Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behavior
We describe an approach to understand the peculiar and counterintuitive generalization properties of deep neural networks. The approach involves going beyond worst-case theoretical capacity control frameworks that have been popular in machine learning in recent years to revisit old ideas in the statistical mechanics of neural networks. Within this approach, we present a prototypical Very Simple Deep Learning model, whose behavior is controlled by two control parameters, one describing an effective amount of data, or load, on the network, and one with an effective temperature interpretation. Using this model, we describe how a very simple application of ideas from the statistical mechanics theory of generalization provides a strong qualitative description of recently-observed empirical results regarding the inability of deep neural networks not to overfit training data, discontinuous learning and sharp transitions in the generalization properties of learning algorithms, etc.
Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behaviorThe authors suggest that statistical mechanics ideas will help to understand generalization properties of deep neural networks, and give an approach that provides strong qualitative descriptions of empirical results regarding deep neural networks and learning algorithms.A set of ideas related to theoretical understanding generalization properties of multilayer neural networks, and a qualitative analogy between behaviours in deep learning and results from quantitative statistical physics analysis of single and two-layer neural networks.