Your answer is also terrible. It does not answer his question.

Look at the top 2 replies to see correct interpretations of the question.

If you keep the matrices separate, you can control the rank of the learned weights.

Otherwise, the (single) matrix will be full rank.

Correct. Physical intuition (symmetry) should inform how one models the problem.

Here, Galilean invariance is invoked to reduce the relevant degrees of freedom of the objective function.

Yes. It’s called modern search engines.

Look up papers on embedding based retrieval.

You should share your methodology.

s/over/under/d

Objective functions can be negative. What is the issue?

Using reinforcement learning to create AI-powered second life won’t be technically feasible for a long time.

This won’t pan out, unless you consider success to include screwing VCs out of money on smoke and mirrors.