Can we teach a model to encode a semantic feature on a chosen manifold in just three channels?

This is my submission to BlueDot's Technical AI Safety Puzzle #1, for which I received an Honorable Mention. Congratulations to Gustavo Korzune Gurgel, Patryk Perduta (his amazing write-up), Sam Spilllard, Karine Levonyan, and Michael Zlatin for their recognition in the puzzle.My article below focuses on my answer to Task 3: training a small MLP to encode country feature through a chosen nonlinear manifold in three reserved channels.My Task 1 and 2 write-up is available on my homepage, and the i...