In this work, we will introduce a new step in the machine-learning procedure, namely, a parametrically managed activation function. This is designed so that the potential representation in difficult regions inherits the correct physical behavior of lower-dimensional potentials. We will introduce the parametrically managed activation function in the context of the methods of diabatization by deep neural network (DDNN) and permutationally restrained DDNN (PR-DDNN), but the type of approach employed here should also be useful for other uses of neural networks to represent potential energy surfaces. Section 2 reviews the relevant aspects of the DDNN and PR-DNN schemes. Section 3 presents the new method. Section 4 illustrates the new method by using it to obtain improved potential energy surfaces for O + O2 collisions in the 3 A´ electronic state manifold.