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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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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Dec 2, 2022 at 16:49

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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.

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  • $\begingroup$ Hey! This answer looks like it may have been (partially) generated by an AI-based tool like ChatGPT. If this is the case, this should be explicitly stated in the post. Furthermore, there is a new policy in effect (see ai.meta.stackexchange.com/questions/2905/…) which means that such tools should not continue to be used to generate content for future posts on StackExchange. $\endgroup$
    – Dennis Soemers ♦
    Dec 5, 2022 at 16:50
  • $\begingroup$ I'd also like to ask you for a clarification: for the technique of starting with a small network, and gradually increasing its size, you wrote that you should do that until the performance on the validation set starts to improve. Shouldn't that be stops? Afterwards, you wrote that this rule of thumb doesn't account for problem complexity or training data availability. Why not? Wouldn't performance stop improving earlier on an easy problem, for example? $\endgroup$
    – Dennis Soemers ♦
    Dec 5, 2022 at 16:52
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    $\begingroup$ @DennisSoemers thanks for the concern. It was not generated by ChatGPT. You are right that i typod and it should be stops (see edit). Regarding your second, im not saying they are not correlated, they are. However, networks that are too large can cause an optimizer to never converge at all, and some problems do not even have a validation loss. There are various circumstances under which the rule of thumb ddoes not hold. $\endgroup$
    – Robin van Hoorn
    Dec 6, 2022 at 11:56

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