Shallow Representation is Deep: Learning Uncertainty-aware and Worst-case Random Feature Dynamics

• URL: http://arxiv.org/abs/2106.13066v1
• Date: Thu, 24 Jun 2021 14:48:12 GMT
• Title: Shallow Representation is Deep: Learning Uncertainty-aware and Worst-case Random Feature Dynamics
• Authors: Diego Agudelo-Espa\~na, Yassine Nemmour, Bernhard Sch\"olkopf, Jia-Jie Zhu
• Abstract summary: This paper views uncertain system models as unknown or uncertain smooth functions in universal kernel Hilbert spaces. By directly approximating the one-step dynamics function using random features with uncertain parameters, we then view the whole dynamical system as a multi-layer neural network.
• Score: 1.1470070927586016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions in universal reproducing kernel Hilbert spaces. By directly approximating the one-step dynamics function using random features with uncertain parameters, which are equivalent to a shallow Bayesian neural network, we then view the whole dynamical system as a multi-layer neural network. Exploiting the structure of Hamiltonian dynamics, we show that finding worst-case dynamics realizations using Pontryagin's minimum principle is equivalent to performing the Frank-Wolfe algorithm on the deep net. Various numerical experiments on dynamics learning showcase the capacity of our modeling methodology.

Related papers

• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• NeuralEF: Deconstructing Kernels by Deep Neural Networks [47.54733625351363]
  Traditional nonparametric solutions based on the Nystr"om formula suffer from scalability issues. Recent work has resorted to a parametric approach, i.e., training neural networks to approximate the eigenfunctions. We show that these problems can be fixed by using a new series of objective functions that generalizes to space of supervised and unsupervised learning problems.
  arXiv  Detail & Related papers  (2022-04-30T05:31:07Z)
• Discovering dynamical features of Hodgkin-Huxley-type model of physiological neuron using artificial neural network [0.0]
  We consider Hodgkin-Huxley-type system with two fast and one slow variables. For these two systems we create artificial neural networks that are able to reproduce their dynamics. For the bistable model it means that the network being trained only on one brunch of the solutions recovers another without seeing it during the training.
  arXiv  Detail & Related papers  (2022-03-26T19:04:19Z)
• Training Integrable Parameterizations of Deep Neural Networks in the Infinite-Width Limit [0.0]
  Large-width dynamics has emerged as a fruitful viewpoint and led to practical insights on real-world deep networks. For two-layer neural networks, it has been understood that the nature of the trained model radically changes depending on the scale of the initial random weights. We propose various methods to avoid this trivial behavior and analyze in detail the resulting dynamics.
  arXiv  Detail & Related papers  (2021-10-29T07:53:35Z)
• Artificial neural network as a universal model of nonlinear dynamical systems [0.0]
  The map is built as an artificial neural network whose weights encode a modeled system. We consider the Lorenz system, the Roessler system and also Hindmarch-Rose neuron. High similarity is observed for visual images of attractors, power spectra, bifurcation diagrams and Lyapunovs exponents.
  arXiv  Detail & Related papers  (2021-03-06T16:02:41Z)
• UNIPoint: Universally Approximating Point Processes Intensities [125.08205865536577]
  We provide a proof that a class of learnable functions can universally approximate any valid intensity function. We implement UNIPoint, a novel neural point process model, using recurrent neural networks to parameterise sums of basis function upon each event.
  arXiv  Detail & Related papers  (2020-07-28T09:31:56Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• Approximation Bounds for Random Neural Networks and Reservoir Systems [8.143750358586072]
  This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. In particular, this proves that echo state networks with randomly generated weights are capable of approximating a wide class of dynamical systems arbitrarily well.
  arXiv  Detail & Related papers  (2020-02-14T09:43:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.