A Theory of Generalization in Deep Learning (arxiv.org)

A recent study introduces a non-asymptotic theory of generalization in deep learning that utilizes the empirical neural tangent kernel to analyze output space partitioning. The research highlights how error dissipates rapidly in signal-related directions while remaining trapped in dimensions corresponding to noise, which has significant implications for understanding various deep learning phenomena, including benign overfitting and grokking. Notably, the study shows that generalization can still occur even when the kernel changes modestly, thus maintaining effective learning in dynamic environments. The researchers propose a novel population-risk objective derived from a single training run without validation data, applicable to any architecture or optimizer. This objective accurately quantifies the noise within the signal channel and can be implemented alongside popular algorithms like Adam, enhancing performance by five times on grokking and improving robustness in fine-tuning under noisy conditions. This work not only elucidates the intricacies of error management in deep learning but also provides practical tools that could accelerate the development of more efficient and resilient AI models.