Every Local Minimum Value is the Global Minimum Value of Induced Model in Non-convex Machine Learning

Understand

For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point.

• As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the handcrafted basis over the perturbable gradient basis.
• The proofs of these results are derived under mild assumptions.
• Accordingly, the proven results are directly applicable to many machine learning models, including practical deep neural networks, without any modification of practical methods.