Tensor operations (add, mul, matmul) in PyTorch - Model Pipeline Trace

Model Pipeline - Tensor operations (add, mul, matmul)

This pipeline shows how tensors (multi-dimensional arrays) are combined using addition, element-wise multiplication, and matrix multiplication. These operations are the building blocks for many machine learning models.

Data Flow - 4 Stages

1Input tensors

2 rows x 3 columns→Create two tensors A and B→2 rows x 3 columns

A = [[1, 2, 3], [4, 5, 6]], B = [[7, 8, 9], [10, 11, 12]]

↓

2Tensor addition

2 rows x 3 columns→Add tensors A and B element-wise→2 rows x 3 columns

A + B = [[8, 10, 12], [14, 16, 18]]

↓

3Element-wise multiplication

2 rows x 3 columns→Multiply tensors A and B element-wise→2 rows x 3 columns

A * B = [[7, 16, 27], [40, 55, 72]]

↓

4Matrix multiplication

A: 2 rows x 3 columns, B_transposed: 3 rows x 2 columns→Multiply tensor A by the transpose of B→2 rows x 2 columns

A @ B.T = [[50, 68], [122, 167]]

Training Trace - Epoch by Epoch

Loss
0.8 |****
0.6 |***
0.4 |**
0.3 |*
0.2 |

Epoch	Loss ↓	Accuracy ↑	Observation
1	0.8	0.45	Initial random weights, loss is high, accuracy low
2	0.6	0.60	Loss decreased, accuracy improved
3	0.4	0.75	Model learning well, loss dropping steadily
4	0.3	0.85	Good convergence, accuracy increasing
5	0.2	0.90	Training nearing completion, loss low

Prediction Trace - 4 Layers

Layer 1: Input tensors

Layer 2: Addition (A + B)

Layer 3: Element-wise multiplication (A * B)

Layer 4: Matrix multiplication (A @ B.T)

Model Quiz - 3 Questions

What is the shape of the result when you add two tensors of shape 2x3?

A 3 rows x 2 columns

B 2 rows x 3 columns

C 2 rows x 2 columns

D 3 rows x 3 columns

Key Insight

Tensor operations like addition, element-wise multiplication, and matrix multiplication are fundamental for building and training machine learning models. Understanding how shapes change and how these operations combine data helps in designing correct and efficient models.