Is numerical optimization theory irrelevant to machine learning practice in 2026?

We are seeing more numerical optimization theory papers published than ever before. These papers often make unrealistic assumptions or propose algorithms that never get adopted. So is all this optimization theory largely useless?

In this tutorial I show how some surprisingly simple optimization ideas can explain a wide variety of the implementation choices we make when training modern deep learning models. Some of these ideas might have let us skip some generations of grad-student descent, or have led to state-of-the-art tricks in modern architectures. On the other hand, I will highlight how some important practical ideas are not explained by optimization theory and where we can go from here.

Here is a list of keywords to get you (and your LLM sidekick) interested in attending: Adam and []A[]d[]a[]m[*], Muon and its friends/enemies, critical-ish batch size, the RMSnorm and skip connection love affair, dead ReLUs and living SwiGLU, Schedule-Free and WSD and muP and max_grad_norm = 1.0, variance reduction and shuffle=True, and maybe edge-of-stability/catapults/feature-learning. I may also tell you why your second-order stochastic optimization method did not work.