamentals and Tensors¶

Learn the foundations of PyTorch, understand tensors, tensor operations, device management, automatic differentiation, neural network modules, parameters, GPU acceleration, and the core building blocks required to develop Deep Learning models using PyTorch.

🎯 Learning Objectives¶

After completing this chapter, you will be able to:

Explain what PyTorch is
Understand the architecture of PyTorch
Understand PyTorch tensors
Understand tensor dimensions, shape, rank, and data types
Create tensors using different methods
Perform tensor indexing and slicing
Perform tensor arithmetic and matrix operations
Understand broadcasting
Reshape, transpose, squeeze, and unsqueeze tensors
Understand tensor devices
Move tensors between CPU and GPU
Understand tensor memory and performance considerations
Understand requires_grad
Understand the role of tensors in automatic differentiation
Understand torch.nn
Build neural network components using nn.Module
Understand parameters and trainable variables
Build a basic PyTorch neural network
Understand the PyTorch training workflow
Understand the difference between training and inference
Save and load PyTorch models
Understand PyTorch GPU acceleration
Understand the relationship between tensors, models, autograd, and optimizers
Prepare for PyTorch datasets, DataLoaders, and custom training loops

📖 Overview¶

PyTorch is an open-source Deep Learning framework widely used for:

Neural network development
Computer Vision
Natural Language Processing
Generative AI
Reinforcement Learning
Research
Production Machine Learning

The core PyTorch ecosystem can be viewed as:

PyTorch
   │
   ├── Tensors
   │
   ├── Autograd
   │
   ├── torch.nn
   │
   ├── Optimizers
   │
   ├── Data Utilities
   │
   ├── GPU / CUDA
   │
   └── Model Serialization

🧠 What Is PyTorch?¶

PyTorch is a tensor-based Deep Learning framework that provides:

Tensor Computation
+
Automatic Differentiation
+
Neural Network APIs
+
Optimization
+
GPU Acceleration
+
Data Loading

A typical PyTorch Deep Learning workflow is:

flowchart LR

    DATA["Data"]

    TENSOR["PyTorch Tensors"]

    MODEL["Neural Network"]

    LOSS["Loss"]

    AUTOGRAD["Autograd"]

    OPT["Optimizer"]

    UPDATE["Updated Parameters"]

    DATA --> TENSOR
    TENSOR --> MODEL
    MODEL --> LOSS
    LOSS --> AUTOGRAD
    AUTOGRAD --> OPT
    OPT --> UPDATE
    UPDATE --> MODEL

🧠 PyTorch vs TensorFlow¶

Both frameworks provide the fundamental capabilities required for Deep Learning.

Capability	PyTorch	TensorFlow
Tensor Operations	`torch.Tensor`	`tf.Tensor`
Neural Networks	`torch.nn`	`tf.keras`
Automatic Differentiation	`torch.autograd`	`tf.GradientTape`
Optimizers	`torch.optim`	`tf.keras.optimizers`
Data Pipeline	`Dataset` / `DataLoader`	`tf.data`
GPU	CUDA / device APIs	CUDA / device APIs
Model Definition	`nn.Module`	Keras Model
Training	Custom / higher-level tooling	`model.fit()` / custom
Ecosystem	PyTorch ecosystem	TensorFlow ecosystem

The important point is that both frameworks implement similar Deep Learning concepts using different APIs and abstractions.

🧠 The PyTorch Mental Model¶

A useful mental model is:

Tensor
  ↓
Model
  ↓
Prediction
  ↓
Loss
  ↓
Autograd
  ↓
Gradients
  ↓
Optimizer
  ↓
Parameter Update

This loop is repeated across batches and epochs.

🔢 What Is a PyTorch Tensor?¶

A PyTorch tensor is a multidimensional data structure used for numerical computation.

Examples:

Scalar
Vector
Matrix
3D Tensor
4D Tensor
5D Tensor

Deep Learning models operate primarily on tensors.

📐 Tensor Rank¶

Tensor rank represents the number of dimensions.

Rank 0 — Scalar¶

x = torch.tensor(5)

Conceptually:

Rank 1 — Vector¶

x = torch.tensor(
    [1, 2, 3]
)

Conceptually:

[1, 2, 3]

Rank 2 — Matrix¶

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

Conceptually:

[
    [1, 2],
    [3, 4]
]

Rank 3 Tensor¶

x = torch.tensor(
    [
        [
            [1, 2],
            [3, 4]
        ],
        [
            [5, 6],
            [7, 8]
        ]
    ]
)

🧠 Tensor Dimensions¶

A tensor can be represented as:

Shape
 ↓
(D1, D2, D3, ...)

For example:

(32, 224, 224, 3)

may represent:

Batch Size = 32
Height     = 224
Width      = 224
Channels   = 3

flowchart LR

    B["Batch<br>32"]

    H["Height<br>224"]

    W["Width<br>224"]

    C["Channels<br>3"]

    B --> H
    H --> W
    W --> C

🐍 Importing PyTorch¶

import torch

For neural networks:

import torch.nn as nn

For optimization:

import torch.optim as optim

🧪 Creating Tensors¶

From Python Lists¶

x = torch.tensor(
    [1, 2, 3]
)

Matrix¶

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

Random Tensor¶

x = torch.rand(
    3,
    4
)

Normal Distribution¶

x = torch.randn(
    3,
    4
)

Zeros¶

x = torch.zeros(
    3,
    4
)

Ones¶

x = torch.ones(
    3,
    4
)

Empty Tensor¶

x = torch.empty(
    3,
    4
)

empty() allocates memory without initializing the values to a meaningful default.

🧠 Tensor Creation Summary¶

Function	Purpose
`torch.tensor()`	Create from existing data
`torch.zeros()`	Create zeros
`torch.ones()`	Create ones
`torch.rand()`	Uniform random values
`torch.randn()`	Normal random values
`torch.empty()`	Uninitialized tensor
`torch.arange()`	Sequence of values
`torch.linspace()`	Evenly spaced values

🔢 `torch.arange()`¶

x = torch.arange(
    0,
    10
)

Result:

[0, 1, 2, ..., 9]

📏 `torch.linspace()`¶

x = torch.linspace(
    0,
    1,
    5
)

Conceptually:

[0.00, 0.25, 0.50, 0.75, 1.00]

🔍 Inspecting a Tensor¶

x = torch.randn(
    32,
    784
)

print(x)
print(x.shape)
print(x.ndim)
print(x.dtype)
print(x.device)

Typical information:

Shape
Number of Dimensions
Data Type
Device

🧠 Tensor Shape¶

For:

x = torch.randn(
    32,
    784
)

the shape is:

(32, 784)

This commonly means:

32 samples
784 features

🧠 Tensor `ndim`¶

x.ndim

returns the number of dimensions.

Example:

x = torch.randn(
    32,
    224,
    224,
    3
)

print(x.ndim)

Result:

🧠 Tensor Data Types¶

Common PyTorch data types include:

torch.float32
torch.float64
torch.float16
torch.bfloat16
torch.int32
torch.int64
torch.uint8
torch.bool

For many Deep Learning workloads:

float32

is a common default.

🔄 Converting Data Types¶

x = torch.tensor(
    [1, 2, 3]
)

x = x.float()

Or:

x = x.to(
    torch.float32
)

🧠 Why Data Type Matters¶

Data type affects:

Memory Usage
Computation Speed
Numerical Precision
GPU Performance

For example:

float32
   ↓
Higher Precision

float16 / bfloat16
   ↓
Lower Memory
Potentially Faster Training

Mixed precision is explored further in advanced training and optimization topics.

🔢 Tensor Indexing¶

x = torch.tensor(
    [
        [10, 20, 30],
        [40, 50, 60]
    ]
)

Access the first row:

x[0]

Access the first element:

x[0, 0]

Access the second row, third element:

x[1, 2]

✂️ Tensor Slicing¶

x[:, 0]

selects the first column.

x[0, :]

selects the first row.

x[:, 1:3]

selects columns 1 and 2.

🧮 Tensor Arithmetic¶

a = torch.tensor(
    [1, 2, 3]
)

b = torch.tensor(
    [4, 5, 6]
)

print(a + b)
print(a - b)
print(a * b)
print(a / b)

These operations are element-wise.

✖️ Matrix Multiplication¶

Matrix multiplication is fundamental to neural networks.

a = torch.tensor(
    [
        [1.0, 2.0],
        [3.0, 4.0]
    ]
)

b = torch.tensor(
    [
        [5.0, 6.0],
        [7.0, 8.0]
    ]
)

result = torch.matmul(
    a,
    b
)

You can also use:

result = a @ b

Mathematically:

[ C=AB ]

🧮 Dot Product¶

For vectors:

a = torch.tensor(
    [1.0, 2.0, 3.0]
)

b = torch.tensor(
    [4.0, 5.0, 6.0]
)

result = torch.dot(
    a,
    b
)

🔄 Reshaping¶

PyTorch provides:

reshape()

Example:

x = torch.arange(
    12
)

x = x.reshape(
    3,
    4
)

Result:

3 × 4

🧠 `view()`¶

view() can reshape tensors when the underlying memory layout permits it.

x = torch.arange(
    12
)

y = x.view(
    3,
    4
)

In modern PyTorch code, reshape() is often more convenient because it can handle non-contiguous tensors by creating a copy when necessary.

🔄 Flattening¶

x = torch.randn(
    32,
    28,
    28
)

flat = x.reshape(
    32,
    -1
)

The result is:

32 × 784

This is commonly used when transitioning from image feature maps to fully connected layers.

↔️ Transpose¶

x = torch.randn(
    3,
    4
)

y = x.T

For more general dimensions:

y = x.transpose(
    0,
    1
)

🧩 `permute()`¶

permute() changes the ordering of dimensions.

Example:

x = torch.randn(
    32,
    224,
    224,
    3
)

y = x.permute(
    0,
    3,
    1,
    2
)

Shape changes from:

Batch × Height × Width × Channels

to:

Batch × Channels × Height × Width

This is particularly important because many PyTorch vision layers commonly use channel-first tensor layouts.

🧠 Tensor Layout¶

A common PyTorch image tensor format is:

N × C × H × W

where:

N = Batch
C = Channels
H = Height
W = Width

For example:

32 × 3 × 224 × 224

🖼️ Image Tensor Pipeline¶

flowchart LR

    IMAGE["Image"]

    LOAD["Load"]

    TENSOR["Tensor"]

    FORMAT["N × C × H × W"]

    CNN["CNN"]

    IMAGE --> LOAD
    LOAD --> TENSOR
    TENSOR --> FORMAT
    FORMAT --> CNN

🔄 `unsqueeze()`¶

unsqueeze() adds a dimension.

x = torch.tensor(
    [1, 2, 3]
)

y = x.unsqueeze(
    0
)

Shape:

(3)

becomes:

(1, 3)

🔄 `squeeze()`¶

squeeze() removes dimensions of size 1.

x = torch.randn(
    1,
    3,
    1
)

y = x.squeeze()

🧠 Broadcasting¶

PyTorch supports broadcasting for compatible shapes.

x = torch.tensor(
    [
        [1.0, 2.0],
        [3.0, 4.0]
    ]
)

y = torch.tensor(
    [10.0, 20.0]
)

result = x + y

Conceptually:

[1, 2]    [10, 20]
[3, 4] +  [10, 20]

Result:

[11, 22]
[13, 24]

🧠 Tensor Reduction¶

Common reduction operations include:

x.mean()
x.sum()
x.max()
x.min()

Example:

x = torch.tensor(
    [1.0, 2.0, 3.0]
)

print(
    x.mean()
)

📊 Reduction Along a Dimension¶

x = torch.tensor(
    [
        [1.0, 2.0],
        [3.0, 4.0]
    ]
)

row_mean = x.mean(
    dim=1
)

column_mean = x.mean(
    dim=0
)

Understanding dimensions is critical when building neural networks.

🧠 Device Management¶

PyTorch tensors can live on different devices.

Common examples:

CPU
CUDA GPU
MPS

A tensor's device can be inspected using:

x.device

🖥️ CPU Tensor¶

x = torch.tensor(
    [1.0, 2.0, 3.0]
)

print(
    x.device
)

Typical result:

cpu

🚀 GPU Availability¶

For NVIDIA CUDA:

torch.cuda.is_available()

Example:

if torch.cuda.is_available():

    print(
        "CUDA GPU available"
    )

🧠 Selecting a Device¶

A common pattern is:

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

Then:

x = torch.randn(
    32,
    784
).to(device)

🧠 Device-Agnostic Code¶

A production-friendly approach is:

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

model = model.to(
    device
)

x = x.to(
    device
)

This allows the same code to run on:

GPU
or
CPU

without hardcoding one environment.

🧠 CPU → GPU¶

x = torch.randn(
    1000,
    1000
)

if torch.cuda.is_available():

    x = x.to(
        "cuda"
    )

🧠 GPU → CPU¶

x_cpu = x.to(
    "cpu"
)

When converting tensors to NumPy:

array = x_cpu.numpy()

For a GPU tensor:

array = x.detach().cpu().numpy()

⚠ Device Mismatch¶

Model and input tensors generally need to be on compatible devices.

Incorrect:

Model → GPU
Input → CPU

This can produce runtime errors.

Correct:

Model → GPU
Input → GPU

flowchart LR

    MODEL["Model"]

    INPUT["Input"]

    DEVICE["Same Device"]

    MODEL --> DEVICE
    INPUT --> DEVICE

🧠 GPU Memory¶

GPU memory is consumed by:

Model Parameters
+
Gradients
+
Optimizer State
+
Activations
+
Input Batches

Therefore, GPU memory usage can increase significantly with:

Larger Models
Larger Batch Sizes
Longer Sequences
Higher Resolution Images
Larger Activations

🧠 PyTorch Autograd¶

PyTorch provides automatic differentiation through:

torch.autograd

The key concept is:

requires_grad=True

Example:

x = torch.tensor(
    3.0,
    requires_grad=True
)

🧮 Automatic Differentiation¶

Suppose:

[ y=x^2 ]

Then:

[ \frac{dy}{dx}=2x ]

PyTorch can calculate this automatically.

🧪 Basic Autograd Example¶

import torch


x = torch.tensor(
    3.0,
    requires_grad=True
)

y = x ** 2

y.backward()

print(
    x.grad
)

Result:

🧠 Autograd Workflow¶

flowchart TD

    X["Input Tensor<br>requires_grad=True"]

    FORWARD["Forward Computation"]

    LOSS["Output / Loss"]

    BACK["backward()"]

    GRAD["Gradients"]

    X --> FORWARD
    FORWARD --> LOSS
    LOSS --> BACK
    BACK --> GRAD
    GRAD --> X

🧠 Computational Graph¶

PyTorch tracks operations involving tensors that require gradients.

For:

y = x * x

the computational graph conceptually becomes:

x
│
├── ×
│
└── x
    ↓
    y

During:

y.backward()

PyTorch traverses the graph backward to compute gradients.

🧠 Gradient Accumulation¶

PyTorch gradients accumulate by default.

Example:

x = torch.tensor(
    2.0,
    requires_grad=True
)

y = x ** 2

y.backward()

print(
    x.grad
)

If another backward pass is performed without clearing the gradient, the gradient can accumulate.

Therefore, training loops commonly reset gradients.

🧹 Clearing Gradients¶

With an optimizer:

optimizer.zero_grad()

Then:

loss.backward()

Then:

optimizer.step()

The standard sequence is:

zero_grad()
    ↓
forward
    ↓
loss
    ↓
backward()
    ↓
step()

🧠 PyTorch Neural Networks¶

PyTorch provides:

torch.nn

for neural network components.

Common modules include:

nn.Linear
nn.Conv2d
nn.ReLU
nn.Dropout
nn.BatchNorm2d
nn.MaxPool2d
nn.LSTM
nn.GRU
nn.Embedding

🧱 `nn.Module`¶

The fundamental abstraction for neural network models is:

nn.Module

A model generally:

class MyModel(
    nn.Module
):

🧪 Basic PyTorch Model¶

import torch
import torch.nn as nn


class SimpleNetwork(
    nn.Module
):

    def __init__(self):

        super().__init__()

        self.fc1 = nn.Linear(
            784,
            128
        )

        self.fc2 = nn.Linear(
            128,
            64
        )

        self.output = nn.Linear(
            64,
            10
        )

    def forward(
        self,
        x
    ):

        x = torch.relu(
            self.fc1(x)
        )

        x = torch.relu(
            self.fc2(x)
        )

        return self.output(x)

🧠 PyTorch Model Architecture¶

flowchart LR

    INPUT["784 Features"]

    FC1["Linear 128"]

    RELU1["ReLU"]

    FC2["Linear 64"]

    RELU2["ReLU"]

    OUT["Linear 10"]

    INPUT --> FC1
    FC1 --> RELU1
    RELU1 --> FC2
    FC2 --> RELU2
    RELU2 --> OUT

🧠 Why `nn.Module`?¶

nn.Module automatically manages:

Parameters
Child modules
Model hierarchy
Device movement
Training/inference modes
State dictionaries

For example:

model.parameters()

returns trainable parameters.

🔍 Inspecting Model Parameters¶

model = SimpleNetwork()

for name, parameter in model.named_parameters():

    print(
        name,
        parameter.shape
    )

Typical parameters include:

fc1.weight
fc1.bias
fc2.weight
fc2.bias
output.weight
output.bias

🧮 Parameter Count¶

For:

nn.Linear(784, 128)

the parameter count is:

[ 784\times128+128 ]

This includes:

Weights
+
Bias

🧠 `forward()`¶

The forward() method defines the forward computation.

Example:

def forward(
    self,
    x
):

    x = self.fc1(
        x
    )

    x = torch.relu(
        x
    )

    return self.output(
        x
    )

You normally invoke the model as:

output = model(
    x
)

rather than calling:

model.forward(x)

directly.

🧠 Model Call Flow¶

flowchart TD

    INPUT["Input"]

    MODEL["model(x)"]

    CALL["nn.Module Call"]

    FORWARD["forward(x)"]

    OUTPUT["Output"]

    INPUT --> MODEL
    MODEL --> CALL
    CALL --> FORWARD
    FORWARD --> OUTPUT

The nn.Module call mechanism also supports hooks and other framework behavior.

🧠 `nn.Linear`¶

The PyTorch equivalent of a fully connected layer is:

nn.Linear(
    in_features,
    out_features
)

Mathematically:

[ y=xW^T+b ]

Example:

layer = nn.Linear(
    784,
    128
)

🧠 Activation Functions¶

PyTorch provides activation functions such as:

nn.ReLU()
nn.Sigmoid()
nn.Tanh()
nn.GELU()
nn.Softmax()

Example:

self.relu = nn.ReLU()

or:

x = torch.relu(
    x
)

🧪 Using `nn.Sequential`¶

PyTorch also provides a convenient sequential model API.

model = nn.Sequential(

    nn.Linear(
        784,
        128
    ),

    nn.ReLU(),

    nn.Linear(
        128,
        64
    ),

    nn.ReLU(),

    nn.Linear(
        64,
        10
    )
)

This is conceptually similar to Keras Sequential.

🧠 Sequential vs Custom `nn.Module`¶

Approach	Best Use
`nn.Sequential`	Simple linear stacks
Custom `nn.Module`	Complex architectures
Functional Tensor Operations	Specialized computations

For architectures involving:

Branches
Skip Connections
Multiple Inputs
Multiple Outputs
Custom Logic

a custom nn.Module is generally more appropriate.

🧠 Training Mode and Evaluation Mode¶

PyTorch models have two important modes:

model.train()

and:

model.eval()

Training mode enables training-specific behavior such as:

Dropout
Batch Normalization behavior

Evaluation mode switches the model to inference behavior.

🧪 Training Mode¶

model.train()

predictions = model(
    x
)

🧪 Evaluation Mode¶

model.eval()

with torch.no_grad():

    predictions = model(
        x
    )

🧠 `torch.no_grad()`¶

During inference, gradients are generally unnecessary.

with torch.no_grad():

    output = model(
        x
    )

This reduces unnecessary autograd tracking and can lower memory usage.

🧠 Training vs Inference¶

flowchart LR

    TRAIN["Training"]

    TRAIN --> MODE1["model.train()"]
    MODE1 --> FORWARD1["Forward"]
    FORWARD1 --> LOSS["Loss"]
    LOSS --> BACK["Backward"]
    BACK --> UPDATE["Optimizer Step"]

    INFER["Inference"]

    INFER --> MODE2["model.eval()"]
    MODE2 --> NOGRAD["torch.no_grad()"]
    NOGRAD --> FORWARD2["Forward"]
    FORWARD2 --> OUTPUT["Prediction"]

🧠 PyTorch Training Workflow¶

The fundamental training loop is:

for x_batch, y_batch in train_loader:

    optimizer.zero_grad()

    predictions = model(
        x_batch
    )

    loss = loss_fn(
        predictions,
        y_batch
    )

    loss.backward()

    optimizer.step()

The workflow is:

Zero Gradients
      ↓
Forward Pass
      ↓
Calculate Loss
      ↓
Backward Pass
      ↓
Update Parameters

🧠 PyTorch Training Loop Architecture¶

flowchart TD

    DATA["DataLoader"]

    BATCH["Batch"]

    ZERO["optimizer.zero_grad()"]

    FORWARD["model(x)"]

    LOSS["loss_fn()"]

    BACKWARD["loss.backward()"]

    STEP["optimizer.step()"]

    DATA --> BATCH
    BATCH --> ZERO
    ZERO --> FORWARD
    FORWARD --> LOSS
    LOSS --> BACKWARD
    BACKWARD --> STEP
    STEP --> BATCH

🧠 Loss Functions¶

PyTorch provides many loss functions.

Common examples:

nn.MSELoss()
nn.L1Loss()
nn.CrossEntropyLoss()
nn.BCEWithLogitsLoss()

Example:

loss_fn = nn.CrossEntropyLoss()

🧠 Optimizers¶

PyTorch provides:

torch.optim

Common optimizers include:

SGD
Adam
AdamW
RMSprop

Example:

optimizer = torch.optim.AdamW(
    model.parameters(),
    lr=0.001
)

🧠 Optimizer Workflow¶

flowchart LR

    MODEL["Model"]

    PRED["Prediction"]

    LOSS["Loss"]

    GRAD["Gradients"]

    OPT["Optimizer"]

    UPDATE["Updated Parameters"]

    MODEL --> PRED
    PRED --> LOSS
    LOSS --> GRAD
    GRAD --> OPT
    OPT --> UPDATE
    UPDATE --> MODEL

🧪 Complete PyTorch Classification Example¶

import torch
import torch.nn as nn


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


class Classifier(
    nn.Module
):

    def __init__(self):

        super().__init__()

        self.network = nn.Sequential(

            nn.Linear(
                784,
                128
            ),

            nn.ReLU(),

            nn.Linear(
                128,
                64
            ),

            nn.ReLU(),

            nn.Linear(
                64,
                10
            )
        )

    def forward(
        self,
        x
    ):

        return self.network(
            x
        )


model = Classifier().to(
    device
)


loss_fn = nn.CrossEntropyLoss()


optimizer = torch.optim.AdamW(
    model.parameters(),
    lr=0.001
)

Training:

for epoch in range(
    10
):

    model.train()

    for x_batch, y_batch in train_loader:

        x_batch = x_batch.to(
            device
        )

        y_batch = y_batch.to(
            device
        )

        optimizer.zero_grad()

        predictions = model(
            x_batch
        )

        loss = loss_fn(
            predictions,
            y_batch
        )

        loss.backward()

        optimizer.step()

🧠 Why `CrossEntropyLoss` Expects Logits¶

For multi-class classification, the model commonly returns raw logits:

outputs = model(
    x
)

The final layer is usually:

nn.Linear(
    64,
    10
)

without explicitly applying:

Softmax

when using:

nn.CrossEntropyLoss()

CrossEntropyLoss internally combines the required log-softmax and negative log-likelihood behavior.

Therefore:

Model
 ↓
Raw Logits
 ↓
CrossEntropyLoss

is the common PyTorch pattern.

🧠 PyTorch Classification Architecture¶

flowchart LR

    INPUT["Input"]

    FC1["Linear"]

    RELU1["ReLU"]

    FC2["Linear"]

    RELU2["ReLU"]

    LOGITS["Class Logits"]

    LOSS["CrossEntropyLoss"]

    INPUT --> FC1
    FC1 --> RELU1
    RELU1 --> FC2
    FC2 --> RELU2
    RELU2 --> LOGITS
    LOGITS --> LOSS

🧪 PyTorch Regression Example¶

class RegressionModel(
    nn.Module
):

    def __init__(self):

        super().__init__()

        self.network = nn.Sequential(

            nn.Linear(
                10,
                64
            ),

            nn.ReLU(),

            nn.Linear(
                64,
                32
            ),

            nn.ReLU(),

            nn.Linear(
                32,
                1
            )
        )

    def forward(
        self,
        x
    ):

        return self.network(
            x
        )

Loss:

loss_fn = nn.MSELoss()

Optimizer:

optimizer = torch.optim.AdamW(
    model.parameters(),
    lr=0.001
)

🧠 Classification vs Regression¶

Problem	Output	Typical Loss
Binary Classification	Logit / Sigmoid interpretation	`BCEWithLogitsLoss`
Multi-Class Classification	Class Logits	`CrossEntropyLoss`
Regression	Continuous Value	`MSELoss` / `L1Loss`

🧠 PyTorch Parameters¶

Parameters are represented by:

nn.Parameter

They are tensors that PyTorch tracks as trainable model parameters.

Example:

self.weight = nn.Parameter(
    torch.randn(
        10,
        5
    )
)

🧠 Parameter Registration¶

When layers are assigned as attributes of an nn.Module:

self.fc = nn.Linear(
    10,
    5
)

PyTorch automatically registers the layer and its parameters.

This allows:

model.parameters()

to discover them.

🧠 `state_dict()`¶

A PyTorch model's parameters and persistent buffers can be accessed through:

model.state_dict()

Example:

state = model.state_dict()

for key, value in state.items():

    print(
        key,
        value.shape
    )

💾 Saving Model Weights¶

A common approach is:

torch.save(
    model.state_dict(),
    "model.pth"
)

Load:

model.load_state_dict(
    torch.load(
        "model.pth",
        weights_only=True
    )
)

The exact loading approach can depend on the PyTorch version and whether the artifact contains weights, a checkpoint, or another object.

🧠 Model Checkpoint¶

A production checkpoint may contain more than model weights.

For example:

checkpoint = {

    "model_state_dict":
        model.state_dict(),

    "optimizer_state_dict":
        optimizer.state_dict(),

    "epoch":
        epoch,

    "loss":
        loss
}

Save:

torch.save(
    checkpoint,
    "checkpoint.pth"
)

This allows training to resume more completely.

🧠 Checkpoint Architecture¶

flowchart TD

    TRAIN["Training"]

    MODEL["Model State"]

    OPT["Optimizer State"]

    META["Training Metadata"]

    CHECK["Checkpoint"]

    TRAIN --> MODEL
    TRAIN --> OPT
    TRAIN --> META

    MODEL --> CHECK
    OPT --> CHECK
    META --> CHECK

    CHECK --> RESUME["Resume Training"]

🧠 PyTorch Device + Model¶

A common production pattern:

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

model = model.to(
    device
)

For each batch:

x_batch = x_batch.to(
    device
)

y_batch = y_batch.to(
    device
)

🧠 GPU Training Architecture¶

flowchart LR

    DATA["CPU Dataset"]

    LOADER["DataLoader"]

    CPU_BATCH["CPU Batch"]

    GPU["GPU"]

    MODEL["PyTorch Model"]

    GRAD["Gradients"]

    UPDATE["Parameter Update"]

    DATA --> LOADER
    LOADER --> CPU_BATCH
    CPU_BATCH --> GPU
    GPU --> MODEL
    MODEL --> GRAD
    GRAD --> UPDATE
    UPDATE --> MODEL

⚡ CUDA Device Selection¶

For multiple GPUs:

device = torch.device(
    "cuda:0"
)

Check GPU count:

torch.cuda.device_count()

Get device name:

torch.cuda.get_device_name(
    0
)

🧠 CUDA Memory¶

Useful information:

torch.cuda.memory_allocated()

and:

torch.cuda.memory_reserved()

These help diagnose GPU memory consumption.

🧠 CPU ↔ GPU Data Movement¶

Moving data between devices has a cost.

CPU Memory
    │
    │ Data Transfer
    ▼
GPU Memory

Therefore, efficient Deep Learning systems try to avoid unnecessary transfers.

⚠ Common Device Mistake¶

Avoid repeatedly moving tensors:

for batch in data:

    x = x.to(
        device
    )

    # unnecessary repeated transfers

Instead, structure the pipeline so that device movement occurs at a predictable point.

When converting data from NumPy:

x = torch.from_numpy(
    numpy_array
)

PyTorch may share the underlying memory with the NumPy array.

This differs from:

torch.tensor(
    numpy_array
)

which generally creates a new tensor and copies the data.

This distinction can matter for performance and mutation behavior.

🧠 Detaching Tensors¶

If a tensor is part of an autograd graph:

x.detach()

creates a tensor that does not require gradient tracking through that history.

Example:

prediction = model(
    x
)

prediction_cpu = (
    prediction
    .detach()
    .cpu()
)

🧠 NumPy Conversion¶

For tensors that do not require gradients:

array = tensor.numpy()

For tensors that require gradients:

array = (
    tensor
    .detach()
    .cpu()
    .numpy()
)

🧠 `detach()` Mental Model¶

flowchart LR

    TENSOR["Tensor"]

    GRAPH["Autograd Graph"]

    DETACH["detach()"]

    OUTPUT["Detached Tensor"]

    TENSOR --> GRAPH
    GRAPH --> DETACH
    DETACH --> OUTPUT

🧠 `torch.no_grad()` vs `detach()`¶

These are related but serve different purposes.

`torch.no_grad()`¶

Disables gradient tracking for operations inside the context.

with torch.no_grad():

    output = model(
        x
    )

`detach()`¶

Creates a tensor disconnected from the current autograd graph.

output = prediction.detach()

🧠 `inference_mode()`¶

For inference workloads, PyTorch also provides:

with torch.inference_mode():

    output = model(
        x
    )

This can provide additional performance benefits compared with ordinary no_grad() in appropriate inference scenarios.

🧠 PyTorch Model Lifecycle¶

A typical workflow is:

flowchart LR

    DATA["Dataset"]

    TENSOR["Tensor"]

    MODEL["nn.Module"]

    COMPILE["Configure Loss + Optimizer"]

    TRAIN["Training"]

    CHECKPOINT["Checkpoint"]

    EVAL["Evaluation"]

    DEPLOY["Deployment"]

    DATA --> TENSOR
    TENSOR --> MODEL
    MODEL --> COMPILE
    COMPILE --> TRAIN
    TRAIN --> CHECKPOINT
    CHECKPOINT --> EVAL
    EVAL --> DEPLOY

🧠 PyTorch vs Keras Mental Mapping¶

Concept	Keras / TensorFlow	PyTorch
Tensor	`tf.Tensor`	`torch.Tensor`
Layer	`tf.keras.layers.Layer`	`nn.Module`
Model	`tf.keras.Model`	`nn.Module`
Dense	`Dense`	`nn.Linear`
Conv2D	`Conv2D`	`nn.Conv2d`
ReLU	`ReLU`	`nn.ReLU`
Gradient	`GradientTape`	Autograd
Optimizer	`tf.keras.optimizers`	`torch.optim`
Dataset Pipeline	`tf.data`	`Dataset` / `DataLoader`
Training	`model.fit()`	Training loop
Evaluation Mode	`training=False`	`model.eval()`
No Gradients	Context / inference logic	`torch.no_grad()` / `inference_mode()`
Save Model	`.keras` / SavedModel workflows	`state_dict()` / checkpoints

🧠 The Core PyTorch Training Equation¶

The fundamental parameter update is:

[ \theta_{t+1} = \theta_t - \eta \nabla_\theta L ]

Where:

θ  = Model Parameters
η  = Learning Rate
L  = Loss
∇θL = Gradient

The PyTorch training loop implements this concept through:

loss.backward()
        ↓
Gradients
        ↓
optimizer.step()
        ↓
Updated Parameters

🏢 Enterprise Perspective¶

PyTorch should not be viewed only as a model-building library.

In production, it is one component of a larger Deep Learning platform:

Data Sources
     ↓
Data Pipeline
     ↓
Dataset / DataLoader
     ↓
PyTorch Model
     ↓
Training Infrastructure
     ↓
GPU / Accelerator
     ↓
Checkpoint
     ↓
Model Validation
     ↓
Model Registry
     ↓
Serving
     ↓
Monitoring

Production concerns include:

Dataset versioning
Reproducibility
Configuration management
GPU utilization
Checkpointing
Model versioning
Experiment tracking
Model validation
Deployment
Monitoring
Security
Cost management

Production Insight

PyTorch gives you significant control over the Deep Learning execution model.

That flexibility is powerful, but it also means the engineering team must explicitly manage:

Device Placement
+
Memory
+
Gradient Lifecycle
+
Checkpointing
+
Training State
+
Reproducibility

A model that trains successfully on a developer laptop is not automatically production-ready.

⚠ Common Mistakes¶

Avoid these common PyTorch mistakes:

Mixing CPU and GPU tensors
Forgetting to move the model to the target device
Forgetting to move input batches to the target device
Forgetting optimizer.zero_grad()
Calling backward() without understanding gradient accumulation
Forgetting model.train() during training
Forgetting model.eval() during evaluation
Calculating inference with unnecessary gradient tracking
Using an inappropriate output activation with a chosen loss function
Applying Softmax before CrossEntropyLoss unnecessarily
Ignoring tensor shape conventions
Confusing view() and reshape()
Misusing squeeze() and accidentally removing meaningful dimensions
Using incorrect permute() ordering
Performing unnecessary CPU/GPU transfers
Converting GPU tensors directly to NumPy
Failing to detach tensors before converting them for logging
Saving only partial training state when resuming is required
Ignoring GPU memory consumption
Using unnecessarily large batch sizes
Creating tensors on the wrong device inside the model

🧠 Interview Questions¶

Beginner¶

1. What is PyTorch?¶

PyTorch is a Deep Learning framework providing tensor computation, automatic differentiation, neural network abstractions, optimization, and hardware acceleration.

2. What is a tensor?¶

A tensor is a multidimensional numerical data structure used as the fundamental data representation in PyTorch.

3. What is `nn.Module`?¶

nn.Module is the base class used to define neural network models and reusable neural network components in PyTorch.

4. What does `forward()` do?¶

It defines how input data flows through a PyTorch model.

5. What is `requires_grad=True`?¶

It tells PyTorch to track operations involving the tensor so gradients can be computed through autograd.

Intermediate¶

6. What is autograd?¶

PyTorch's automatic differentiation system that records differentiable operations and computes gradients during backward propagation.

7. What is the standard PyTorch training loop?¶

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

8. Why call `optimizer.zero_grad()`?¶

Because PyTorch gradients accumulate by default. Existing gradients need to be cleared before computing the next update.

9. What is the difference between `model.train()` and `model.eval()`?¶

They switch the model between training and evaluation behavior, which affects layers such as Dropout and Batch Normalization.

10. Why use `torch.no_grad()` during inference?¶

It disables gradient tracking for the enclosed operations, reducing unnecessary computation and memory usage.

11. What is `state_dict()`?¶

It provides the model's parameters and persistent buffers in a dictionary-like structure that is commonly used for saving and loading model state.

12. Why use `DataLoader`?¶

DataLoader provides batching, iteration, shuffling, and other mechanisms for efficiently feeding data into a training loop. Its details are covered in the next chapter.

Advanced¶

13. Why does PyTorch use `nn.Module` for both layers and models?¶

Because complex neural networks can be composed hierarchically from reusable modules. This allows PyTorch to recursively track parameters and submodules.

14. Why are model and tensors required to be on compatible devices?¶

Operations generally require tensors participating in the same computation to reside on compatible devices.

15. Why does `CrossEntropyLoss` typically receive raw logits?¶

PyTorch's CrossEntropyLoss combines the relevant log-softmax and negative-log-likelihood computation internally, so an explicit Softmax layer is normally unnecessary before it.

16. What is the difference between `detach()` and `torch.no_grad()`?¶

detach() disconnects a tensor from its existing autograd history. torch.no_grad() disables gradient tracking for operations executed inside its context.

17. Why can `view()` fail when `reshape()` works?¶

view() requires a compatible memory layout, while reshape() can create a copy when necessary.

18. Why is `permute()` important in Computer Vision?¶

Different frameworks and operations expect different dimension orders. PyTorch vision models commonly use:

N × C × H × W

so tensors may need to be permuted into that format.

19. What consumes GPU memory during training?¶

Typically:

Parameters
+
Gradients
+
Optimizer State
+
Activations
+
Input Batches

20. How would you design production PyTorch training?¶

Separate:

Dataset
DataLoader
Model
Loss
Optimizer
Training Loop
Evaluation
Checkpointing
Configuration
Logging

and make device placement, reproducibility, checkpointing, and monitoring explicit.

🧪 Practical Exercises¶

Exercise 1 — Tensor Fundamentals¶

Create:

Scalar
Vector
Matrix
3D Tensor
4D Tensor

For each tensor print:

Value
Shape
Rank
Data Type
Device

Exercise 2 — Tensor Operations¶

Implement:

Addition
Subtraction
Multiplication
Matrix Multiplication
Reshape
Transpose
Permute
Squeeze
Unsqueeze
Mean
Sum

Verify the resulting shapes.

Exercise 3 — Autograd¶

Create:

x = torch.tensor(
    3.0,
    requires_grad=True
)

Calculate:

[ y=x^3+2x2+x ]

and use:

y.backward()

to calculate the gradient.

Exercise 4 — Build a Classification Model¶

Create:

Input
 ↓
Linear
 ↓
ReLU
 ↓
Linear
 ↓
ReLU
 ↓
Linear
 ↓
Class Logits

Use:

nn.CrossEntropyLoss()

for training.

Exercise 5 — Build a Regression Model¶

Create:

Input
 ↓
Linear
 ↓
ReLU
 ↓
Linear
 ↓
Regression Output

Use:

nn.MSELoss()

and:

AdamW

for optimization.

Exercise 6 — CPU vs GPU¶

Detect:

torch.cuda.is_available()

Train the same model using:

CPU
GPU

Compare:

Training Time
Throughput
Memory Usage

Exercise 7 — Model Checkpointing¶

Save:

Model State
Optimizer State
Epoch
Training Loss

Create a checkpoint and resume training from it.

Exercise 8 — Tensor Layout¶

Create an image batch in:

N × H × W × C

and convert it to:

N × C × H × W

using:

permute()

Verify the resulting shape.

📌 Key Takeaways¶

PyTorch is a tensor-based Deep Learning framework.
Tensors are the fundamental data structure in PyTorch.
Tensor rank represents the number of dimensions.
Tensor shape describes the size of each dimension.
Tensor data types affect memory, precision, and performance.
PyTorch supports CPU and accelerator-based tensor computation.
Device management is critical when using GPUs.
torch.autograd provides automatic differentiation.
requires_grad=True enables gradient tracking for tensors.
backward() computes gradients through the autograd graph.
PyTorch gradients accumulate by default.
optimizer.zero_grad() clears previous gradients.
optimizer.step() updates model parameters.
nn.Module is the fundamental abstraction for PyTorch neural networks.
forward() defines the model's forward computation.
nn.Linear represents a fully connected layer.
nn.Sequential is useful for simple linear architectures.
Complex architectures should generally use custom nn.Module implementations.
model.train() enables training behavior.
model.eval() enables evaluation behavior.
torch.no_grad() and torch.inference_mode() help avoid unnecessary gradient tracking during inference.
state_dict() is commonly used for model state serialization.
Efficient GPU training requires careful management of device placement and memory.
PyTorch gives developers significant control over the training process.
That flexibility also creates greater responsibility for training infrastructure, reproducibility, checkpointing, and production reliability.

📚 Further Reading¶

Continue with:

The next chapter goes deeper into PyTorch Autograd, Dataset, and DataLoader, connecting tensor computation with efficient real-world data pipelines and training workflows.

➡️ Next Chapter¶

17. PyTorch Autograd, Dataset and DataLoader

Enterprise AI Engineering Handbook
Building Production-Grade Enterprise AI Systems — One Chapter at a Time.

16. PyTorch Fundamentals and Tensors¶

🎯 Learning Objectives¶

📖 Overview¶

🧠 What Is PyTorch?¶

🧠 PyTorch vs TensorFlow¶

🧠 The PyTorch Mental Model¶

🔢 What Is a PyTorch Tensor?¶

📐 Tensor Rank¶

Rank 0 — Scalar¶

Rank 1 — Vector¶

Rank 2 — Matrix¶

Rank 3 Tensor¶

🧠 Tensor Dimensions¶

🐍 Importing PyTorch¶

🧪 Creating Tensors¶

From Python Lists¶

Matrix¶

Random Tensor¶

Normal Distribution¶

Zeros¶

Ones¶

Empty Tensor¶

🧠 Tensor Creation Summary¶

🔢 torch.arange()¶

📏 torch.linspace()¶

🔍 Inspecting a Tensor¶

🧠 Tensor Shape¶

🧠 Tensor ndim¶

🧠 Tensor Data Types¶

🔄 Converting Data Types¶

🧠 Why Data Type Matters¶

🔢 Tensor Indexing¶

✂️ Tensor Slicing¶

🧮 Tensor Arithmetic¶

✖️ Matrix Multiplication¶

🧮 Dot Product¶

🔄 Reshaping¶

🧠 view()¶

🔄 Flattening¶

↔️ Transpose¶

🧩 permute()¶

🧠 Tensor Layout¶

🖼️ Image Tensor Pipeline¶

🔄 unsqueeze()¶

🔄 squeeze()¶

🧠 Broadcasting¶

🧠 Tensor Reduction¶

📊 Reduction Along a Dimension¶

🧠 Device Management¶

🖥️ CPU Tensor¶

🚀 GPU Availability¶

🧠 Selecting a Device¶

🧠 Device-Agnostic Code¶

🧠 CPU → GPU¶

🧠 GPU → CPU¶

⚠ Device Mismatch¶

🧠 GPU Memory¶

🧠 PyTorch Autograd¶

🧮 Automatic Differentiation¶

🧪 Basic Autograd Example¶

🧠 Autograd Workflow¶

🧠 Computational Graph¶

🧠 Gradient Accumulation¶

🧹 Clearing Gradients¶

🧠 PyTorch Neural Networks¶

🧱 nn.Module¶

🧪 Basic PyTorch Model¶

🧠 PyTorch Model Architecture¶

🧠 Why nn.Module?¶

🔍 Inspecting Model Parameters¶

🧮 Parameter Count¶

🧠 forward()¶

🧠 Model Call Flow¶

🧠 nn.Linear¶

🧠 Activation Functions¶

🧪 Using nn.Sequential¶

🧠 Sequential vs Custom nn.Module¶

🧠 Training Mode and Evaluation Mode¶

🧪 Training Mode¶

🧪 Evaluation Mode¶

🔢 `torch.arange()`¶

📏 `torch.linspace()`¶

🧠 Tensor `ndim`¶

🧠 `view()`¶

🧩 `permute()`¶

🔄 `unsqueeze()`¶

🔄 `squeeze()`¶

🧱 `nn.Module`¶

🧠 Why `nn.Module`?¶

🧠 `forward()`¶

🧠 `nn.Linear`¶

🧪 Using `nn.Sequential`¶

🧠 Sequential vs Custom `nn.Module`¶

🧠 `torch.no_grad()`¶

🧠 Why `CrossEntropyLoss` Expects Logits¶

🧠 `state_dict()`¶

🧠 `detach()` Mental Model¶

🧠 `torch.no_grad()` vs `detach()`¶

`torch.no_grad()`¶

`detach()`¶

🧠 `inference_mode()`¶

3. What is `nn.Module`?¶

4. What does `forward()` do?¶

5. What is `requires_grad=True`?¶

8. Why call `optimizer.zero_grad()`?¶

9. What is the difference between `model.train()` and `model.eval()`?¶

10. Why use `torch.no_grad()` during inference?¶

11. What is `state_dict()`?¶

12. Why use `DataLoader`?¶

13. Why does PyTorch use `nn.Module` for both layers and models?¶

15. Why does `CrossEntropyLoss` typically receive raw logits?¶

16. What is the difference between `detach()` and `torch.no_grad()`?¶

17. Why can `view()` fail when `reshape()` works?¶

18. Why is `permute()` important in Computer Vision?¶