A dimensional R2 regression metric

ICLR 2026 Conference Submission21663 Authors

Keywords: Regression, Evaluation metric, Multidimensional data, Multidimensional score, Noise resilience, Recurrent neural network, Motor cortex recording

TL;DR: A new dimensional R2 regression metric that accepts multidimenional data, shows dimensional view, and is resilient to noise compared to conventional R2 score.

Abstract: Evaluation metrics are the primary guide in modeling. For regression tasks, the R2 score is the gold standard, offering a magnitude-agnostic measure of accuracy that captures variance. However, R2 has three key limitations: it is limited to at most two dimensional inputs, it reduces the score to a single scalar that hides rich patterns of prediction accuracy, and it is sensitive to low-variance noise channels which can yield large, uninterpretable negative values. We introduce the Dimensional R2 score (Dim-R2), a simple extension of R2 that accepts data of arbitrary dimensionality, provides a multidimensional view of accuracy, and reduces sensitivity to noise. We demonstrate its advantages on both synthetic sinusoidal data and data-constrained recurrent neural networks trained to simulate mouse neural activity during a skilled motor task. Dim-R2 offers an interpretable and flexible metric that illuminates patterns in regression accuracy, guiding regression modeling.

Primary Area: interpretability and explainable AI

Submission Number: 21663