Chapter 6: Tensor Indexing & Reshaping¶

“Tensors may be infinite in dimension, but mastery begins with the first slice.”

6.1 Why Indexing & Reshaping Matter¶

Before you train a single model, you’ll spend a good chunk of time doing this:

Selecting rows, columns, or channels
Flattening or expanding shapes
Swapping axes
Prepping tensors for layers like Dense, Conv2D, or RNN

Think of this as data martial arts—getting your tensors into the right stance before the real fight begins.

6.2 Basic Indexing (Rank 1 and 2)¶

import tensorflow as tf

# Rank 1 (vector)
vec = tf.constant([10, 20, 30, 40])
print(vec[0])     # 10
print(vec[-1])    # 40

# Rank 2 (matrix)
mat = tf.constant([[1, 2], [3, 4], [5, 6]])
print(mat[1])        # [3, 4]
print(mat[1, 0])     # 3

Slicing also works:

print(mat[:, 0])     # First column: [1, 3, 5]
print(mat[0:2, :])   # First two rows: [[1, 2], [3, 4]]

6.3 Reshaping Tensors¶

tf.reshape() lets you change a tensor’s shape without changing its data:

x = tf.constant([[1, 2, 3], [4, 5, 6]])  # Shape: (2, 3)
reshaped = tf.reshape(x, [3, 2])         # Shape: (3, 2)
print(reshaped)

You can also flatten:

flat = tf.reshape(x, [-1])  # Automatically infer length
print(flat)  # [1, 2, 3, 4, 5, 6]

6.4 Expanding and Squeezing Dimensions¶

These are crucial when batching data or feeding into specific layer shapes:

x = tf.constant([1, 2, 3])  # Shape: (3,)

# Expand
x_expanded = tf.expand_dims(x, axis=0)  # Shape: (1, 3)
x_expanded2 = tf.expand_dims(x, axis=1) # Shape: (3, 1)

# Squeeze
x_squeezed = tf.squeeze(tf.constant([[1], [2], [3]]))  # Shape: (3,)

Use cases:

expand_dims → simulate a batch: [3] → [1, 3]
squeeze → remove unnecessary dimensions (e.g. from model outputs)

6.5 Transposing and Permuting Axes¶

You can swap dimensions using tf.transpose():

x = tf.constant([[1, 2, 3], [4, 5, 6]])  # Shape: (2, 3)
print(tf.transpose(x))  # Shape: (3, 2)

For higher-rank tensors, use perm:

x = tf.random.normal([2, 3, 4])
x_transposed = tf.transpose(x, perm=[0, 2, 1])  # Swaps last two dims

6.6 Tensor Shape Tricks You’ll Actually Use¶

Goal	Command
Flatten a tensor	tf.reshape(tensor, [-1])
Add batch dimension	tf.expand_dims(tensor, axis=0)
Remove singleton dims	tf.squeeze(tensor)
Change channel-last to first	tf.transpose(tensor, [0, 3, 1, 2])
Recover original shape	tf.reshape(tensor, orig_shape)

6.7 Summary¶

Indexing lets you extract elements, rows, columns, or slices from tensors of any rank.
tf.reshape() allows you to safely change tensor shapes—crucial before feeding into models.
expand_dims() and squeeze() help manage batch dimensions and singleton axes.
transpose() and perm are useful for rearranging axes, especially in image and sequence data.
Shape manipulation is not just a utility—it’s how you adapt data to flow through deep learning systems.

“Tensors may be infinite in dimension, but mastery begins with the first slice.”