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I have seen many links about MA for batch normalization but nothing answered my question.

In Batch normalization, you get means and variance for each mini-batches in the training process. And the default process, you calculate through the moving average.

Those mini-batches are chosen randomly so there is no higher priority for the recent mini-batch. But why should we calculate the mean and variance for the evaluation process with MA and not just the normal average?

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The mean and variance of each mini-batch varies and each one may not represent the original input distribution fully. Also in the presence of outliers, the statistics of mini-batch containing them might be biased towards the outliers. So in order to avoid equal weightage assignment to each mini-batch moving average is used.

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