Globally Aware Optimization with Resurgence (arxiv.org)

Researchers propose a new optimization framework that brings global landscape awareness to gradient-based training by applying resurgence theory from complex analysis. The core idea is to treat the loss L(θ) like an energy in statistical mechanics, form the partition function Z(g)=∫ e^{-L(θ)/g} dθ at small coupling g≪1, and study the factorially divergent perturbative expansion of Z. By taking the Borel transform of that series, singularities in the Borel plane can be read off and—crucially—map one-to-one to the objective values of all critical points in the loss landscape. Those recovered objective-value “targets” provide globally grounded information that local optimizers lack. Technically, the method leverages the correspondence between Borel-plane singularities and critical action values, using asymptotic coefficient extraction to locate these singularities. Practically, the targets can guide principled learning-rate adjustments and directed escapes from suboptimal basins, offering an alternative to heuristic adaptive schemes. The approach promises improved initialization robustness and a way to integrate landscape-level structure into optimization. Caveats include the computational cost of estimating partition-function coefficients and performing Borel analysis in high dimensions, but the paper provides code and demos; if scalable, this could be a significant step toward landscape-aware optimizers grounded in rigorous asymptotic theory.