Tensor operations (add, mul, matmul) in PyTorch - Model Metrics & Evaluation

Metrics & Evaluation - Tensor operations (add, mul, matmul)

Which metric matters for Tensor operations and WHY

When working with tensor operations like add, multiply, and matrix multiply, the key metric is correctness. This means the output tensor values must be exactly what math says they should be. For example, adding two tensors should give a tensor where each element is the sum of the corresponding elements. Multiplying element-wise should multiply each element pair. Matrix multiplication should follow the rules of linear algebra.

Correctness matters because these operations are the building blocks of machine learning models. If the math is wrong, the model will learn wrong patterns or crash.

Confusion matrix or equivalent visualization

For tensor operations, we don't use confusion matrices. Instead, we check outputs by comparing expected and actual tensors.

Input A:       Input B:
[[1, 2],     [[3, 4],
 [5, 6]]      [7, 8]]

Add (A + B):
[[4, 6],
 [12, 14]]

Mul (A * B) element-wise:
[[3, 8],
 [35, 48]]

Matmul (A @ B):
[[17, 20],
 [53, 62]]
    

We verify that the output matches these expected results exactly.

Tradeoff: Speed vs Precision in Tensor Operations

Sometimes, faster tensor operations use less precise numbers (like float16 instead of float32). This speeds up training but can cause small errors.

If you want very accurate results (like in scientific computing), use higher precision. If you want faster training and can accept tiny errors, use lower precision.

Choosing the right balance depends on your task and hardware.

What good vs bad tensor operation results look like

Good: Output tensors exactly match expected values from math. No unexpected NaNs or infinities. Shapes are correct.

Bad: Outputs have wrong values, shapes don't match, or contain NaNs/Infs. This means a bug or hardware issue.

Common pitfalls with tensor operations

• Shape mismatch errors when adding or multiplying tensors of incompatible sizes.
• Confusing element-wise multiplication (mul) with matrix multiplication (matmul).
• Using wrong data types causing precision loss or overflow.
• Forgetting broadcasting rules, leading to unexpected results.
• Not checking for NaNs or Infs after operations, which can break training.

Self-check question

Your tensor addition outputs values that are off by a small amount (like 1e-5). Is this a problem?

Answer: Usually, small floating point differences are normal due to how computers handle decimals. But if differences are large or cause errors, then it is a problem.

Key Result

Correctness of tensor outputs (matching expected math results) is the key metric for tensor operations.