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Recent work has noted that all bad local minima can be removed from neuralnetwork loss landscapes, by adding a single unit with a particularparameterization. We show that the core technique from these papers can be usedto remove all bad local minima from any loss landscape, so long as the globalminimum has a loss of zero. This procedure does not require the addition ofauxiliary units, or even that the loss be associated with a neural network. Themethod of action involves all bad local minima being converted into bad(non-local) minima at infinity in terms of auxiliary parameters.

Eliminating all bad Local Minima from Loss Landscapes without even adding an Extra Unit