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Let's say, I completed a training with 10k images on neural network with a certain number of epoch, which means all of 10k images went through forward and backpropagate epoch times.

Let' say, I get extra new 100 more data and wanto to train my machine further.

Do I have to start all over again from cleared weight with 10k+100 images? Or Can I train by starting with a current trained neural network and its learned weight saving some time? if I can, any risk of local minimum?

I also noticed that answer might be different between Classification and Regression case.. In regressio case, adding new training data is more likely fall into local minimum? Thanky you

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You can do a combination of both. You don't need to clear the weights, however you have to keep 'training' the first set of images as well, otherwise the network will converge to the newer set while forgetting the older set.

So take your trained network, and train it the 10k + 100 images

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