# Joint Feature and Differentiable  k -NN Graph Learning using Dirichlet Energy

arXiv: https://arxiv.org/abs/2305.12396 · HTML: https://mlsanity.com/paper/2305.12396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 52 references that are in the map.
- First posted on arXiv 21 May 2023.

## Builds on (most cited first, 11 of 11)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Differentiable Ranks and Sorting using Optimal Transport](https://mlsanity.com/paper/1905.11885/) (2019)
- [Weakly-Supervised Concealed Object Segmentation with SAM-based Pseudo Labeling and Multi-scale Feature Grouping](https://mlsanity.com/paper/2305.11003/) (2023)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [Interpretable Geometric Deep Learning via Learnable Randomness Injection](https://mlsanity.com/paper/2210.16966/) (2022)
- [Where to Pay Attention in Sparse Training for Feature Selection?](https://mlsanity.com/paper/2211.14627/) (2022)

## Built on by (most cited first, 1 of 1)

- [Spectral Initialization and Scheduled Graph Smoothness for Uncertain Knowledge Graph Completion](https://mlsanity.com/paper/2609.02519/) (2026)

## Abstract (arXiv)

Feature selection (FS) plays an important role in machine learning, which extracts important features and accelerates the learning process. In this paper, we propose a deep FS method that simultaneously conducts feature selection and differentiable  k -NN graph learning based on the Dirichlet Energy. The Dirichlet Energy identifies important features by measuring their smoothness on the graph structure, and facilitates the learning of a new graph that reflects the inherent structure in new feature subspace. We employ Optimal Transport theory to address the non-differentiability issue of learning  k -NN graphs in neural networks, which theoretically makes our method applicable to other graph neural networks for dynamic graph learning. Furthermore, the proposed framework is interpretable, since all modules are designed algorithmically. We validate the effectiveness of our model with extensive experiments on both synthetic and real-world datasets.