> Tensor product is basically the mathematical way to express if condition.
Not really, no. The way mathematicians actually express if conditions is with the word "if". The obvious pointlessly formal way to do it is with a pair of functions `ThingConditionedOn -> {0, 1}` and `{0, 1} -> Result`, but why would you?
> dealing with tensor matrix is simply a waste of memory since 90% of the time people are dealing with sparse system.
Tensors are not their components, any more than locations are their coordinates. Whether you choose a sparse or dense (or symbolic) encoding does not change the object being encoded.
> encoding does not change the object being encoded
Here I am talking about real memory space. There exist more efficient isometrical representation of the same object but since mathematicians don't usually know computer, inefficient tensor matrix is by default. That's the problem.
Not really, no. The way mathematicians actually express if conditions is with the word "if". The obvious pointlessly formal way to do it is with a pair of functions `ThingConditionedOn -> {0, 1}` and `{0, 1} -> Result`, but why would you?
> dealing with tensor matrix is simply a waste of memory since 90% of the time people are dealing with sparse system.
Tensors are not their components, any more than locations are their coordinates. Whether you choose a sparse or dense (or symbolic) encoding does not change the object being encoded.