Deep learning with transfer functions: new applications in system identification

Abstract This paper presents a linear dynamical operator described in terms of rational transfer function, endowed with well-defined and efficient back-propagation behavior for automatic derivatives computation. The enables end-to-end training structured networks containing functions other differentiable units by exploiting standard deep learning software. Two relevant applications the system identification are presented. first one consists integration prediction error methods learning. is included as last layer neural network order to obtain optimal one-step-ahead error. second considers general block-oriented models from quantized data. These constructed combining operators static nonlinearities feed-forward networks. A custom loss function corresponding log-likelihood output observations defined. For gradient-based optimization, computed applying algorithm through whole network. benchmarks used show effectiveness proposed methodologies.