global minimizer here and Gd store stays in this set so it's a statement about local geometry is saying that locally things essentially look convex as long as you find a critical point in this local set it will be a global minimizer and in fact you do stay in this set so roughly the global geometry of deep networks is it's probably pretty bad I think there's definitely it should have exponentially many bad local minima local minima with even high values of crane loss however locally there is a global minima locally there exists