The paper introduces H(psi)-convexity and H(Psi)-smoothness via Legendre functions, proves generalized GD/SGD convergence rates, and reformulates DNN training as composite optimization controlled by gradient energy and Jacobian induced norms.
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Generalized Convexity and Smoothness via Conjugate Duality: Optimization Theory for Deep Neural Networks
The paper introduces H(psi)-convexity and H(Psi)-smoothness via Legendre functions, proves generalized GD/SGD convergence rates, and reformulates DNN training as composite optimization controlled by gradient energy and Jacobian induced norms.