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What if we have very few training examples for a deep learning model, will employing more number of epochs help the model have better accuracy?

Considering, i have 5 training example under the label 'dog' and 5 under the label 'cat'. Will more number of epochs help me train a Deep Learning Model with a good accuracy?

I would advise you to look into the topic of overfitting/underfitting.

Generally, if you train for more epochs, you will at a certain point start overfitting. So more epochs will lead to a better performance on the training set, but a worse performance on any other set (generalization error). This is why most deep-learning models use a validation set for early stopping:

A general idea is: fit to training set for one epoch check if validation set got predicted worse (if yes, reduce patience) if patience is 0 stop and use last mode, where validation got better

If you have very little data, you should probably use leave-n-out cross-validation instead of simple train/valid/test split.

Short answer: More epochs will help you perform better on the training data, but might (will) lead to worse performance on any new data.

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