Takeuchi's Information Criteria as Generalization Measures for DNNs Close to NTK Regime
Generalization measures are intensively studied in the machine learning community for better modeling generalization gaps. However, establishing a reliable generalization measure for statistical singular models such as deep neural networks (DNNs) is challenging due to the complex nature of the singular models. We focus on a classical measure called Takeuchi's Information Criteria (TIC) to investigate allowed conditions in which the criteria can well explain generalization gaps caused by DNNs. In fact, theory indicates the applicability of TIC near the neural tangent kernel (NTK) regime. Experimentally, we trained more than 5,000 DNN models with 12 DNN architectures including large models (e.g., VGG16) and 4 datasets, and estimated corresponding TICs in order to comprehensively study the relationship between the generalization gap and the TIC estimates. We examine several approximation methods to estimate TIC with feasible computational load and investigate the accuracy trade-off. Experimental results indicate that estimated TIC well correlates generalization gaps under the conditions that are close to NTK regime. Outside the NTK regime, such correlation disappears, shown theoretically and empirically. We further demonstrate that TIC can yield better trial pruning ability for hyperparameter optimization over existing methods.
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