Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN.

Due to the recurrent structure of RNN, the long information propagation path poses limitations in capturing long-term dependencies, gradient explosion/vanishing issues, and inefficient sequential execution. Based on this, we propose a novel paradigm called Parallel Gated Network (PGN) as the new successor to RNN. PGN directly captures information from previous time steps through the designed Historical Information Extraction (HIE) layer and leverages gated mechanisms to select and fuse it with the current time step information. This reduces the information propagation path to $\mathcal{O}(1)$, effectively addressing the limitations of RNN. To enhance PGN's performance in long-range time series forecasting tasks, we propose a novel temporal modeling framework called Temporal PGN (TPGN). TPGN incorporates two branches to comprehensively capture the semantic information of time series. One branch utilizes PGN to capture long-term periodic patterns while preserving their local characteristics. The other branch employs patches to capture short-term information and aggregate the global representation of the series. TPGN achieves a theoretical complexity of $\mathcal{O}(\sqrt{L})$, ensuring efficiency in its operations. Experimental results on five benchmark datasets demonstrate the state-of-the-art (SOTA) performance and high efficiency of TPGN, further confirming the effectiveness of PGN as the new successor to RNN in long-range time series forecasting. The code is available in this repository: \url{https://github.com/Water2sea/TPGN}.

Despite large incentives, correctness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a combinatorial reduction in complexity in programming in terms of specifications instead of algorithms, and arbitrary desired properties can be expressed and enforced in specifications directly. However, limitations on performance have prevented programming with declarative specifications from becoming a mainstream technique for general-purpose programming. To address the performance bottleneck in deriving an algorithm from a specification, I propose information-gain computation, a framework where an adaptive evaluation strategy is used to efficiently perform a search which derives algorithms that provide information about a query via the most efficient routes. Within this framework, opportunities to compress the search space present themselves, which suggest that information-theoretic bounds on the performance of such a system might be articulated and a system designed to achieve them. In a preliminary empirical study of adaptive evaluation for a simple test program, the evaluation strategy adapts successfully to evaluate a query efficiently.