Recursive Least Squares

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The Condition-Number Barrier in Sparse Least Squares
Aug 3, 2026Honghao Lin, Vahab Mirrokni, David P. WoodruffRecursive Least Squares Sparse Recovery
Google Research, Carnegie Mellon University / Texas A&M University. · Google Research. · Google Research and Carnegie Mellon University.
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Aug 1, 2026Viacheslav Barkov, Jonas Schmidinger, Robin Gebbers +1Tabular Foundation Models Recursive Least Squares
Osnabrück University, Joint Lab Artificial Intelligence and Data Science, Osnabrück, Germany · Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Department of Agromechatronics, Potsdam, Germany · German Research Center for Artificial Intelligence (DFKI), Cooperative and Autonomous Systems (CAS), Osnabrück, Germany
Dense Soft Weighting for Radar Ego-Velocity Estimation
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Imperial College London
Near-Optimal Learning of Gaussian Sobolev Operators
Jul 8, 2026Ben Adcock, Michael Griebel, Gregor MaierRecursive Least Squares Operator Learning
Department of Mathematics, Simon Fraser University, Burnaby BC, Canada · Institute for Numerical Simulation, University of Bonn, Bonn, Germany · Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin, Germany
Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics
Jun 13, 2026Weibin Gu, Chen Yang, Lu Shi +1Online System Identification Recursive Least Squares
1Tsinghua University, PR China · 2China University of Petroleum-Beijing at Karamay, PR China · 3Xinchen Qihang Inc., PR China
Attitude-Aided Linear Calibration of Triaxial Accelerometers
Jun 4, 2026Yongqiang Yu, Tian Huang, Yipeng YangRecursive Least Squares Model Calibration
1Independent researcher · 2Harbin Institute of Technology
PLS in the Mirror of Self-Attention
May 27, 2026Jiangsheng, YouRecursive Least Squares Self-Attention
Jason
Online Nonstochastic Prediction: Logarithmic Regret via Predictive Online Least Squares
May 6, 2026Chih-Fan Pai, Yang ZhengRecursive Least Squares Regret Minimization
Department of Electrical and Computer Engineering, UC San Diego
Real-Time Non-Contact Force Compensation for Wrist-Mounted Force/Torque Sensors in Haptic-Enabled Robotic Surgery Training
Apr 26, 2026Walid Shaker, Mustafa Suphi ErdenRecursive Least Squares Haptic Feedback
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

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The Condition-Number Barrier in Sparse Least Squares

Honghao Lin, Vahab Mirrokni, David P. Woodruff

Google Research, Carnegie Mellon University / Texas A&M University. · Google Research. · Google Research and Carnegie Mellon University.

Recursive Least Squares Sparse Recovery Approximation Algorithms

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In [AS21], Axiotis and Sviridenko conjectured that the linear dependence on the restricted condition number in sparse convex optimization cannot be improved by a polynomial-time algorithm. We establish their conjectured lower bound for least-squares objectives, conditional on the randomized exact-volume Small-Set Expansion Hypothesis in the weighted regular-graph formulation of Raghavendra, Steurer, and Tulsiani [RST12]. Concretely, for every fixed

γ\in(0,1]

, there is no randomized polynomial-time algorithm that, with probability at least

2/3

, returns a vector

x

such that, writing

s=\lVert x\rVert_0

\lVert Ax-b\rVert_2^2 \leq \min_{\lVert z\rVert_0\leq k}\lVert Az-b\rVert_2^2+\varepsilon \quad\text{and}\quad s=O\!\left(k\,κ_{s+k}^{\,1-γ}\right),

where

κ_r

is the restricted condition number at sparsity level

r

. The result holds even on rational instances with

A

of full column rank. The proof was first obtained using a fully automated Gemini-based agentic system developed internally at Google. The authors have verified the proof and edited it for clarity of presentation.

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