I2dl xavierInitialization

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= Xavier Iniatialization = Xavier initialization is a method for initializing the weights of a neural network such that the variance of the activations remains constant across different layers. The goal of this initialization is to ensure that the weights are initialized in a way that prevents the activations from exploding or vanishing, which can make training difficult or slow.

The idea behind Xavier initialization is that the variance of the activations should be equal to 1/n, where n is the number of input neurons in the layer. The weights are initialized randomly from a Gaussian distribution with mean 0 and variance 2/n for each layer. For a layer with m outputs and n inputs, the variance of the activations will be equal to m/n, which is close to 1 for most cases.

The formula for initializing the weights in a layer with n inputs and m outputs using Xavier initialization is:

w = np.random.randn(n, m) * np.sqrt(2/n)

where np is the Numpy library and randn is the Numpy function for generating random numbers from a standard normal distribution.

Xavier initialization is a simple and effective method for initializing the weights of a neural network, and it is widely used in practice. It has been shown to work well for a wide range of network architectures and activation functions, and it can help to prevent overfitting by initializing the weights in a way that promotes stability during training.