Beyond Least Squares: Robust Regression Transformer (R2T)

Roman Gutierrez; Tony Kai Tang; Isabel Gutierrez

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arXiv · 2508.02874

Beyond Least Squares: Robust Regression Transformer (R2T)

Roman Gutierrez·Tony Kai Tang·Isabel Gutierrez

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Abstract

Robust regression techniques rely on least-squares optimization, which works well for Gaussian noise but fails in the presence of asymmetric structured noise. We propose a hybrid neural-symbolic architecture where a transformer encoder processes numerical sequences, a compression NN predicts symbolic parameters, and a fixed symbolic equation reconstructs the original sequence. Using synthetic data, the training objective is to recover the original sequence after adding asymmetric structured noise, effectively learning a symbolic fit guided by neural parameter estimation. Our model achieves a median regression MSE of 6e-6 to 3.5e-5 on synthetic wearable data, which is a 10-300 times improvement when compared with ordinary least squares fit and robust regression techniques such as Huber loss or SoftL1.

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BibTeX RIS

Roman Gutierrez, Tony Kai Tang, Isabel Gutierrez. 2025-08-04. Beyond Least Squares: Robust Regression Transformer (R2T). https://arxiv.org/abs/2508.02874

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