Gated Recurrent Neural Networks with Weighted Time-Delay Feedback

In this paper, we present a novel approach to modeling long-term dependencies in sequential data by introducing a gated recurrent unit (GRU) with a weighted time-delay feedback mechanism. Our proposed model, named $\tau$-GRU, is a discretized version of a continuous-time formulation of a recurrent unit, where the dynamics are governed by delay differential equations (DDEs). We prove the existence and uniqueness of solutions for the continuous-time model and show that the proposed feedback mechanism can significantly improve the modeling of long-term dependencies. Our empirical results indicate that $\tau$-GRU outperforms state-of-the-art recurrent units and gated recurrent architectures on a range of tasks, achieving faster convergence and better generalization.

@article{erichson2025_2212.00228,
  title={ Gated Recurrent Neural Networks with Weighted Time-Delay Feedback },
  author={ N. Benjamin Erichson and Soon Hoe Lim and Michael W. Mahoney },
  journal={arXiv preprint arXiv:2212.00228},
  year={ 2025 }
}