Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity
Read the original on arXiv Machine Learning →The paper introduces proximal equilibrium operators (PEOs), a class of neural operators that can simultaneously solve infinitely many convex optimization problems over a separable Hilbert space. A short training algorithm is presented that constructs PEOs using finite‑dimensional deep equilibrium layers, and a theoretical guarantee shows that, for inputs from a suitable infinite‑dimensional set, the trained PEOs uniformly approximate the solutions to arbitrary precision with logarithmic rank and width and linear depth in the inverse error. The authors validate their approach on applications to nonlinear PDEs, stochastic optimal control, and portfolio optimization and hedging in mathematical finance.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.