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What happens during the backward pass in batch normalization?
This step during the forward pass was the final step of the normalization combining the two branches (nominator and denominator) of the computational graph. During the backward pass we will calculate the gradients that will flow separately through these two branches backwards.
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
When did batch normalization start in deep learning?
Since its inception in 2015 by Ioffe and Szegedy, Batch Normalization has gained popularity among Deep Learning practitioners as a technique to achieve faster convergence by reducing the internal covariate shift and to some extent regularizing the network.
How are gradients calculated in batch normalization layer?
Backpropagation through Batch Normalization layer During backpropagation, we are given the gradients of the loss with respect to the outputs (∂L ∂yi ∂ L ∂ y i) and are asked to calculate the gradients with respect to parameters (∂L ∂γ ∂ L ∂ γ and ∂L ∂β ∂ L ∂ β) and inputs (∂L ∂xi ∂ L ∂ x i).
What is the last line of the batchnorm algorithm?
Let’s take a look at the BatchNorm Algorithm: Algorithm of Batch Normalization copied from the Paper by Ioffe and Szegedy mentioned above. Look at the last line of the algorithm. After normalizing the input x the result is squashed through a linear function with parameters gamma and beta.
What does a column wise summation during a backward pass mean?
With that in mind, it should not be that hard to conclude, that a column-wise summation during the forward pass, during the backward pass means that we evenly distribute the gradient over all rows for each column. And not much more is done here.
Which is more powerful, batchnorm or batch normalization?
But BatchNorm consists of one more step which makes this algorithm really powerful. Let’s take a look at the BatchNorm Algorithm: Algorithm of Batch Normalization copied from the Paper by Ioffe and Szegedy mentioned above.