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In a neural network, batch normalization is achieved through a normalization step that fixes the means and variances of each layer's inputs. Ideally, the normalization would be conducted over the entire training set, but to use this step jointly with stochastic optimization methods, it is impractical to use the global information.
The FixNorm method divides the output vectors from a transformer by their L2 norms, then multiplies by a learned parameter . The ScaleNorm replaces all LayerNorms inside a transformer by division with L2 norm, then multiplying by a learned parameter ′ (shared by all ScaleNorm modules of a transformer).
A hyperparameter is a parameter whose value is used to control the learning process, which must be configured before the process starts. [ 2 ] [ 3 ] Hyperparameter optimization determines the set of hyperparameters that yields an optimal model which minimizes a predefined loss function on a given data set . [ 4 ]
In machine learning, a hyperparameter is a parameter that can be set in order to define any configurable part of a model's learning process. Hyperparameters can be classified as either model hyperparameters (such as the topology and size of a neural network) or algorithm hyperparameters (such as the learning rate and the batch size of an optimizer).
The norm (see also Norms) can be used to approximate the optimal norm via convex relaxation. It can be shown that the L 1 {\displaystyle L_{1}} norm induces sparsity. In the case of least squares, this problem is known as LASSO in statistics and basis pursuit in signal processing.
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller. It was developed by John G. Ziegler and Nathaniel B. Nichols . It is performed by setting the I (integral) and D (derivative) gains to zero.
The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. [5] The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization ...