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The BatchNorm module does not operate over individual inputs. Instead, it must operate over one batch of inputs at a time. Concretely, suppose we have a batch of inputs () (), (), …, (), fed all at once into the network. We would obtain in the middle of the network some vectors:
Furthermore, batch normalization seems to have a regularizing effect such that the network improves its generalization properties, and it is thus unnecessary to use dropout to mitigate overfitting. It has also been observed that the network becomes more robust to different initialization schemes and learning rates while using batch normalization.
The form the population iteration, which converges to , but cannot be used in computation, while the form the sample iteration which usually converges to an overfitting solution. We want to control the difference between the expected risk of the sample iteration and the minimum expected risk, that is, the expected risk of the regression function:
By combining both using Bayesian statistics, one can compute a posterior, that includes both information sources and therefore stabilizes the estimation process. By trading off both objectives, one chooses to be more aligned to the data or to enforce regularization (to prevent overfitting).
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On the left is a fully connected neural network with two hidden layers. On the right is the same network after applying dropout. Dilution and dropout (also called DropConnect [1]) are regularization techniques for reducing overfitting in artificial neural networks by preventing complex co-adaptations on training data.
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Overfitting occurs when the learned function becomes sensitive to the noise in the sample. As a result, the function will perform well on the training set but not perform well on other data from the joint probability distribution of x {\displaystyle x} and y {\displaystyle y} .