The effective noise of stochastic gradient descent

  title={The effective noise of stochastic gradient descent},
  author={Francesca Mignacco and Pierfrancesco Urbani},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
Stochastic gradient descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted according to the performance on this specific subset of examples. The mini-batch sampling procedure introduces a stochastic dynamics to the gradient descent, with a non-trivial state-dependent noise. We characterize the stochasticity of SGD and a recently… 

Dynamical Mean Field Theory of Kernel Evolution in Wide Neural Networks

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Close-form equations for the exact high-dimensional asymptotics of a family of first order gradient-based methods, learning an estimator from observations on Gaussian data with empirical risk minimization are proved.

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Journal of Physics A: Mathematical and Theoretical 44

  • 483001
  • 2011

Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem

Dynamical mean-field theory from statistical physics is applied to characterize analytically the full trajectories of gradient-based algorithms in their continuous-time limit, with a warm start, and for large system sizes to unveil several intriguing properties of the landscape and the algorithms.

The inverse variance–flatness relation in stochastic gradient descent is critical for finding flat minima

  • Yu FengY. Tu
  • Computer Science
    Proceedings of the National Academy of Sciences
  • 2021
By analyzing SGD-based learning dynamics together with the loss function landscape, a robust inverse relation between weight fluctuation and loss landscape flatness opposite to the fluctuation–dissipation relation in physics is discovered.

and a at

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and s

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