FM-LLM: A frequency-enhanced mixture-of-experts framework for adapting LLMs to time series forecasting

FM-LLM (Frequency-Enhanced Mixture-of-Experts for adapting LLMs to Time Series Forecasting) is a framework proposed in this paper for adapting frozen Large Language Models (LLMs) to time-series forecasting. The core idea is to enable prompt-free, frequency-aware adaptation of frozen LLMs by grounding the approach in the principle of constrained asymmetric coupling.

The paper identifies two central questions motivating the work: Can we extract richer and more structured representations from time-series patches, beyond treating them as flat tokens, to better inform LLMs? and In multivariate forecasting, where variables exhibit diverse temporal and spectral characteristics, is a single linear decoder sufficient to model such heterogeneous patterns effectively?

The methodology consists of three main components:

1. Spectrum-Time Decoupling for Frozen LLM Adaptation: The paper proposes a prompt-free spectral token aligner that replaces traditional text-based prompts with high-density harmonic representations. This is achieved through a Fourier Analysis Network (FAN)-based spectral token aligner that injects structured harmonic representations directly into the frozen LLM with numerical compatibility. This design establishes an efficient information pathway into frozen LLMs, bypassing the inference latency overhead caused by sequence expansion.

2. Constrained Asymmetric Decoding Strategy: The paper introduces a heterogeneous MoE decoder with explicit structural constraints to resolve the superimposed entanglement of temporal dynamics. The decoder enforces "explicit role separation: shared experts equipped with lightweight FAN layers reconstruct the global periodic backbone, while routed experts—restricted exclusively to standard feedforward networks (FFNs)—specialize in modeling non-periodic residual dynamics. This prevents spectral bias from contaminating residual specialization, effectively disentangling periodic backbones from non-stationary residuals."

3. Holistic Time-Frequency Optimization: The paper designs a hybrid loss function that jointly supervises temporal accuracy and spectral consistency. This dual-domain objective reinforces the structural decoupling of the decoder and significantly mitigates error accumulation in long-horizon autoregressive forecasting. The loss combines a frequency-domain loss (using discrete Fourier transform with l1 norm) and a time-domain loss (MSE with signal-decay weighting), along with a sequence-wise balance loss for the MoE routing.

The main contributions are summarized as:

• Spectrum-Time Decoupling for Frozen LLM Adaptation via a prompt-free spectral token aligner

• Constrained Asymmetric Decoding Strategy with a heterogeneous MoE decoder

• Holistic Time-Frequency Optimization through a hybrid loss function

In terms of experimental results, the paper states: "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 Mean Squared Error (MSE) and 5.6% in Mean Absolute Error (MAE), with maximum gains reaching 8.0% for MSE and 8.4% for MAE. The paper also notes that FM-LLM also demonstrates robust transferability, maintaining superior performance in 10% few-shot and zero-shot forecasting scenarios."

The paper concludes: "By purposefully wiring spectral alignment and decoding—distinct from prompt-dependent alignment strategies or uniform spectral processing approaches—FM-LLM establishes an accurate, efficient, and interpretable paradigm for next-generation time-series LLMs."

Improvements to AI Systems:

1. Frequency-Aware Tokenization for Multivariate Data

• Replace flat token embeddings with Fourier Analysis Network (FAN)-based spectral token aligners that encode harmonic structures directly into frozen LLMs. This eliminates the need for text-based prompts, reducing inference latency while preserving rich temporal-frequency information.

• Improved capability: The system can process multivariate time-series (e.g., sensor arrays, financial tickers) without manual prompt engineering, achieving faster and more accurate forecasting across heterogeneous variables.

2. Constrained Asymmetric Mixture-of-Experts (MoE) Decoding

• Implement a decoder with two expert types: (a) shared experts with lightweight FAN layers for global periodic patterns, and (b) routed experts restricted to standard FFNs for non-periodic residuals. Enforce explicit role separation to prevent spectral bias contamination.

• Improved capability: The system disentangles periodic trends (e.g., seasonality) from irregular shocks (e.g., anomalies), enabling robust long-horizon forecasting and interpretable decomposition of signal components.

3. Dual-Domain Loss Optimization

• Train with a hybrid loss combining: (i) frequency-domain l1 loss on discrete Fourier transforms, (ii) time-domain MSE with signal-decay weighting, and (iii) sequence-wise balance loss for MoE routing. This jointly supervises temporal accuracy and spectral consistency.

• Improved capability: The system reduces error accumulation in autoregressive forecasting, achieving stable predictions over long horizons (e.g., 96–720 steps) and better generalization to unseen data distributions.

4. Prompt-Free Transfer Learning for Frozen LLMs

• Adapt frozen LLMs via spectral token injection rather than fine-tuning or prompt-based alignment. This preserves the LLM’s pre-trained knowledge while enabling domain-agnostic time-series processing.

• Improved capability: The system can be deployed across diverse domains (energy, traffic, finance) with minimal retraining, maintaining high performance in few-shot (10%) and zero-shot scenarios, as demonstrated by the paper’s benchmarks.

5. Scalable Heterogeneous Forecasting

• Use the constrained asymmetric decoder to handle multivariate outputs where each variable may have distinct spectral signatures, without a single linear decoder bottleneck.

• Improved capability: The system scales to high-dimensional multivariate problems (e.g., 7–862 variables) while maintaining state-of-the-art accuracy—outperforming baselines by 5.3% MSE and 5.6% MAE on average, with up to 8.4% improvement in specific cases.

What the Improved AI System Can Do:

• Forecast complex time-series with mixed periodic and non-stationary components, providing both accurate predictions and interpretable spectral decompositions.

• Operate in resource-constrained environments (e.g., edge devices) by leveraging frozen LLMs without prompt overhead, enabling real-time inference.

• Transfer across tasks with minimal data (few-shot/zero-shot) while preserving robustness, making it suitable for rapidly changing real-world scenarios like demand forecasting or anomaly detection.

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.