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Let's say we have a model and have just started to fit it, the first epoch out of many. The first epoch shows awful results. Does it make sense to continue training hoping the results will be better in the next epochs or it's better to stop (and save time/resources) and try to change something?

In my case, I have a classification model, and the first epoch gives loss=5.5, accuracy=1/n where n is the number of outputs. Consequent epochs changed almost nothing, so, the next 10 epochs were just a waste of time and resources.

Is there a rule of thumb to check that you should stop and try something else?

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In general, if a model is no better than random guessing and does not improve, there's a problem. The "no better than random" part is to be expected at the beginning of training, as weights and biases are initialized randomly. The "does not improve" part requires actually training the model and seeing how things change. One tip for classification models I've found useful is to try to train a single class detection first : is class A present yes or no, and then generalize to more classes. The confusion matrix is also helpful once you have something working to see where the model is making bad predictions, i.e. which classes in the input are mis-classified.

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