  Activation functions (AFs) are an important part of the design of neural
networks (NNs), and their choice plays a predominant role in the performance of
a NN. In this work, we are particularly interested in the estimation of
flexible activation functions using tensor-based solutions, where the AFs are
expressed as a weighted sum of predefined basis functions. To do so, we propose
a new learning algorithm which solves a constrained coupled matrix-tensor
factorization (CMTF) problem. This technique fuses the first and zeroth order
information of the NN, where the first-order information is contained in a
Jacobian tensor, following a constrained canonical polyadic decomposition
(CPD). The proposed algorithm can handle different decomposition bases. The
goal of this method is to compress large pretrained NN models, by replacing
subnetworks, {\em i.e.,} one or multiple layers of the original network, by a
new flexible layer. The approach is applied to a pretrained convolutional
neural network (CNN) used for character classification.
