# NPSVC++: Nonparallel Classifiers Encounter Representation Learning

arXiv: https://arxiv.org/abs/2402.06010 · HTML: https://mlsanity.com/paper/2402.06010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [A generalized power iteration method for solving quadratic problem on the Stiefel manifold](https://mlsanity.com/paper/1701.00381/) (2017)
- [SVM-based Deep Stacking Networks](https://mlsanity.com/paper/1902.05731/) (2019)

## Abstract (arXiv)

This paper focuses on a specific family of classifiers called nonparallel support vector classifiers (NPSVCs). Different from typical classifiers, the training of an NPSVC involves the minimization of multiple objectives, resulting in the potential concerns of feature suboptimality and class dependency. Consequently, no effective learning scheme has been established to improve NPSVCs' performance through representation learning, especially deep learning. To break this bottleneck, we develop NPSVC++ based on multi-objective optimization, enabling the end-to-end learning of NPSVC and its features. By pursuing Pareto optimality, NPSVC++ theoretically ensures feature optimality across classes, hence effectively overcoming the two issues above. A general learning procedure via duality optimization is proposed, based on which we provide two applicable instances, K-NPSVC++ and D-NPSVC++. The experiments show their superiority over the existing methods and verify the efficacy of NPSVC++.