Yanjie Fu

Wei Fan, Shun Zheng, Xiaohan Yi et al.

Periodic time series (PTS) forecasting plays a crucial role in a variety of industries to foster critical tasks, such as early warning, pre-planning, resource scheduling, etc. However, the complicated dependencies of the PTS signal on its inherent periodicity as well as the sophisticated composition of various periods hinder the performance of PTS forecasting. In this paper, we introduce a deep expansion learning framework, DEPTS, for PTS forecasting. DEPTS starts with a decoupled formulation by introducing the periodic state as a hidden variable, which stimulates us to make two dedicated modules to tackle the aforementioned two challenges. First, we develop an expansion module on top of residual learning to perform a layer-by-layer expansion of those complicated dependencies. Second, we introduce a periodicity module with a parameterized periodic function that holds sufficient capacity to capture diversified periods. Moreover, our two customized modules also have certain interpretable capabilities, such as attributing the forecasts to either local momenta or global periodicity and characterizing certain core periodic properties, e.g., amplitudes and frequencies. Extensive experiments on both synthetic data and real-world data demonstrate the effectiveness of DEPTS on handling PTS. In most cases, DEPTS achieves significant improvements over the best baseline. Specifically, the error reduction can even reach up to 20% for a few cases. Finally, all codes are publicly available.

Wangyang Ying, Haoyue Bai, Nanxu Gong et al.

The data-to-equation (Data2Eqn) task aims to discover interpretable mathematical equations that map observed values to labels, offering physical insights and broad applicability across academic and industrial domains. Genetic programming and traditional deep learning-based approaches suffer from search inefficiency and poor generalization on small task-specific datasets. Foundation models showed promise in this area, but existing approaches suffer from: 1) They are pretrained on general-purpose data distributions, making them less effective for domain-specific tasks; and 2) their training objectives focus on token-level alignment, overlooking mathematical semantics, which can lead to inaccurate equations. To address these issues, we aim to enhance the domain adaptability of foundation models for Data2Eqn tasks. In this work, we propose a reinforcement learning-based finetuning framework that directly optimizes the generation policy of a pretrained model through reward signals derived from downstream numerical fitness. Our method allows the model to adapt to specific and complex data distributions and generate mathematically meaningful equations. Extensive experiments demonstrate that our approach improves both the accuracy and robustness of equation generation under complex distributions.