# Manifoldron: Direct Space Partition via Manifold Discovery

arXiv: https://arxiv.org/abs/2201.05279 · HTML: https://mlsanity.com/paper/2201.05279/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 96 references that are in the map.
- First posted on arXiv 14 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [A Random Forest Guided Tour](https://mlsanity.com/paper/1511.05741/) (2015)
- [Can contrastive learning avoid shortcut solutions?](https://mlsanity.com/paper/2106.11230/) (2021)
- [On Interpretability of Artificial Neural Networks: A Survey](https://mlsanity.com/paper/2001.02522/) (2020)
- [Learning in High Dimension Always Amounts to Extrapolation](https://mlsanity.com/paper/2110.09485/) (2021)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [Mad Max: Affine Spline Insights into Deep Learning](https://mlsanity.com/paper/1805.06576/) (2018)
- [Why Attentions May Not Be Interpretable?](https://mlsanity.com/paper/2006.05656/) (2020)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Chart Auto-Encoders for Manifold Structured Data](https://mlsanity.com/paper/1912.10094/) (2019)
- [Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution](https://mlsanity.com/paper/1802.06259/) (2018)
- [Enhancing Explainability of Neural Networks through Architecture Constraints](https://mlsanity.com/paper/1901.03838/) (2019)
- [TED-net: Convolution-free T2T Vision Transformer-based Encoder-decoder Dilation network for Low-dose CT Denoising](https://mlsanity.com/paper/2106.04650/) (2021)
- [On Expressivity and Trainability of Quadratic Networks](https://mlsanity.com/paper/2110.06081/) (2021)
- [Transparent Classification with Multilayer Logical Perceptrons and Random Binarization](https://mlsanity.com/paper/1912.04695/) (2019)
- [Learning with Interpretable Structure from Gated RNN](https://mlsanity.com/paper/1810.10708/) (2018)
- [Quasi-Equivalence of Width and Depth of Neural Networks](https://mlsanity.com/paper/2002.02515/) (2020)
- [Learning from Pseudo-Randomness With an Artificial Neural Network - Does God Play Pseudo-Dice?](https://mlsanity.com/paper/1801.01117/) (2018)

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

- [SQ-Swin: a Pretrained Siamese Quadratic Swin Transformer for Lettuce Browning Prediction](https://mlsanity.com/paper/2209.07683/) (2022)
- [You Only Look Omni Gradient Backpropagation for Moving Infrared Small Target Detection](https://mlsanity.com/paper/2511.13013/) (2025)

## Abstract (arXiv)

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, textite.textitg., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in urlhttps://github.com/wdayang/Manifoldron for free download and evaluation.