This article primarily discussed on importance of broadcasting and its easy of implementation using tensors.

Tensor Flow Basics Part-2

Tensor data types

Data Type	Python Type	Description
DT_FLOAT	tf.float32	32 bits floating point.
DT_DOUBLE	tf.float64	64 bits floating point.
DT_INT8	tf.int8	8 bits signed integer.
DT_INT16	tf.int16	16 bits signed integer.
DT_INT32	tf.int32	32 bits signed integer.
DT_INT64	tf.int64	64 bits signed integer.
DT_UINT8	tf.uint8	8 bits unsigned integer.
DT_STRING	tf.string	Variable length byte arrays. Each element of a tensor is a byte array.
DT_BOOL	tf.bool	Boolean.

import tensorflow as tf
print(tf.__version__)

2.15.0

x_new = tf.constant(1,shape=(2,3),dtype=tf.int8)

y_new = tf.constant(2,shape=(2,3),dtype=tf.int8)

Re-cap Operations

Element Wise Operations
Matrix Multiplicaitons

print("Addition:\n", tf.add(x_new,y_new))
print(" ")
print(" ")

print("Subtraction:\n", tf.subtract(x_new,y_new))
print(" ")
print(" ")

Addition:
 tf.Tensor(
[[3 3 3]
 [3 3 3]], shape=(2, 3), dtype=int8)
 
 
Subtraction:
 tf.Tensor(
[[-1 -1 -1]
 [-1 -1 -1]], shape=(2, 3), dtype=int8)

print("Multiplication:\n", tf.multiply(tf.random.normal(shape=(2,3)),tf.random.normal(shape=(2,3))))

Multiplication:
 tf.Tensor(
[[-0.5718114  -0.18780218 -2.0768495 ]
 [ 0.29304612  0.08317164 -1.3320862 ]], shape=(2, 3), dtype=float32)

print("Matrix Multiplication:\n", tf.matmul(tf.random.normal(shape=(2,3)),tf.random.normal(shape=(3,2))))
print(" ")
print(" ")

print("Matrix Multiplication:\n", tf.matmul(tf.random.normal(shape=(2,3)),tf.random.normal(shape=(3,1))))

Matrix Multiplication:
 tf.Tensor(
[[-1.6848389  -0.44041786]
 [-0.9548799  -0.22109865]], shape=(2, 2), dtype=float32)
 
 
Matrix Multiplication:
 tf.Tensor(
[[ 0.37789747]
 [-0.12570143]], shape=(2, 1), dtype=float32)

Broadcasting

Broadcasting is useful when the dimensions of matrices are different from each other. This is highly useful to add and subtract the matrices of different lengths.

Here’s a brief summary of how broadcasting works for addition and subtraction:

Addition: If the shapes of the two tensors are different, TensorFlow compares their shapes element-wise, starting from the trailing dimensions. If the dimensions are compatible or one of the dimensions is 1, broadcasting can occur. For example, you can add a scalar to a matrix, and the scalar value will be added to every element of the matrix.

Subtraction: Similar to addition, broadcasting allows you to subtract a scalar or a vector from a matrix, or subtract matrices of different shapes.

x1 = tf.random.normal(shape=(2,3))

x2 = tf.random.normal(shape=(2,1))

print("x1:\n",x1)
print(" ")
print(" ")
print("x2:\n",x2)

x1:
 tf.Tensor(
[[ 0.39297998 -0.12811422 -0.60474324]
 [ 0.30773026  1.4076523  -0.57274765]], shape=(2, 3), dtype=float32)
 
 
x2:
 tf.Tensor(
[[0.10113019]
 [1.0277312 ]], shape=(2, 1), dtype=float32)

tf.broadcast_to(x2, [2, 3])   ### Broadcasting internally

<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[0.10113019, 0.10113019, 0.10113019],
       [1.0277312 , 1.0277312 , 1.0277312 ]], dtype=float32)>

tf.add(x1,x2)

<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[ 0.49411017, -0.02698404, -0.50361305],
       [ 1.3354614 ,  2.4353833 ,  0.45498353]], dtype=float32)>

tf.subtract(x1,x2)

<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[ 0.2918498 , -0.22924441, -0.7058734 ],
       [-0.7200009 ,  0.37992108, -1.6004789 ]], dtype=float32)>

In the above examples we have seen that broadcasting of same tensor dimension i.e.; of two dimensional.

Below, we will see the beauty of broadcasting of different dimensions.

x3 = tf.random.normal(shape=(2, 2, 2)) #3d tensor
x4 = tf.random.normal(shape=(2, 1)) #2d tensor

tf.add(x3,x4)

<tf.Tensor: shape=(2, 2, 2), dtype=float32, numpy=
array([[[-1.0228443 ,  0.34588122],
        [ 2.188323  , -0.7523911 ]],

       [[-0.56017506, -1.5636952 ],
        [ 1.572252  ,  1.6189265 ]]], dtype=float32)>

tf.broadcast_to(x4, [2,2,2])   ### Broadcasting internally

<tf.Tensor: shape=(2, 2, 2), dtype=float32, numpy=
array([[[-0.66719866, -0.66719866],
        [ 0.92839885,  0.92839885]],

       [[-0.66719866, -0.66719866],
        [ 0.92839885,  0.92839885]]], dtype=float32)>