$\textbf{S}^2$IP-LLM: Semantic Space Informed Prompt Learning with LLM
  for Time Series Forecasting
Zijie Pan Yushan Jiang Sahil Garg Anderson Schneider Yuriy Nevmyvaka Dongjin Song
Recently, there has been a growing interest in leveraging pre-trained large
language models (LLMs) for various time series applications. However, the
semantic space of LLMs, established through the pre-training, is still
underexplored and may help yield more distinctive and informative
representations to facilitate time series forecasting. To this end, we propose
Semantic Space Informed Prompt learning with LLM ($S^2$IP-LLM) to align the
pre-trained semantic space with time series embeddings space and perform time
series forecasting based on learned prompts from the joint space. We first
design a tokenization module tailored for cross-modality alignment, which
explicitly concatenates patches of decomposed time series components to create
embeddings that effectively encode the temporal dynamics. Next, we leverage the
pre-trained word token embeddings to derive semantic anchors and align selected
anchors with time series embeddings by maximizing the cosine similarity in the
joint space. This way, $S^2$IP-LLM can retrieve relevant semantic anchors as
prompts to provide strong indicators (context) for time series that exhibit
different temporal dynamics. With thorough empirical studies on multiple
benchmark datasets, we demonstrate that the proposed $S^2$IP-LLM can achieve
superior forecasting performance over state-of-the-art baselines. Furthermore,
our ablation studies and visualizations verify the necessity of prompt learning
informed by semantic space.