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Another possible reason for the success of batch normalization is that it decouples the length and direction of the weight vectors and thus facilitates better training. By interpreting batch norm as a reparametrization of weight space, it can be shown that the length and the direction of the weights are separated and can thus be trained separately.
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 .
where as before w ij is the synaptic weight between the i th input and j th output neurons, x is the input, y is the postsynaptic output, and we define ε to be a constant analogous the learning rate, and c pre and c post are presynaptic and postsynaptic functions that model the weakening of signals over time.
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 following set of equations:
Weight initialization [ edit ] Kumar suggested that the distribution of initial weights should vary according to activation function used and proposed to initialize the weights in networks with the logistic activation function using a Gaussian distribution with a zero mean and a standard deviation of 3.6/sqrt(N) , where N is the number of ...
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.
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Without normalization, the clusters were arranged along the x-axis, since it is the axis with most of variation. After normalization, the clusters are recovered as expected. In machine learning, we can handle various types of data, e.g. audio signals and pixel values for image data, and this data can include multiple dimensions. Feature ...