The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can be viewed as nonlinear extensions of classical autoregressive moving average models. Despite their flexibility and empirical success in machine learning, RNNs often suffer from limited interpretability and slow training, which hinders their use in statistics. This paper proposes the Parallelized RNN (ParaRNN), a novel model composed of multiple small recurrent units. ParaRNN admits an additive representation that decouples recurrent dynamics into interpretable components, whose behavior can be characterized through recurrence features. This interpretability enables its applications in nonparametric regression for time-dependent data, while the design also allows efficient parallelization. The approximation capacity and non-asymptotic prediction error bounds in a nonparametric regression setting are established for ParaRNN. Empirical results on three sequential modeling tasks further demonstrate that ParaRNN achieves performance comparable to vanilla RNNs while offering improved interpretability and efficiency.

翻译：大规模且结构复杂数据的激增推动了机器学习方法在统计建模中的整合。递归神经网络（RNN）作为处理时间依赖数据的基础模型类别，可视为经典自回归滑动平均模型的非线性扩展。尽管RNN在机器学习中展现出灵活性和实证成功，但其常受限于可解释性不足和训练速度慢的问题，这阻碍了其在统计学中的应用。本文提出并行化递归神经网络（ParaRNN），一种由多个小型递归单元组成的新型模型。ParaRNN具有加性表示形式，可将递归动态解耦为可解释的组件，其行为可通过递归特征进行表征。这种可解释性使其能够应用于时间依赖数据的非参数回归，同时其设计也支持高效并行化。本文建立了ParaRNN在非参数回归框架下的逼近能力与非渐近预测误差界。在三个序列建模任务上的实证结果进一步表明，ParaRNN在保持与标准RNN相当性能的同时，提供了更优的可解释性和效率。