Quantized symbolic time series approximation

2024-11-20

arXiv.org

AI Summary

To address the high storage overhead and poor scalability of symbolic time-series approximation methods—particularly on high-performance hardware and with large language models (LLMs)—this paper proposes QABBA, the first symbolic representation framework integrating low-bit quantization into the ABBA (Adaptive Brownian Bridge Approximation) paradigm. Leveraging theoretical analysis, QABBA derives a tight upper bound on quantization error, enabling high-fidelity symbolic reconstruction without retraining downstream embeddings. The resulting discrete symbol sequences are directly consumable by LLMs for end-to-end time-series regression fine-tuning. Evaluated on the Monash Time Series Regression Benchmark, QABBA achieves new state-of-the-art performance while reducing storage requirements by orders of magnitude. Crucially, it preserves ABBA’s original reconstruction accuracy and computational efficiency. Extensive experiments across diverse domains confirm QABBA’s robustness and generalizability.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Machine Learning: Time-Series/Data Streams
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Develops QABBA for efficient symbolic time series approximation
• Balances quantization error and storage efficiency in QABBA
• Enhances LLM performance for time series regression tasks

Innovation

• Quantization-based ABBA symbolic approximation technique
• Improved storage efficiency with original speed
• Enhances LLMs for time series regression