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We describe an approach to understand the peculiar and counterintuitivegeneralization properties of deep neural networks. The approach involves goingbeyond worst-case theoretical capacity control frameworks that have beenpopular in machine learning in recent years to revisit old ideas in thestatistical mechanics of neural networks. Within this approach, we present aprototypical Very Simple Deep Learning (VSDL) model, whose behavior iscontrolled by two control parameters, one describing an effective amount ofdata, or load, on the network (that decreases when noise is added to theinput), and one with an effective temperature interpretation (that increaseswhen algorithms are early stopped). Using this model, we describe how a verysimple application of ideas from the statistical mechanics theory ofgeneralization provides a strong qualitative description of recently-observedempirical results regarding the inability of deep neural networks not tooverfit training data, discontinuous learning and sharp transitions in thegeneralization properties of learning algorithms, etc.

Rethinking generalization requires revisiting old ideas: statistical mechanics approaches and complex learning behavior