My main question is: why does turning a vector into a matrix under the conditions you describe make it more interpretable? If the goal is to do some kind of learned decomposition from one vector into directions/key features, why not use e.g. PCA? I think I can see what you’re trying to get at, but I’m not sure. For example, one argument you could be making is “the matrices produced by this process will have features that are normally latent in v, such that they would require a linear probe or SAE to extract, but using this process they would just be the rows or eigenvectors of this matrix.” Is this close to what you’re getting at?
Secondary to that question, if the v vectors are the data, what are the u vectors? Can you give an example for u and v using a practical ML application?
To continue the frame of psychology, as I understand it it is usually held that narcissistic self love is in fact not compatible with a healthy self image. The urge to be superior and to dominate sets one up for a great fall, since (even if we were the smartest beings around) the world is too large and complex for us to steer and control perfectly, and our denial of that fact creates the room for a fall. I think superintelligence, so long as it remains running on physical and bounded computational devices, must also grapple with this problem.