Looking for Scale Invariance in Loss Landscape

In this work, we empirically verify the existence of the loss scale invariance property for conventional deep learning experimental setup. Since the theoretical findings hardly apply to large models in practice and the presented experiments involve only a limited set of models, in this work, we fill the gap and explore how training approaches and techniques influence the scale invariance in deep neural networks by examining the exact form of the learning curve. The investigated property can have a practical application in real-life problems. Indeed, when the form of a learning curve is linear under some transformations, then its slope characterizes the possible capacity of the model and can be estimated by a small number of training samples. Hence, we can compare models without exhaustive training on the whole dataset. Thus, the method applies for preliminary analysis of the data and model selection.