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Weight normalization (WeightNorm) [18] is a technique inspired by BatchNorm that normalizes weight matrices in a neural network, rather than its activations. One example is spectral normalization , which divides weight matrices by their spectral norm .
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.
For simplicity, the width + of the readout vector is taken to be 1. The parameters of this network have a prior distribution (), which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the ...
In such methods, during each training iteration, each neural network weight receives an update proportional to the partial derivative of the loss function with respect to the current weight. [1] The problem is that as the network depth or sequence length increases, the gradient magnitude typically is expected to decrease (or grow uncontrollably ...
Also known as min-max scaling or min-max normalization, rescaling is the simplest method and consists in rescaling the range of features to scale the range in [0, 1] or [−1, 1]. Selecting the target range depends on the nature of the data. The general formula for a min-max of [0, 1] is given as: [3]
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
A flow-based generative model is a generative model used in machine learning that explicitly models a probability distribution by leveraging normalizing flow, [1] [2] [3] which is a statistical method using the change-of-variable law of probabilities to transform a simple distribution into a complex one.
In addition to reducing the number of parameters, non-dimensionalized equation helps to gain a greater insight into the relative size of various terms present in the equation. [1] [2] Following appropriate selecting of scales for the non-dimensionalization process, this leads to identification of small terms in the equation. Neglecting the ...