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On the Cone Effect in the Learning Dynamics
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Understanding the learning dynamics of neural networks is a central topic in the deep learning community. In this paper, we take an empirical perspective to study the learning dynamics of neural networks in real-world settings. Specifically, we investigate the evolution process of the empirical Neural Tangent Kernel (eNTK) during training. Our key findings reveal a two-phase learning process: i) in Phase I, the eNTK evolves significantly, signaling the rich regime, and ii) in Phase II, the eNTK keeps evolving but is constrained in a narrow space, a phenomenon we term the cone effect. This two-phase framework builds on the hypothesis proposed by Fort et al. (2020), but we uniquely identify the cone effect in Phase II, demonstrating its significant performance advantages over fully linearized training.
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Reactivation: Empirical NTK Dynamics Under Task Shifts
Task transitions in continual learning cause abrupt, width-persistent changes in the Neural Tangent Kernel of past data, a phenomenon the authors call reactivation, which is modulated by semantic novelty of the new classes.
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