![]() ![]() This problem emerges when trying to generalise to new data sets. Neural networks have been very successful in many applications we often, however, lack a theoretical understanding of what the neural networks are actually learning. Results show that the proposed methodologies are advantageous for a wide range of tasks. We also conduct comparative experiments to evaluate Lanczos-based spectral norm minimization against prior methods. We carry out exploratory experiments to validate the effectiveness of our novel regularization terms. Theoretical justifications and empirical evidence are provided for the proposed paradigm and technique. This technique uses a parallelized implementation of the Lanczos algorithm and is capable of effective and stable regularization of large Jacobian and Hessian matrices. We introduce Lanczos-based spectral norm minimization to tackle this difficulty. On the other hand, the major challenge for Jacobian and Hessian regularization has been high computational complexity. The proposed paradigm allows us to construct novel regularization terms that enforce symmetry or diagonality on square Jacobian and Hessian matrices. In this work, we generalize previous efforts by extending the target matrix from zero to any matrix that admits efficient matrix-vector products. Jacobian and Hessian regularization aim to reduce the magnitude of the first and second-order partial derivatives with respect to neural network inputs, and they are predominantly used to ensure the adversarial robustness of image classifiers. ![]()
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