Researchers have developed fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions.
The work leverages a convex reformulation of the weight-decay penalized training problem as a set of group-ℓ₁-regularized data-local models, utilizing polyhedral cone constraints.
In the case of zero-regularization, the problem is exactly equivalent to unconstrained optimization of a convex 'gated ReLU' network with non-singular gates.
The developed approaches outperform standard training heuristics and commercial interior-point solvers in terms of speed and performance.