# Recursive Least Squares with Variable-Direction Forgetting -- Compensating for the loss of persistency

arXiv: https://arxiv.org/abs/2003.03523 · HTML: https://mlsanity.com/paper/2003.03523/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [Selective Memory Recursive Least Squares: Recast Forgetting into Memory in RBF Neural Network Based Real-Time Learning](https://mlsanity.com/paper/2211.07909/) (2022)
- [Data-Driven H-infinity Control with a Real-Time and Efficient Reinforcement Learning Algorithm: An Application to Autonomous Mobility-on-Demand Systems](https://mlsanity.com/paper/2309.08880/) (2023)
- [EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2609.30929/) (2026)

## Abstract (arXiv)

Learning depends on the ability to acquire and assimilate new information. This ability depends---somewhat counterintuitively---on the ability to forget. In particular, effective forgetting requires the ability to recognize and utilize new information to order to update a system model. This article is a tutorial on forgetting within the context of recursive least squares (RLS). To do this, RLS is first presented in its classical form, which employs uniform-direction forgetting. Next, examples are given to motivate the need for variable-direction forgetting, especially in cases where the excitation is not persistent. Some of these results are well known, whereas others complement the prior literature. The goal is to provide a self-contained tutorial of the main ideas and techniques for students and researchers whose research may benefit from variable-direction forgetting.