Self-Gating Attention for Efficient Time Series Forecasting

Transformer architectures have shown strong potential in time series forecasting, where multi-head self-attention is widely used to capture temporal dependencies across historical timestamps. However, standard self-attention has quadratic time and memory complexity with respect to the look-back length. This cost may limit its use in resource-constrained or high-throughput forecasting systems, where fast and memory-efficient inference is important. Through qualitative and quantitative analyses, we observe that self-attention maps in time series forecasting often contain redundant patterns across different timestamps. This phenomenon can be related to the repeated temporal patterns and relatively stable temporal correlations in many real-world time series. Motivated by this observation, we propose Self-Gating Attention (SGA), a plug-and-play attention mechanism that represents the attention score with a shared learnable matrix and an input-dependent residual component. The shared matrix captures common attention patterns, while the residual component captures input-dependent variations. In this way, SGA avoids the query and key projections used in standard attention score computation, leading to linear time and score-matrix memory complexity with respect to the look-back length. We integrate SGA into several forecasting backbones and compare it with standard self-attention and lightweight attention variants on nine publicly available real-world datasets covering electricity, finance, weather, medical monitoring, human activity, and climate records. The results show that SGA improves inference efficiency on public benchmarks while maintaining competitive forecasting performance against state-of-the-art attention mechanisms. These benchmark results provide deployment-oriented evidence.

LEFT: Learnable Fusion of Tri-view Tokens for Unsupervised Time Series Anomaly Detection

As a fundamental data mining task, unsupervised time series anomaly detection (TSAD) aims to build a model for identifying abnormal timestamps without assuming the availability of annotations. A key challenge in unsupervised TSAD is that many anomalies are too subtle to exhibit detectable deviation in any single view (e.g., time domain), and instead manifest as inconsistencies across multiple views like time, frequency, and a mixture of resolutions. However, most cross-view methods rely on feature or score fusion and do not enforce analysis-synthesis consistency, meaning the frequency branch is not required to reconstruct the time signal through an inverse transform, and vice versa. In this paper, we present Learnable Fusion of Tri-view Tokens (LEFT), a unified unsupervised TSAD framework that models anomalies as inconsistencies across complementary representations. LEFT learns feature tokens from three views of the same input time series: frequency-domain tokens that embed periodicity information, time-domain tokens that capture local dynamics, and multi-scale tokens that learns abnormal patterns at varying time series granularities. By learning a set of adaptive Nyquist-constrained spectral filters, the original time series is rescaled into multiple resolutions and then encoded, allowing these multi-scale tokens to complement the extracted frequency- and time-domain information. When generating the fused representation, we introduce a novel objective that reconstructs fine-grained targets from coarser multi-scale structure, and put forward an innovative time-frequency cycle consistency constraint to explicitly regularize cross-view agreement. Experiments on real-world benchmarks show that LEFT yields the best detection accuracy against SOTA baselines, while achieving a 5x reduction on FLOPs and 8x speed-up for training.