How to normalize a batch of N examples?
A batch normalization layer is given a batch of N examples, each of which is a D -dimensional vector. We can represent the inputs as a matrix X ∈ R N × D where each row x i is a single example. Each example x i is normalized by
How is gradient calculated in batch normalization layer?
The method calculates the gradient of a loss function with respect to all the weights in the network. The gradient is fed to the optimization method which in turn uses it to update the weights, in an attempt to minimize the loss function. Uff, sounds tough, eh?
What is the purpose of batch normalization in neural network?
Batch Normalization is a technique to provide any layer in a Neural Network with inputs that are zero mean/unit variance-and this is basically what they like! But BatchNorm consists of one more step which makes this algorithm really powerful.
Is the forward pass in batch normalization simple?
Anyway, at one point in the assignment, we were tasked with implementing a Batch Normalization layer in our fully-connected net which required writing a forward and backward pass. The forward pass is relatively simple since it only requires standardizing the input features (zero mean and unit standard deviation).
Which is the standard deviation in batch normalization?
However, when we see the axis of the histogram, we can clearly see that the mean of the our data have shifted to 0 (almost) and variance is 1. Just in case, if anyone is wondering, lets review the equation for both cases normalization as well as standardization. Please note μ is the mean and σ is the standard deviation.
How are mean and variance computed in batch-norm backprop equations?
The mean and variance are computed by An affine transform is then applied to the normalized rows to produce the final output where γ, β ∈ R 1 × D are learnable scale parameters for each input dimension. For notational simplicity, we can express the entire layer as