# Sum of Ranked Range Loss for Supervised Learning

arXiv: https://arxiv.org/abs/2106.03300 · HTML: https://mlsanity.com/paper/2106.03300/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 82 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 29 of 29)

- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise](https://mlsanity.com/paper/1802.05300/) (2018)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Learning from Noisy Labels with Distillation](https://mlsanity.com/paper/1703.02391/) (2017)
- [Learning From Noisy Large-Scale Datasets With Minimal Supervision](https://mlsanity.com/paper/1701.01619/) (2017)
- [Learning from Untrusted Data](https://mlsanity.com/paper/1611.02315/) (2016)
- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [Ordered SGD: A New Stochastic Optimization Framework for Empirical Risk Minimization](https://mlsanity.com/paper/1907.04371/) (2019)
- [Deep Bilevel Learning](https://mlsanity.com/paper/1809.01465/) (2018)
- [Object detection via a multi-region & semantic segmentation-aware CNN model](https://mlsanity.com/paper/1505.01749/) (2015)
- [Improving Pairwise Ranking for Multi-label Image Classification](https://mlsanity.com/paper/1704.03135/) (2017)
- [Loss Functions for Top-k Error: Analysis and Insights](https://mlsanity.com/paper/1512.00486/) (2015)
- [On the Consistency of Top-k Surrogate Losses](https://mlsanity.com/paper/1901.11141/) (2019)
- [Minimizing the Maximal Loss: How and Why?](https://mlsanity.com/paper/1602.01690/) (2016)
- [Top-k Multiclass SVM](https://mlsanity.com/paper/1511.06683/) (2015)
- [Learning by Minimizing the Sum of Ranked Range](https://mlsanity.com/paper/2010.01741/) (2020)
- [Choosing the Sample with Lowest Loss makes SGD Robust](https://mlsanity.com/paper/2001.03316/) (2020)
- [Towards Noise-resistant Object Detection with Noisy Annotations](https://mlsanity.com/paper/2003.01285/) (2020)
- [Analysis and Optimization of Loss Functions for Multiclass, Top-k, and Multilabel Classification](https://mlsanity.com/paper/1612.03663/) (2016)
- [Doubly-stochastic mining for heterogeneous retrieval](https://mlsanity.com/paper/2004.10915/) (2020)
- [Stochastic DCA for minimizing a large sum of DC functions with application to Multi-class Logistic Regression](https://mlsanity.com/paper/1911.03992/) (2019)
- [Stochastic Optimization for Machine Learning](https://mlsanity.com/paper/1308.3509/) (2013)
- [Difference of Convex Functions Programming Applied to Control with Expert Data](https://mlsanity.com/paper/1606.01128/) (2016)

## Built on by (most cited first, 23 of 23)

- [Preserving Fairness Generalization in Deepfake Detection](https://mlsanity.com/paper/2402.17229/) (2024)
- [Eyes Tell All: Irregular Pupil Shapes Reveal GAN-generated Faces](https://mlsanity.com/paper/2109.00162/) (2021)
- [Improving Fairness in Deepfake Detection](https://mlsanity.com/paper/2306.16635/) (2023)
- [Robust Attentive Deep Neural Network for Exposing GAN-generated Faces](https://mlsanity.com/paper/2109.02167/) (2021)
- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Robust CLIP-Based Detector for Exposing Diffusion Model-Generated Images](https://mlsanity.com/paper/2404.12908/) (2024)
- [Humor in AI: Massive Scale Crowd-Sourced Preferences and Benchmarks for Cartoon Captioning](https://mlsanity.com/paper/2406.10522/) (2024)
- [Robust Light-Weight Facial Affective Behavior Recognition with CLIP](https://mlsanity.com/paper/2403.09915/) (2024)
- [Distributionally Robust Survival Analysis: A Novel Fairness Loss Without Demographics](https://mlsanity.com/paper/2211.10508/) (2022)
- [UU-Mamba: Uncertainty-aware U-Mamba for Cardiac Image Segmentation](https://mlsanity.com/paper/2405.17496/) (2024)
- [Fairness in Survival Analysis with Distributionally Robust Optimization](https://mlsanity.com/paper/2409.10538/) (2024)
- [Robust COVID-19 Detection in CT Images with CLIP](https://mlsanity.com/paper/2403.08947/) (2024)
- [Open-Eye: An Open Platform to Study Human Performance on Identifying AI-Synthesized Faces](https://mlsanity.com/paper/2205.06680/) (2022)
- [Robustly Optimized Deep Feature Decoupling Network for Fatty Liver Diseases Detection](https://mlsanity.com/paper/2406.17338/) (2024)
- [Outlier Robust Adversarial Training](https://mlsanity.com/paper/2309.05145/) (2023)
- [Uncertainty-Aware Explainable Recommendation with Large Language Models](https://mlsanity.com/paper/2402.03366/) (2024)
- [Robust AI-Generated Face Detection with Imbalanced Data](https://mlsanity.com/paper/2505.02182/) (2025)
- [Robust Fairness Vision-Language Learning for Medical Image Analysis](https://mlsanity.com/paper/2505.03153/) (2025)
- [An Uncertainty-Aware Generalization Framework for Cardiovascular Image Segmentation](https://mlsanity.com/paper/2409.14305/) (2024)
- [Synergistic Network Learning and Label Correction for Noise-robust Image Classification](https://mlsanity.com/paper/2202.13472/) (2022)
- [Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination](https://mlsanity.com/paper/2601.11420/) (2026)
- [Robust Multi-Source Covid-19 Detection in CT Images](https://mlsanity.com/paper/2604.03320/) (2026)
- [Robust Fair Disease Diagnosis in CT Images](https://mlsanity.com/paper/2604.09710/) (2026)

## Abstract (arXiv)

In forming learning objectives, one oftentimes needs to aggregate a set of individual values to a single output. Such cases occur in the aggregate loss, which combines individual losses of a learning model over each training sample, and in the individual loss for multi-label learning, which combines prediction scores over all class labels. In this work, we introduce the sum of ranked range (SoRR) as a general approach to form learning objectives. A ranked range is a consecutive sequence of sorted values of a set of real numbers. The minimization of SoRR is solved with the difference of convex algorithm (DCA). We explore two applications in machine learning of the minimization of the SoRR framework, namely the AoRR aggregate loss for binary/multi-class classification at the sample level and the TKML individual loss for multi-label/multi-class classification at the label level. A combination loss of AoRR and TKML is proposed as a new learning objective for improving the robustness of multi-label learning in the face of outliers in sample and labels alike. Our empirical results highlight the effectiveness of the proposed optimization frameworks and demonstrate the applicability of proposed losses using synthetic and real data sets.