Tensor operations (add, mul, matmul) in PyTorch

Introduction

Tensors are like multi-dimensional arrays. We use operations like add, mul, and matmul to combine or transform data in machine learning.

Adding two images pixel by pixel to blend them.

Multiplying features by weights element-wise in a neural network.

Calculating the output of a layer by matrix multiplying inputs and weights.

Combining sensor data from different sources by adding their tensors.

Performing batch operations on data for faster training.

Syntax

PyTorch

import torch

# Add two tensors
result = torch.add(tensor1, tensor2)

# Multiply two tensors element-wise
result = torch.mul(tensor1, tensor2)

# Matrix multiply two tensors
result = torch.matmul(tensor1, tensor2)

All tensors must have compatible shapes for these operations.

Matrix multiplication follows linear algebra rules, not element-wise multiplication.

Examples

Adds two 1D tensors element-wise: [1+4, 2+5, 3+6] = [5, 7, 9]

PyTorch

a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
add_result = torch.add(a, b)

Multiplies two 1D tensors element-wise: [1*4, 2*5, 3*6] = [4, 10, 18]

PyTorch

a = torch.tensor([1, 2, 3])
b = torch.tensor([4, 5, 6])
mul_result = torch.mul(a, b)

Matrix multiplies two 2x2 tensors following linear algebra rules.

PyTorch

a = torch.tensor([[1, 2], [3, 4]])
b = torch.tensor([[5, 6], [7, 8]])
matmul_result = torch.matmul(a, b)

Sample Model

This program shows how to add, multiply element-wise, and matrix multiply two 2x2 tensors.

PyTorch

import torch

# Define two tensors
x = torch.tensor([[1, 2], [3, 4]])
y = torch.tensor([[5, 6], [7, 8]])

# Add tensors
add = torch.add(x, y)

# Multiply tensors element-wise
mul = torch.mul(x, y)

# Matrix multiply tensors
matmul = torch.matmul(x, y)

print('Add result:\n', add)
print('Mul result:\n', mul)
print('Matmul result:\n', matmul)

Important Notes

Use torch.add and torch.mul for element-wise operations.

Use torch.matmul for matrix multiplication, which is different from element-wise multiplication.

Shapes must match or be broadcastable for add and mul; for matmul, inner dimensions must align.

Summary

Tensors hold data in multi-dimensional arrays.

Use add and mul for element-wise operations.

Use matmul for matrix multiplication following linear algebra.

Practice

1. Which PyTorch function is used for element-wise multiplication of two tensors?

easy

A. torch.matmul()

B. torch.dot()

C. torch.add()

D. torch.mul()

Solution

1. Step 1: Understand element-wise multiplication

   Element-wise multiplication multiplies each element of one tensor by the corresponding element of another tensor.

2. Step 2: Identify the correct PyTorch function

   torch.mul() performs element-wise multiplication, while torch.matmul() is for matrix multiplication.

3. Final Answer:

   torch.mul() -> Option D

4. Quick Check:

   Element-wise multiply = torch.mul() [OK]

Hint: Element-wise multiply uses torch.mul() not matmul [OK]

Common Mistakes:

• Confusing matmul with element-wise multiply
• Using torch.add() instead of multiply
• Trying torch.dot() for element-wise multiply

2. Which of the following is the correct syntax to add two tensors a and b in PyTorch?

easy

A. c = torch.add(a, b)

B. c = a + b + 1

C. c = torch.mul(a, b)

D. c = torch.matmul(a, b)

Solution

1. Step 1: Identify the addition operation

   Adding two tensors element-wise can be done with torch.add(a, b) or a + b.

2. Step 2: Check syntax correctness

   torch.add(a, b) is the correct function call. c = a + b + 1 adds 1 extra, so it's incorrect.

3. Final Answer:

   c = torch.add(a, b) -> Option A

4. Quick Check:

   Tensor add syntax = torch.add(a, b) [OK]

Hint: Use torch.add(a, b) or a + b for tensor addition [OK]

Common Mistakes:

• Adding extra numbers accidentally
• Using mul or matmul instead of add
• Incorrect function call syntax

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

import torch
x = torch.tensor([[1, 2], [3, 4]])
y = torch.tensor([[5, 6], [7, 8]])
z = torch.matmul(x, y)
print(z)

medium

A. tensor([[5, 12], [21, 32]])

B. tensor([[6, 8], [10, 12]])

C. tensor([[19, 22], [43, 50]])

D. tensor([[6, 8], [21, 32]])

Solution

1. Step 1: Perform matrix multiplication manually

   Multiply rows of x by columns of y:
   First row: (1*5 + 2*7) = 19, (1*6 + 2*8) = 22
   Second row: (3*5 + 4*7) = 43, (3*6 + 4*8) = 50

2. Step 2: Confirm output tensor

   The result tensor is [[19, 22], [43, 50]].

3. Final Answer:

   tensor([[19, 22], [43, 50]]) -> Option C

4. Quick Check:

   Matrix multiply result = [[19, 22], [43, 50]] [OK]

Hint: Multiply rows by columns for matmul output [OK]

Common Mistakes:

• Adding elements instead of multiplying
• Confusing element-wise multiply with matmul
• Mixing row and column indices

4. Identify the error in this PyTorch code snippet:

import torch
x = torch.tensor([1, 2, 3])
y = torch.tensor([[4, 5, 6], [7, 8, 9]])
z = torch.matmul(x, y)
print(z)

medium

A. Shape mismatch for matrix multiplication

B. x and y must be the same shape for matmul

C. torch.matmul cannot multiply 1D and 2D tensors

D. No error, code runs fine

Solution

1. Step 1: Check tensor shapes

   x shape is (3,), y shape is (2, 3). For matmul, inner dimensions must match: (N, M) x (M, P).

2. Step 2: Identify mismatch

   Here, x is 1D with length 3, y is 2D with shape (2, 3). The inner dimensions don't align for matmul.

3. Final Answer:

   Shape mismatch for matrix multiplication -> Option A

4. Quick Check:

   Matmul needs matching inner dims = shape mismatch [OK]

Hint: Check tensor shapes before matmul to avoid mismatch [OK]

Common Mistakes:

• Assuming 1D and 2D tensors always multiply
• Ignoring shape rules for matmul
• Thinking matmul works like element-wise multiply

5. Given two tensors a = torch.tensor([[1, 2], [3, 4]]) and b = torch.tensor([[2, 0], [1, 2]]), which code correctly computes the element-wise product and then adds the matrix product of a and b?

hard

A. torch.matmul(torch.mul(a, b), torch.add(a, b))

B. torch.add(torch.mul(a, b), torch.matmul(a, b))

C. torch.mul(torch.add(a, b), torch.matmul(a, b))

D. torch.add(torch.matmul(b, a), torch.mul(a, b))

Solution

1. Step 1: Understand the operations order

   First, compute element-wise product: torch.mul(a, b). Then compute matrix product: torch.matmul(a, b).

2. Step 2: Add the two results

   Use torch.add() to sum the element-wise and matrix products.

3. Final Answer:

   torch.add(torch.mul(a, b), torch.matmul(a, b)) -> Option B

4. Quick Check:

   Element-wise mul + matmul = torch.add(torch.mul(), torch.matmul()) [OK]

Hint: Add element-wise mul and matmul results with torch.add() [OK]

Common Mistakes:

• Mixing order of operations
• Using mul on sums instead of add on products
• Confusing arguments order in add or mul