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It can be derived as the backpropagation algorithm for a single-layer neural ... we calculate the partial derivative ... Stochastic gradient descent; Backpropagation;
Strictly speaking, the term backpropagation refers only to an algorithm for efficiently computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm – including how the gradient is used, such as by stochastic gradient descent, or as an intermediate step in a more ...
The properties of gradient descent depend on the properties of the objective function and the variant of gradient descent used (for example, if a line search step is used). The assumptions made affect the convergence rate, and other properties, that can be proven for gradient descent. [ 33 ]
As observed above, is the negative gradient of at , so the gradient descent method would require to move in the direction r k. Here, however, we insist that the directions must be conjugate to each other. A practical way to enforce this is by requiring that the next search direction be built out of the current residual and all previous search ...
steepest descent (with variable learning rate and momentum, resilient backpropagation); quasi-Newton (Broyden–Fletcher–Goldfarb–Shanno, one step secant); Levenberg–Marquardt and conjugate gradient (Fletcher–Reeves update, Polak–Ribiére update, Powell–Beale restart, scaled conjugate gradient). [4]
The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization.
It is a generalisation of the least mean squares algorithm in the linear perceptron and the Delta Learning Rule. It implements gradient descent search through the space possible network weights, iteratively reducing the error, between the target values and the network outputs.
The deep BSDE method constructs neural networks to approximate the solutions for and , and utilizes stochastic gradient descent and other optimization algorithms for training. [1] The fig illustrates the network architecture for the deep BSDE method.