A numerical method I keep returning to
2026-08-13
Before the richness question, there was a more ordinary applied-math object: recover an image with missing pixels by solving an L1-regularized problem in the DCT domain. Compare a modeling language against a proximal gradient method you actually wrote down. Tune the regularizer until the reconstruction stops looking like a theory and starts looking like a photograph.
I keep returning to it because the shape is honest. There is a loss, a proximal map, a Lipschitz constant, and a picture that either comes back or does not. Neural-network theory is allowed to be stranger than that. It is not allowed to be vaguer than that.