Eye movement biometrics is a secure and innovative identification method. Deep learning methods have shown good performance, but their network architecture relies on manual design and combined priori knowledge. To address these issues, we introduce automated network search (NAS) algorithms to the field of eye movement recognition and present Relax DARTS, which is an improvement of the Differentiable Architecture Search (DARTS) to realize more efficient network search and training. The key idea is to circumvent the issue of weight sharing by independently training the architecture parameters $\alpha$ to achieve a more precise target architecture. Moreover, the introduction of module input weights $\beta$ allows cells the flexibility to select inputs, to alleviate the overfitting phenomenon and improve the model performance. Results on four public databases demonstrate that the Relax DARTS achieves state-of-the-art recognition performance. Notably, Relax DARTS exhibits adaptability to other multi-feature temporal classification tasks.

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