Learning K-U-Net with constant complexity: An Application to time series forecasting

TL;DR

This paper introduces a novel exponentially weighted stochastic gradient descent algorithm that achieves constant time complexity in training deep models for time series forecasting, addressing temporal redundancy and improving accuracy.

Contribution

The paper proposes a new stochastic gradient descent method that guarantees constant time complexity, a significant advancement over existing linear-time methods for deep time series models.

Findings

Achieves constant training complexity theoretically.

Reduces training time significantly on synthetic datasets.

Improves forecasting accuracy with K-U-Net.

Abstract

Training deep models for time series forecasting is a critical task with an inherent challenge of time complexity. While current methods generally ensure linear time complexity, our observations on temporal redundancy show that high-level features are learned 98.44\% slower than low-level features. To address this issue, we introduce a new exponentially weighted stochastic gradient descent algorithm designed to achieve constant time complexity in deep learning models. We prove that the theoretical complexity of this learning method is constant. Evaluation of this method on Kernel U-Net (K-U-Net) on synthetic datasets shows a significant reduction in complexity while improving the accuracy of the test set.