multilayer neural networks

Stochastic generalized gradient methods for training nonconvex nonsmooth neural networks

  • Vladimir I. Norkin
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    The paper observes a similarity between the stochastic optimal control of discrete dynamical systems and the learning multilayer neural networks. It focuses on contemporary deep networks with nonconvex nonsmooth loss and activation functions. The machine learning problems are treated as nonconvex nonsmooth stochastic optimization problems. As a model of nonsmooth nonconvex dependences, the so-called generalized … Read more

    Substantiation of the Backpropagation Technique via the Hamilton-Pontryagin Formalism for Training Nonconvex Nonsmooth Neural Networks

  • Vladimir I. Norkin
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    The paper observes the similarity between the stochastic optimal control of discrete dynamical systems and the training multilayer neural networks. It focuses on contemporary deep networks with nonconvex nonsmooth loss and activation functions. In the paper, the machine learning problems are treated as nonconvex nonsmooth stochastic optimization problems. As a model of nonsmooth nonconvex dependences, … Read more

    Generalized Gradients in Problems of Dynamic Optimization, Optimal Control, and Machine Learning

  • Vladimir I. Norkin
    • Categories Nonsmooth Optimization, Stochastic Programming Tags , , , , , , ,

    In this work, nonconvex nonsmooth problems of dynamic optimization, optimal control in discrete time (including feedback control), and machine learning are considered from a common point of view. An analogy is observed between tasks of controlling discrete dynamic systems and training multilayer neural networks with nonsmooth target function and connections. Methods for calculating generalized gradients … Read more