LLM-ABBA: Understanding time series via symbolic approximation

The success of large language models (LLMs) for time series has been demonstrated in previous work. Utilizing a symbolic time series representation, one can efficiently bridge the gap between LLMs and time series. However, the remaining challenge is to exploit the semantic information hidden in time series by using symbols or existing tokens of LLMs, while aligning the embedding space of LLMs according to the hidden information of time series. The symbolic time series approximation (STSA) method called adaptive Brownian bridge-based symbolic aggregation (ABBA) shows outstanding efficacy in preserving salient time series features by modeling time series patterns in terms of amplitude and period while using existing tokens of LLMs. In this paper, we introduce a method, called LLM-ABBA, that integrates ABBA into large language models for various downstream time series tasks. By symbolizing time series, LLM-ABBA compares favorably to the recent state-of-the-art (SOTA) in UCR and three medical time series classification tasks. Meanwhile, a fixed-polygonal chain trick in ABBA is introduced to \kc{avoid obvious drifting} during prediction tasks by significantly mitigating the effects of cumulative error arising from misused symbols during the transition from symbols to numerical values. In time series regression tasks, LLM-ABBA achieves the new SOTA on Time Series Extrinsic Regression (TSER) benchmarks. LLM-ABBA also shows competitive prediction capability compared to recent SOTA time series prediction results. We believe this framework can also seamlessly extend to other time series tasks.

Quantized symbolic time series approximation

Time series are ubiquitous in numerous science and engineering domains, e.g., signal processing, bioinformatics, and astronomy. Previous work has verified the efficacy of symbolic time series representation in a variety of engineering applications due to its storage efficiency and numerosity reduction. The most recent symbolic aggregate approximation technique, ABBA, has been shown to preserve essential shape information of time series and improve downstream applications, e.g., neural network inference regarding prediction and anomaly detection in time series. Motivated by the emergence of high-performance hardware which enables efficient computation for low bit-width representations, we present a new quantization-based ABBA symbolic approximation technique, QABBA, which exhibits improved storage efficiency while retaining the original speed and accuracy of symbolic reconstruction. We prove an upper bound for the error arising from quantization and discuss how the number of bits should be chosen to balance this with other errors. An application of QABBA with large language models (LLMs) for time series regression is also presented, and its utility is investigated. By representing the symbolic chain of patterns on time series, QABBA not only avoids the training of embedding from scratch, but also achieves a new state-of-the-art on Monash regression dataset. The symbolic approximation to the time series offers a more efficient way to fine-tune LLMs on the time series regression task which contains various application domains. We further present a set of extensive experiments performed across various well-established datasets to demonstrate the advantages of the QABBA method for symbolic approximation.