On summarized validation curves and generalization

The validation curve is widely used for model selection and hyper-parameter search with the curve usually summarized over all the training tasks. However, this summarization tends to lose the intricacies of the per-task curves and it isn't able to reflect if all the tasks are at their validation optimum even if the summarized curve might be. In this work, we explore this loss of information, how it affects the model at testing and how to detect it using interval plots. We propose two techniques as a proof-of-concept of the potential gain in the test performance when per-task validation curves are accounted for. Our experiments on three large datasets show up to a 2.5% increase (averaged over multiple trials) in the test accuracy rate when model selection uses the per-task validation maximums instead of the summarized validation maximum. This potential increase is not a result of any modification to the model but rather at what point of training the weights were selected from. This presents an exciting direction for new training and model selection techniques that rely on more than just averaged metrics.