Deep learning with transfer functions: new applications in system identification

• URL: http://arxiv.org/abs/2104.09839v1
• Date: Tue, 20 Apr 2021 08:58:55 GMT
• Title: Deep learning with transfer functions: new applications in system identification
• Authors: Dario Piga, Marco Forgione, Manas Mejari
• Abstract summary: This paper presents a linear dynamical operator endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units {by} exploiting standard deep learning software. Two relevant applications of the operator in system identification are presented. The first one consists in the integration of {prediction error methods} in deep learning. The dynamical operator is included as {the} last layer of a neural network in order to obtain the optimal one-step-ahead prediction error. The second one considers identification of general block-oriented models from quantized data. These block-oriented models are constructed by combining linear dynamical operators with static nonlinearities described as standard feed-forward neural networks. A custom loss function corresponding to the log-likelihood of quantized output observations is defined. For gradient-based optimization, the derivatives of the log-likelihood are computed by applying the back-propagation algorithm through the whole network. Two system identification benchmarks are used to show the effectiveness of the proposed methodologies.

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