Title: Minimal Convolutional RNNs Accelerate Spatiotemporal Learning Show Chinese title

Title: 最小卷积RNN加速时空学习

Abstract: We introduce MinConvLSTM and MinConvGRU, two novel spatiotemporal models that combine the spatial inductive biases of convolutional recurrent networks with the training efficiency of minimal, parallelizable RNNs. Our approach extends the log-domain prefix-sum formulation of MinLSTM and MinGRU to convolutional architectures, enabling fully parallel training while retaining localized spatial modeling. This eliminates the need for sequential hidden state updates during teacher forcing - a major bottleneck in conventional ConvRNN models. In addition, we incorporate an exponential gating mechanism inspired by the xLSTM architecture into the MinConvLSTM, which further simplifies the log-domain computation. Our models are structurally minimal and computationally efficient, with reduced parameter count and improved scalability. We evaluate our models on two spatiotemporal forecasting tasks: Navier-Stokes dynamics and real-world geopotential data. In terms of training speed, our architectures significantly outperform standard ConvLSTMs and ConvGRUs. Moreover, our models also achieve lower prediction errors in both domains, even in closed-loop autoregressive mode. These findings demonstrate that minimal recurrent structures, when combined with convolutional input aggregation, offer a compelling and efficient alternative for spatiotemporal sequence modeling, bridging the gap between recurrent simplicity and spatial complexity. Show Chinese abstract

Abstract: 我们引入了MinConvLSTM和MinConvGRU，两种新颖的时空模型，它们结合了卷积循环网络的空间归纳偏差与最小、可并行化RNN的训练效率。 我们的方法将MinLSTM和MinGRU的对数域前缀和公式扩展到卷积架构，实现了完全并行训练，同时保留了局部空间建模。 这消除了在教师强制过程中对序列隐藏状态更新的需求——这是传统ConvRNN模型中的主要瓶颈。 此外，我们将受xLSTM架构启发的指数门控机制引入MinConvLSTM，进一步简化了对数域计算。 我们的模型结构简单且计算高效，参数数量减少且可扩展性提高。 我们在两个时空预测任务上评估了我们的模型：纳维-斯托克斯动力学和真实世界大地水准面数据。 在训练速度方面，我们的架构显著优于标准的ConvLSTMs和ConvGRUs。 此外，我们的模型在两个领域中都实现了更低的预测误差，即使在闭环自回归模式下也是如此。 这些发现表明，当与卷积输入聚合相结合时，最小循环结构为时空序列建模提供了一种有吸引力且高效的替代方案，弥合了循环结构的简洁性与空间复杂性之间的差距。