Generalization Analysis and Method for Domain Generalization for a Family of Recurrent Neural Networks
This work addresses the poor out-of-distribution (OOD) generalization, lack of theoretical guarantees, and limited interpretability of recurrent neural networks (RNNs) on temporal data. By modeling the post-training RNN state dynamics as a nonlinear closed-loop system, the authors introduce Koopman operator theory—applied here for the first time to RNNs—to approximate this system with a linear representation. Combining this linearization with spectral analysis, they rigorously quantify the worst-case impact of domain shift on generalization error. Based on this analysis, they derive a generalization error bound for non-i.i.d. temporal data and propose an interpretable, robust domain generalization training method. Experiments across multiple temporal tasks demonstrate that the proposed approach significantly reduces OOD generalization error and enhances model robustness to domain shifts.