While Transformer-based architectures have established themselves as a dominant paradigm in Multivariate Time Series Forecasting (MTSF), their core self-attention mechanism inherently functions as a low-pass filter, systematically smoothing out high-frequency signals vital for sharp local changes. Recent advancements have increasingly incorporated frequency-domain operations to address this bias, however, most existing designs rely on fixed spectral bases and apply sequence-wise (uniform) modulation, implicitly assuming a time-invariant frequency response. This overlooks a key property of real-world series that their spectral characteristics often evolve over time, making uniform modulation insufficient for capturing fine-grained temporal dynamics. To tackle these limitations, we propose FAiT, a Frequency-Aware inverted Transformer. Specifically, FAiT rectifies the spectral bias internally through Inverted Attention, which interprets the attention map as a learnable low-pass operator and constructs a dedicated complementary high-pass branch by inverting the attention matrix to recover attenuated transient signals. Furthermore, FAiT introduces Dynamic Temporal-Frequency Modulation (DTFM), which synthesizes instance-conditioned weights to adaptively re-calibrate the energy of spectral sub-bands, enabling fine-grained control over evolving multi-scale patterns. Extensive experiments on widely used benchmarks demonstrate that FAiT consistently outperforms state-of-the-art Transformer-based and frequency-enhanced baselines, while maintaining computational efficiency.
Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. Existing Transformer- and diffusion-based imputers achieve strong performance, but they often rely mainly on time-domain modeling and lack adaptive spectral bias for recovering structured temporal gaps. We propose FADTI, a Fourier- and attention-driven diffusion framework for multivariate time series imputation. FADTI introduces a Fourier Bias Projection (FBP) module that injects learnable frequency-aware bias into intermediate hidden states during denoising. It projects intermediate hidden states onto Fourier bases, avoiding direct spectral estimation from masked or zero-filled inputs. With DFT, STFT, and FSST instantiations, FBP captures global periodicity, localized time--frequency variations, and non-stationary oscillatory patterns. By coupling FBP with self-attention and gated convolution, FADTI integrates frequency-domain guidance, temporal dependency modeling, and probabilistic denoising in a unified framework. Experiments on multiple benchmarks, including a new biological imputation benchmark, show that FADTI improves accuracy, uncertainty estimation, and sampling efficiency, especially under high missing rates and structured missing patterns. Code is available at https://github.com/RazeenLI/FADTI
A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers. We argue that this gap arises from a mismatch in the sequence-modeling primitive: while many time-series dynamics are governed by global temporal operators (e.g., filtering and harmonic structure), standard attention forms each output as a convex combination of inputs. This restricts its ability to represent signed and oscillatory transformations that are fundamental to temporal signal processing. We formalize this limitation as a simplex-constrained mixing bottleneck in softmax attention, which becomes especially restrictive for operator-driven time-series tasks. To address this, we propose Temporal Operator Attention (TOA), a framework that augments attention with explicit, learnable sequence-space operators, enabling direct signed mixing across time while preserving input-dependent adaptivity. To make dense N×N operators practical, we introduce Stochastic Operator Regularization, a high-variance dropout mechanism that stabilizes training and prevents trivial memorization. Across forecasting, anomaly detection, and classification benchmarks, TOA consistently improves performance when integrated into standard backbones such as PatchTST and iTransformer, with particularly strong gains in reconstruction-heavy tasks. These results suggest that explicit operator learning is a key ingredient for effective time-series modeling.
Time series forecasting plays a pivotal role in critical sectors such as finance, energy, transportation, and meteorology. However, Long-term Time Series Forecasting (LTSF) remains a significant challenge because real-world signals contain highly entangled temporal dynamics that are difficult to fully capture from a purely 1D perspective. To break this representation bottleneck, we propose TriTS, a novel cross-modal disentanglement framework that projects 1D time series into orthogonal time, frequency, and 2D-vision spaces.To seamlessly bridge the 1D-to-2D modality gap without the prohibitive O(N2) computational overhead of Vision Transformers (ViTs), we introduce a Period-Aware Reshaping strategy and incorporate Visual Mamba (Vim). This approach efficiently models cross-period dependencies as global visual textures while maintaining linear computational complexity. Complementing this, we design a Multi-Resolution Wavelet Mixing (MR-WM) module for the frequency modality, which explicitly decouples non-stationary signals into trend and noise components to achieve fine-grained time-frequency localization. Finally, a streaming linear branch is retained in the time domain to anchor numerical stability. By dynamically fusing these three complementary representations, TriTS effectively adapts to diverse data contexts. Extensive experiments across multiple benchmark datasets demonstrate that TriTS achieves state-of-the-art (SOTA) performance, fundamentally outperforming existing vision-based forecasters by drastically reducing both parameter count and inference latency.