Tensor math operations in TensorFlow - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a tensor in TensorFlow?

A tensor is a multi-dimensional array used to represent data in TensorFlow. It can have any number of dimensions, like scalars (0D), vectors (1D), matrices (2D), or higher.

beginner

How do you add two tensors in TensorFlow?

You can add two tensors using tf.add(tensor1, tensor2) or simply using the + operator if tensors have the same shape.

intermediate

What does broadcasting mean in tensor operations?

Broadcasting lets TensorFlow automatically expand smaller tensors to match the shape of larger tensors during math operations, so you don't have to manually reshape them.

beginner

How do you multiply two tensors element-wise in TensorFlow?

Use tf.multiply(tensor1, tensor2) or the * operator to multiply tensors element by element, assuming they have compatible shapes.

intermediate

What function computes the dot product of two tensors in TensorFlow?

Use tf.tensordot(tensor1, tensor2, axes) to compute the dot product along specified axes. For matrix multiplication, tf.matmul is commonly used.

Which TensorFlow function adds two tensors element-wise?

A tf.add()

B tf.matmul()

C tf.multiply()

D tf.reshape()

tf.add() adds two tensors element-wise.

What happens if you add tensors of different shapes without broadcasting?

A The smaller tensor is ignored

B TensorFlow automatically reshapes them

C An error occurs

D The operation returns zeros

TensorFlow throws an error if shapes are incompatible and broadcasting is not possible.

Which operation performs element-wise multiplication of tensors?

A tf.tensordot()

B tf.matmul()

C tf.add()

D tf.multiply()

tf.multiply() multiplies tensors element-wise.

What does tf.matmul() do?

A Matrix multiplication

B Reshape tensor

C Element-wise addition

D Calculate mean

tf.matmul() performs matrix multiplication between two tensors.

Broadcasting helps by:

A Reducing tensor size

B Automatically expanding smaller tensors to match larger ones

C Changing tensor data types

D Sorting tensor elements

Broadcasting automatically expands smaller tensors to compatible shapes for operations.

Explain how broadcasting works in TensorFlow tensor math operations.

Think about how smaller arrays can be used with bigger ones without errors.

Describe the difference between element-wise multiplication and matrix multiplication in TensorFlow.

One multiplies matching elements, the other combines rows and columns.

Practice

1. What does the TensorFlow function tf.add(tensor1, tensor2) do?

easy

A. Adds two tensors element-wise

B. Multiplies two tensors element-wise

C. Performs matrix multiplication of two tensors

D. Subtracts the second tensor from the first

Solution

1. Step 1: Understand the function name and purpose

   The function tf.add is designed to add values, so it performs addition.

2. Step 2: Check the operation type

   In TensorFlow, tf.add adds two tensors element-wise, meaning it adds corresponding elements from both tensors.

3. Final Answer:

   Adds two tensors element-wise -> Option A

4. Quick Check:

   tf.add = element-wise addition [OK]

Hint: Add means element-wise sum, not matrix multiply [OK]

Common Mistakes:

• Confusing tf.add with matrix multiplication
• Thinking tf.add subtracts tensors
• Assuming tf.add multiplies tensors

2. Which of the following is the correct syntax to perform matrix multiplication of two tensors a and b in TensorFlow?

easy

A. tf.multiply(a, b)

B. tf.add(a, b)

C. tf.matmul(a, b)

D. a.dot(b)

Solution

1. Step 1: Identify the function for matrix multiplication

   TensorFlow uses tf.matmul specifically for matrix multiplication.

2. Step 2: Check other options

   tf.multiply does element-wise multiplication, tf.add adds tensors, and a.dot(b) is invalid since tf.Tensor has no .dot method.

3. Final Answer:

   tf.matmul(a, b) -> Option C

4. Quick Check:

   Matrix multiply = tf.matmul [OK]

Hint: Matrix multiply uses tf.matmul, not tf.multiply [OK]

Common Mistakes:

• Using tf.multiply for matrix multiplication
• Using a.dot(b) like in NumPy
• Confusing addition with multiplication

3. What is the output of the following TensorFlow code?

import tensorflow as tf
x = tf.constant([[1, 2], [3, 4]])
y = tf.constant([[5, 6], [7, 8]])
result = tf.add(x, y)
print(result.numpy())

medium

A. [[6 12]
[10 32]]

B. [[6 8]
[10 12]]

C. [[5 12]
[21 32]]

D. [[1 2]
[3 4]]

Solution

1. Step 1: Understand the operation

   The code uses tf.add to add two 2x2 tensors element-wise.

2. Step 2: Calculate element-wise addition

   Adding corresponding elements: [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

3. Final Answer:

   [[6 8] [10 12]] -> Option B

4. Quick Check:

   Element-wise add = [[6 8] [10 12]] [OK]

Hint: Add each element pair to get the result [OK]

Common Mistakes:

• Confusing element-wise add with matrix multiply
• Adding rows or columns incorrectly
• Printing tensor object instead of numpy array

4. Identify the error in this TensorFlow code snippet and choose the fix:

import tensorflow as tf
x = tf.constant([[1, 2], [3, 4]])
y = tf.constant([5, 6])
result = tf.matmul(x, y)
print(result.numpy())

medium

A. No error, code runs fine

B. Use tf.add instead of tf.matmul

C. Change x to a 1D tensor

D. Change y to a 2x1 tensor: tf.constant([[5], [6]])

Solution

1. Step 1: Understand matrix multiplication shape rules

   x is shape (2,2), y is shape (2,). TensorFlow tf.matmul requires both inputs to be at least rank 2 tensors.

2. Step 2: Identify the error

   Passing a 1D tensor y to tf.matmul causes a shape error because tf.matmul expects rank >= 2 tensors.

3. Step 3: Fix the error

   Change y to a 2D tensor with shape (2,1): tf.constant([[5], [6]]) to make matrix multiplication valid.

4. Final Answer:

   Change y to a 2x1 tensor: tf.constant([[5], [6]]) -> Option D

5. Quick Check:

   tf.matmul requires rank 2 tensors [OK]

Hint: tf.matmul requires 2D tensors; reshape 1D vector to 2D [OK]

Common Mistakes:

• Assuming 1D tensors cause no shape errors in matmul
• Unnecessarily reshaping y to 2D
• Confusing matmul with element-wise operations

5. You have two tensors:
a = tf.constant([[1, 2], [3, 4]])
b = tf.constant([[2, 0], [1, 2]])
Which TensorFlow operation will give the element-wise product of a and b?

hard

A. tf.multiply(a, b)

B. tf.matmul(a, b)

C. tf.add(a, b)

D. tf.tensordot(a, b, axes=1)

Solution

1. Step 1: Understand element-wise product

   Element-wise product multiplies each element of a with the corresponding element of b.

2. Step 2: Identify TensorFlow function for element-wise multiplication

   tf.multiply performs element-wise multiplication, while tf.matmul does matrix multiplication.

3. Final Answer:

   tf.multiply(a, b) -> Option A

4. Quick Check:

   Element-wise multiply = tf.multiply [OK]

Hint: Use tf.multiply for element-wise product, not tf.matmul [OK]

Common Mistakes:

• Using tf.matmul instead of tf.multiply
• Confusing addition with multiplication
• Using tf.tensordot incorrectly