Analytical derivatives of neural networks

We propose a simple recursive algorithm that allows the computation of the first-and second-order derivatives with respect to the inputs of an arbitrary deep feed forward neural network (DFNN). The algorithm naturally incorporates the derivatives with respect to the network parameters. To test the algorithm, we apply it to the study of the quantum mechanical variational problem for few cases of simple potentials, modeling the ground-state wave function in terms of a DFNN. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study presents a simple recursive algorithm for computing the first-and second-order derivatives with respect to the inputs of a deep feed forward neural network, incorporating derivatives with respect to network parameters. The algorithm is tested in the context of quantum mechanical variational problems for simple potentials, modeling ground-state wave function using a DFNN.