Are there techniques for estimating optimal neural network size?
To replicate "AND gate", one does not need 1e1000 nodes in hidden layer. What would be the metric hinting at "too much nodes"?
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There are several techniques for estimating the optimal size of a neural network, including cross-validation, Bayesian optimization, and early stopping. In general, having too many nodes in a hidden layer can lead to overfitting, which means that the model will perform well on the training data but will not generalize well to new, unseen data. One way to detect overfitting is to monitor the performance of the model on a validation set during training. If the performance on the training set continues to improve while the performance on the validation set starts to deteriorate, this is a sign of overfitting and suggests that the model may have too many nodes.
There are some general rules of thumb for determining the size of a neural network, but these are only rough guidelines and may not be applicable in all cases. For example, one common rule of thumb is to start with a small network and gradually increase the size until the performance on the validation set stops to improve. However, this rule of thumb does not take into account the complexity of the problem being solved or the amount of training data available, so it may not always produce optimal results/be applicable. In general, it is best to use a combination of techniques, such as cross-validation and early stopping, to determine the optimal size of a neural network for a given problem.