LLMODE: Aligning ODEs with LLMs via Gated Token Injection for Irregular Spatio-Temporal Forecasting
Authors: Di Zhang, Jingyang Zhang, Ziqian Wang, Chi Zhang, Yikun Ban, Ziwei Zhang, Ruijie Wang
Organizations: Beihang University Beijing, China
Abstract
Large language models (LLMs) have shown promise for spatio-temporal forecasting, but existing approaches often rely on regularly sampled token sequences and struggle with irregular observations because of temporal asynchrony, representation-space misalignment, and limited context windows. We propose LLMODE, a token-efficient framework for irregular spatio-temporal forecasting with a frozen LLM backbone. LLMODE first uses a graph-aware ODE encoder to reconstruct irregular graph observations as a continuous-time latent trajectory. A Fixed-Budget Perceiver Resampler then compresses this variable-length trajectory into a fixed number of dynamic memory tokens. In parallel, compact statistical descriptors are encoded and resampled into context memory tokens. A dual-source gated cross-attention module injects both memories into the frozen LLM, enabling controlled utilization of external spatio-temporal evidence. Experiments on three real-world urban datasets and two physical-dynamics benchmarks show competitive overall performance, with clearer advantages under sparse or dynamically complex irregular sampling. Additional evaluations on unseen urban regions further demonstrate strong zero-shot generalization without adaptation.
Spatio-temporal traffic forecasting is a fundamental big data analytics task for intelligent transportation systems, where massive urban sensor streams exhibit heterogeneous, non-stationary, and structurally dynamic patterns. Although recent deep learning and large language model (LLM)-based methods have advanced traffic forecasting, they often remain temporally centered and lack effective coordination of temporal, spectral, pairwise spatial, and higher-order structural cues under evolving traffic regimes. To address this heterogeneous dependency coordination problem, we propose STHMoE, a Spatio-Temporal Hypergraph-Enhanced Mixture of Experts framework for urban traffic data forecasting. STHMoE decouples traffic dynamics into frequency-domain, time-domain, spatio-domain, and higher-order spatial representations, which are modeled by prompt-guided heterogeneous experts built upon a partially frozen LLM backbone. The first three experts leverage domain-specific statistical prompts, while the higher-order spatio expert uses a structural placeholder prompt and obtains dependency information from an adaptive hypergraph module. To capture evolving spatial structures in traffic data,, STHMoE jointly learns first-order graph dependencies and higher-order group interactions without predefined topologies. An entropy-aware MoE router with coefficient-of-variation load balancing adaptively fuses expert outputs while improving expert utilization and routing confidence. Experiments on 10 real-world traffic benchmarks show that STHMoE achieves competitive performance against temporal, spatio-temporal graph, and LLM-based baselines.
The efficient operation of modern cellular networks hinges on the accurate analysis of spatio-temporal traffic data. Mastering these patterns is essential for core network functions, chiefly forecasting future load to pre-empt congestion and imputing missing values caused by sensor failures or transmission errors to ensure data continuity. While deeply connected, forecasting and imputation have historically evolved as separate sub-fields. The dominant paradigm, Spatio-Temporal Graph Neural Networks (STGNNs), while effective, are often specialized, computationally intensive, and exhibit limited generalization. Concurrently, adapting large pre-trained language models (LLMs) offers a powerful alternative for sequence modeling, yet existing approaches provide weak structural guidance, leading to unstable convergence and a narrow focus on forecasting. To bridge these gaps, we propose U-STS-LLM, a unified framework built on a spatio-temporally steered LLM. Our core innovation is a Dynamic Spatio-Temporal Attention Bias Generator that synthesizes a persistent functional graph with transient nodal states to explicitly steer the LLM's attention. Coupled with a partially frozen backbone tuned via Low-Rank Adaptation (LoRA) and a Gated Adaptive Fusion mechanism, the model achieves stable, parameter-efficient adaptation. Trained under a unified multi-task objective, U-STS-LLM learns a holistic data representation. Extensive experiments on real-world cellular datasets demonstrate that U-STS-LLM establishes new state-of-the-art performance in both long-horizon forecasting and high-missing-rate imputation, while maintaining remarkable training efficiency and stability, offering a novel blueprint for harnessing foundation models in structured, non-linguistic domains.
Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.