IMRouter: Imbalance-aware Temporal Pattern Routing for LLM-based Time Series Forecasting

Large Language Models (LLMs) have shown strong potential in multivariate time series forecasting and anomaly detection. Existing studies predominantly inject temporal information into LLMs via direct numerical tokenization or heuristic textual descriptions. However, LLMs still face difficulty in perceiving the underlying structural patterns of numerical time series, particularly the seasonal and trend components obscured by discrete numerical tokens. To bridge this gap, we propose FreSia, a frequency-aware framework that establishes an effective alignment between the semantic space of LLMs and the frequency space of time series. Specifically, FGPrompt, a Frequency-Guided Prompt mechanism within FreSia, distills the frequency-domain structures of time series and projects them into prompts tailored to the semantic space of LLMs. Furthermore, we introduce a Global-driven Context Learning (GCL) component, which uses a global CLS-driven probe to generate global context to bridge the time-frequency domain gap and fuse the multi-modal information. Experiments on eight forecasting benchmarks show that FreSia achieves average improvements of 13.48% and 8.06% in MSE and MAE, respectively.

Adapting pretrained Large Language Models (LLMs) for time series forecasting primarily relies on token-level linguistic-temporal alignment, leading to the stacking of logically disjointed tokens as input. While empirically effective, these methods overlook a fundamental capability of LLMs: modeling linguistic logic and structure, rather than merely processing token features. To address this limitation, we propose the Markovian-Guided Structure-Aware Alignment (MGSAA). Our core contribution is a framework that transcends pointwise feature matching to achieve global structural isomorphism between the linguistic and temporal domains. Specifically, MGSAA distills latent evolutionary patterns of language within LLMs into a Markovian state transition graph, which is transferred as a structural prior to the time series domain. Under this prior, time series patches are decoded into latent states and then aligned via state-constrained cross-attention. Ultimately, MGSAA generates a token sequence topologically isomorphic to the LLM's inherent mental structure, reactivating its reasoning capabilities for forecasting. Comprehensive evaluations across multiple benchmarks demonstrate that MGSAA achieves state-of-the-art performance, providing an innovative solution for cross-modal alignment in LLM for time series forecasting. Code is available at https://github.com/sunzju/MGSAA.

Recent advances in Large Language Models (LLMs) have spurred cross-modal solutions for time-series forecasting. However, existing methods rely heavily on textual prompts for modality alignment-introducing nontrivial computational overhead and failing to leverage the rich spectral dynamics inherent in time-series data. To enable prompt-free, frequency-aware adaptation of frozen LLMs, we propose FM-LLM (Frequency-Enhanced Mixture-of-Experts for adapting LLMs to Time Series Forecasting), an autoregressive framework grounded in constrained asymmetric coupling. A Fourier Analysis Network (FAN)-based spectral token aligner injects structured harmonic representations directly into the frozen LLM with numerical compatibility. An asymmetric Mixture-of-Experts (MoE) decoder enforces role separation: shared experts with lightweight FAN layers reconstruct the global periodic backbone, while routed experts-restricted to standard FFNs-specialize in modeling non-periodic residual dynamics. A time-frequency hybrid loss function jointly optimizes temporal accuracy and spectral consistency, mitigating error accumulation during long-horizon autoregressive rollouts. Evaluated across eleven public benchmarks, FM-LLM achieves state-of-the-art performance on 59 out of 78 evaluation metrics. Compared to the strongest autoregressive LLM-based baseline, it delivers average improvements of 5.3% in MSE and 5.6% in MAE, with maximum gains reaching 8.0% for MSE and 8.4% for MAE. FM-LLM also demonstrates robust transferability, maintaining superior performance in 10% few-shot and zero-shot forecasting scenarios.