# Gradient Aligned Regression via Pairwise Losses

arXiv: https://arxiv.org/abs/2402.06104 · HTML: https://mlsanity.com/paper/2402.06104/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Delving into Deep Imbalanced Regression](https://mlsanity.com/paper/2102.09554/) (2021)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [Balanced MSE for Imbalanced Visual Regression](https://mlsanity.com/paper/2203.16427/) (2022)
- [Rank-N-Contrast: Learning Continuous Representations for Regression](https://mlsanity.com/paper/2210.01189/) (2022)
- [Efficient Algorithms for Outlier-Robust Regression](https://mlsanity.com/paper/1803.03241/) (2018)
- [RankSim: Ranking Similarity Regularization for Deep Imbalanced Regression](https://mlsanity.com/paper/2205.15236/) (2022)
- [A Framework and Benchmark for Deep Batch Active Learning for Regression](https://mlsanity.com/paper/2203.09410/) (2022)
- [Improving Deep Regression with Ordinal Entropy](https://mlsanity.com/paper/2301.08915/) (2023)
- [Machine learning modeling of superconducting critical temperature](https://mlsanity.com/paper/1709.02727/) (2017)
- [Online Robust Regression via SGD on the l1 loss](https://mlsanity.com/paper/2007.00399/) (2020)
- [ConR: Contrastive Regularizer for Deep Imbalanced Regression](https://mlsanity.com/paper/2309.06651/) (2023)
- [A survey and taxonomy of loss functions in machine learning](https://mlsanity.com/paper/2301.05579/) (2023)
- [Label Distributionally Robust Losses for Multi-class Classification: Consistency, Robustness and Adaptivity](https://mlsanity.com/paper/2112.14869/) (2021)

## Built on by (most cited first, 2 of 2)

- [LLM-Augmented Computational Phenotyping of Long Covid](https://mlsanity.com/paper/2603.18115/) (2026)
- [Revisiting Tabular Deep Regression: Objectives and the Limits of Global Early Stopping](https://mlsanity.com/paper/2610.13909/) (2026)

## Abstract (arXiv)

Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model prediction with the ground truth for each individual data sample. Recent research endeavors have introduced novel perspectives by incorporating label similarity to regression via imposing extra pairwise regularization on the latent feature space and demonstrated the effectiveness. However, there are two drawbacks for those approaches: i) their pairwise operation in latent feature space is computationally more expensive than conventional regression losses; ii) it lacks of theoretical justifications behind such regularization. In this work, we propose GAR (Gradient Aligned Regression) as a competitive alternative method in label space, which is constituted by a conventional regression loss and two pairwise label difference losses for gradient alignment including magnitude and direction. GAR enjoys: i) the same level efficiency as conventional regression loss because the quadratic complexity for the proposed pairwise losses can be reduced to linear complexity; ii) theoretical insights from learning the pairwise label difference to learning the gradient of the ground truth function. We limit our current scope as regression on the clean data setting without noises, outliers or distributional shifts, etc. We demonstrate the effectiveness of the proposed method practically on two synthetic datasets and on eight extensive real-world tasks from six benchmark datasets with other eight competitive baselines. Running time experiments demonstrate the superior efficiency of the proposed GAR over existing methods with pairwise regularization in latent feature space and ablation studies demonstrate the effectiveness of each component for GAR.