Optimizer ideas

Optimizer update-rule variants and parameter-specific step sizes, benchmarked against a learning-rate-tuned baseline.

Unverified 2026

Convex-mixture graph Langevin optimizer

Put a gradient-Gibbs prior on differences between connected neural parameters rather than on individual parameters, and evolve the parameters with Langevin steps generated from randomly selected strictly convex component energies. The aggregate regularizer may be non-convex, but every sampled component has controlled curvature and outward drift, providing a practical stability mechanism for noisy training.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Gradient Gibbs measures with non-convex potentials and the universality class of the Gaussian Free Field arXiv:2608.14526