Adding One Neuron Can Eliminate All Bad Local Minima
This addresses the challenge of non-convex optimization in neural networks for binary classification, potentially improving training reliability, though it is incremental as it builds on existing landscape analysis.
The paper tackles the problem of non-convex loss functions in neural networks by proving that adding one special neuron with a skip connection or one per layer eliminates all bad local minima for binary classification tasks, ensuring every local minimum is a global minimum.
One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima. In this paper, we study the landscape of neural networks for binary classification tasks. Under mild assumptions, we prove that after adding one special neuron with a skip connection to the output, or one special neuron per layer, every local minimum is a global minimum.