# A dimensional R2 regression metric

arXiv: https://arxiv.org/abs/2605.01066 · HTML: https://mlsanity.com/paper/2605.01066/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 8 of 8)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Tutorial on Variational Autoencoders](https://mlsanity.com/paper/1606.05908/) (2016)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Toward Next-Generation Artificial Intelligence: Catalyzing the NeuroAI Revolution](https://mlsanity.com/paper/2210.08340/) (2022)
- [Artificial neural networks for neuroscientists: A primer](https://mlsanity.com/paper/2006.01001/) (2020)
- [Image Response Regression via Deep Neural Networks](https://mlsanity.com/paper/2006.09911/) (2020)
- [Review learning: Real world validation of privacy preserving continual learning across medical institutions](https://mlsanity.com/paper/2210.09394/) (2022)
- [Dual policy as self-model for planning](https://mlsanity.com/paper/2306.04440/) (2023)

## Abstract (arXiv)

R2 score is the standard metric for evaluating regression tasks, offering a normalized 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 three multidimensional regression datasets. Dim-R2 offers an interpretable and flexible metric that highlights patterns in regression accuracy, guiding regression modeling.