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I'm new in this community and I don't know whether my question is proper for this community. I will delete this post if it is not proper.

I'm interested in deep learning network models and have a question about this.

Suppose we have a feedforward neural network models with different hyperparameters (for example, the number of layers, neurons and so on), say $H_1,..., H_n$. Also assume all the samples are selected from a particular distribution.

First we got $100$ samples. If we find that a typical hyperparameter set, $H_i$, performs best. Now I want to increase the number of samples to $1000, 10000,$ even millions. Is $H_i$ still the best hyperparameter set to perform among $H_i$'s? I want to know whether there are references about such topics. The best is a mathematical proof about this fact.

Again, please tell me if this question is not proper to the community. Thanks a lot!

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No. You're asking about model selection. Larger sample sizes will allow you to choose more complex models. Read up on the keywords overfit/underfit, model selection, Structural Risk Minimization, and in particular this article: https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=705570

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  • $\begingroup$ My question is for fixed parameters set, do not consider about more complex models. Anyway, I will read this paper. Thank you very much $\endgroup$ – CSH Feb 26 at 11:33
  • $\begingroup$ If you use "number of layers" as a hyperparameter (as in your OP), this is NOT a fixed-parameter model, since more layers => more parameters. $\endgroup$ – Aryeh Feb 26 at 12:09
  • $\begingroup$ Sorry I didn't mention in details. Since we have hyperparameter sets $H_1$ to $H_n$, numbers of layers, for example, can be chosen only from those $n$ choices, but I found it is not a common way because as you said, we can construct more complex models to enhance the results. $\endgroup$ – CSH Feb 26 at 12:17

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