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Regularized Least Squares Training of Quadratic Neural Networks with Applications to System Identification

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

This paper proposes a least squares approach for the training of quadratic neural networks with regularization. The proposed methodology yields a lower bound on the solution of the training optimization problem for the case where the regularization coefficient is positive. Moreover, it yields closed-form expressions for the approximate solution and its sensitivity The lower bound is tight and the approximate solution is the optimal solution when the regularization coefficient is zero. Having a closed-form expression for the weights reduces considerably the computational time when compared with

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