Multivariate time-series (MTS) forecasting is a challenging task in many real-world non-stationary dynamic scenarios. In addition to intra-series temporal signals, the inter-series dependency also plays a crucial role in shaping future trends. How to enable the model's awareness of dependency information has raised substantial research attention. Previous approaches have either presupposed dependency constraints based on domain knowledge or imposed them using real-time feature similarity. However, MTS data often exhibit both enduring long-term static relationships and transient short-term interactions, which mutually influence their evolving states. It is necessary to recognize and incorporate the complementary dependencies for more accurate MTS prediction. The frequency information in time series reflects the evolutionary rules behind complex temporal dynamics, and different frequency components can be used to well construct long-term and short-term interactive dependency structures between variables. To this end, we propose FCDNet, a concise yet effective framework for multivariate time-series forecasting. Specifically, FCDNet overcomes the above limitations by applying two light-weight dependency constructors to help extract long- and short-term dependency information adaptively from multi-level frequency patterns. With the growth of input variables, the number of trainable parameters in FCDNet only increases linearly, which is conducive to the model's scalability and avoids over-fitting. Additionally, adopting a frequency-based perspective can effectively mitigate the influence of noise within MTS data, which helps capture more genuine dependencies. The experimental results on six real-world datasets from multiple fields show that FCDNet significantly exceeds strong baselines, with an average improvement of 6.82% on MAE, 4.98% on RMSE, and 4.91% on MAPE.

With the advance in user-friendly and powerful video editing tools, anyone can easily manipulate videos without leaving prominent visual traces. Frame-rate up-conversion (FRUC), a representative temporal-domain operation, increases the motion continuity of videos with a lower frame-rate and is used by malicious counterfeiters in video tampering such as generating fake frame-rate video without improving the quality or mixing temporally spliced videos. FRUC is based on frame interpolation schemes and subtle artifacts that remain in interpolated frames are often difficult to distinguish. Hence, detecting such forgery traces is a critical issue in video forensics. This paper proposes a frame-rate conversion detection network (FCDNet) that learns forensic features caused by FRUC in an end-to-end fashion. The proposed network uses a stack of consecutive frames as the input and effectively learns interpolation artifacts using network blocks to learn spatiotemporal features. This study is the first attempt to apply a neural network to the detection of FRUC. Moreover, it can cover the following three types of frame interpolation schemes: nearest neighbor interpolation, bilinear interpolation, and motion-compensated interpolation. In contrast to existing methods that exploit all frames to verify integrity, the proposed approach achieves a high detection speed because it observes only six frames to test its authenticity. Extensive experiments were conducted with conventional forensic methods and neural networks for video forensic tasks to validate our research. The proposed network achieved state-of-the-art performance in terms of detecting the interpolated artifacts of FRUC. The experimental results also demonstrate that our trained model is robust for an unseen dataset, unlearned frame-rate, and unlearned quality factor.