Riemannian Optimization in Modular Systems
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the success of neural networks. Despite its empirical success, a strong theoretical understanding of it is lacking. Here, we combine tools from Riemannian geometry, optimal control theory, and theoretical physics to advance this understanding. We make three key contributions: First, we revisit the derivation of backpropagation as a constrained optimization problem and combine it with the insight that Riemannian gradient descent trajectories can be understood ...
| Authors | Christian Pehle, Jean-Jacques Slotine |
|---|---|
| Primary category | cs.LG |
| Published | 4 March 2026 |
| Last updated at source | 4 March 2026 |
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