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Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...
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 ...
Pronounced "A-star". A graph traversal and pathfinding algorithm which is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. abductive logic programming (ALP) A high-level knowledge-representation framework that can be used to solve problems declaratively based on abductive reasoning. It extends normal logic programming by allowing some ...
If used in gradient descent methods, random preconditioning can be viewed as an implementation of stochastic gradient descent and can lead to faster convergence, compared to fixed preconditioning, since it breaks the asymptotic "zig-zag" pattern of the gradient descent.
Gradient descent methods are first-order, iterative, optimization methods. Each iteration updates an approximate solution to the optimization problem by taking a step in the direction of the negative of the gradient of the objective function.
The associated process theory of neuronal dynamics is based on minimising free energy through gradient descent. This corresponds to generalised Bayesian filtering (where ~ denotes a variable in generalised coordinates of motion and D {\displaystyle D} is a derivative matrix operator): [ 39 ]
While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. A too high learning rate will make the learning jump over minima but a too low learning rate will either take too long to converge or get stuck in an undesirable local minimum.
In optimization, a descent direction is a vector that points towards a local minimum of an objective function :.. Computing by an iterative method, such as line search defines a descent direction at the th iterate to be any such that , <, where , denotes the inner product.