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Training is the part of machine learning whereby a model is "trained" on a define portion of a dataset to learn attributes and statistical features of the data. It's counterparts are called Testing and Validation. After training a model is tested and validated on another portion of the dataset.

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How does training a ConvNet with huge number of parameters on a smaller number of images work?

Is it also true that when you use $N$ number of epochs, you "effectively" have $K*N$ training datasets, where $K$ is the number of training datasets you have? In the case above, $K$ = 1.3 million. …
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