Function regression using the forward forward training and inferring paradigm

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm is a novel approach for training neural networks without backpropagation, and is well suited for implementation in neuromorphic computing and physical analogs for neural networks. To the best of the authors' knowledge, the Forward Forward paradigm of training and inferencing NNs is currently only restricted to classification tasks. This paper introduces a new methodology for approximating functions (function regression) using the Forward-Forward algorithm. Furthermore, the paper evaluates the developed methodology on univariate and multivariate functions, and provides preliminary studies of extending the proposed Forward-Forward regression to Kolmogorov Arnold Networks, and Deep Physical Neural Networks.