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Say we have N of labeled data, and we need to take some part for the cross validation (we will skip test part for this case). We chose, 0.6 part for the training and 0.4 for validation.

After training neural Network with early stop, we have found 8 epochs, as optimal to stop, and have received good enough results.

Q. In case, we have very limited N training samples. May we use all samples in new model training, and just stop it's training after discovered epochs? Without separating it to train and cross validation, and testing it, at all (or even, change rate of separating, to 0.9 train, 0.1 cross validation).

Maybe there is known technologies for such cases? Thanks.

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Due to stochastic nature of NN training, the best epoch may vary upon each restart. In other words, at epoch 8, each of (the best, under-fitted, over-fitted) cases may happen. However, if you train multiple times and the best model is consistently found at (or around) 8th epoch, it is safe to say 8th epoch gives the best model away from under- or over-fitting, thus definitely validation set can be added to training set to improve the performance.

A more solid approach would be to plot the effect of training size (10% up to 90%) on the best epoch and the validation error. This means producing two plots (training size, the best epoch) and (training size, validation error), where each point is an average over multiple restarts. This way you can better find (1) the best epoch, and (2) the degree to which the added validation set will going to boost the performance on unseen test data, i.e. extrapolating the validation error for training size 100%.

It is possible that performance goes flat after for example 70% of training set, implying that adding the validation set has no gain.

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