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Gradient Descent in 2D. Gradient descent is a method for unconstrained mathematical optimization. ... Online book teaching gradient descent in deep neural network ...
For example, the developing of information-geometric optimization methods (mirror descent [6] and natural gradient descent [7]). The standard references in the field are Shun’ichi Amari and Hiroshi Nagaoka's book, Methods of Information Geometry, [8] and the more recent book by Nihat Ay and others. [9]
A Riemannian manifold is a smooth manifold together with a Riemannian metric. The techniques of differential and integral calculus are used to pull geometric data out of the Riemannian metric. For example, integration leads to the Riemannian distance function, whereas differentiation is used to define curvature and parallel transport.
The gradient of the function f(x,y) = −(cos 2 x + cos 2 y) 2 depicted as a projected vector field on the bottom plane. The gradient (or gradient vector field) of a scalar function f(x 1, x 2, x 3, …, x n) is denoted ∇f or ∇ → f where ∇ denotes the vector differential operator, del.
However, in the limit of large layer width the NTK becomes constant, revealing a duality between training the wide neural network and kernel methods: gradient descent in the infinite-width limit is fully equivalent to kernel gradient descent with the NTK. As a result, using gradient descent to minimize least-square loss for neural networks ...
But they can be broadly understood in 4 categories of learning methods, though these categories don't have clear boundaries and they tend to belong to multiple categories of learning methods [3] - Hebbian - Neocognitron, Brain-state-in-a-box [4] Gradient Descent - ADALINE, Hopfield Network, Recurrent Neural Network
In the mathematical theory of artificial neural networks, universal approximation theorems are theorems [1] [2] of the following form: Given a family of neural networks, for each function from a certain function space, there exists a sequence of neural networks ,, … from the family, such that according to some criterion.
The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction techniques in machine learning. Many techniques of dimensional reduction make the assumption that data lies along a low-dimensional submanifold, such as manifold sculpting, manifold alignment, and manifold regularization.