# Multiclass Graph-Based Large Margin Classifiers: Unified Approach for Support Vectors and Neural Networks

arXiv: https://arxiv.org/abs/2512.13410 · HTML: https://mlsanity.com/paper/2512.13410/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 51 references that are in the map.
- First posted on arXiv 15 Dec 2025.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [Well-tuned Simple Nets Excel on Tabular Datasets](https://mlsanity.com/paper/2106.11189/) (2021)

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

- [Large margin classifier with graph-based adaptive regularization](https://mlsanity.com/paper/2605.02027/) (2026)
- [Learning Kernels by Alignment for Multiclass Bayes Classification](https://mlsanity.com/paper/2609.06474/) (2026)

## Abstract (arXiv)

While large margin classifiers are originally an outcome of an optimization framework, support vectors (SVs) can be obtained from geometric approaches. This article presents advances in the use of Gabriel graphs (GGs) in binary and multiclass classification problems. For Chipclass, a hyperparameter-less and optimization-less GG-based binary classifier, we discuss how activation functions and support edge (SE)-centered neurons affect the classification, proposing smoother functions and structural SV (SSV)-centered neurons to achieve margins with low probabilities and smoother classification contours. We extend the neural network architecture, which can be trained with backpropagation with a softmax function and a cross-entropy loss, or by solving a system of linear equations. A new subgraph-/distance-based membership function for graph regularization is also proposed, along with a new GG recomputation algorithm that is less computationally expensive than the standard approach. Experimental results with the Friedman test show that our method was better than previous GG-based classifiers and statistically equivalent to tree-based models.