# LaplaceNet: A Hybrid Graph-Energy Neural Network for Deep Semi-Supervised Classification

arXiv: https://arxiv.org/abs/2106.04527 · HTML: https://mlsanity.com/paper/2106.04527/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [Residual Attention Network for Image Classification](https://mlsanity.com/paper/1704.06904/) (2017)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Label Propagation for Deep Semi-supervised Learning](https://mlsanity.com/paper/1904.04717/) (2019)
- [Interpolation Consistency Training for Semi-Supervised Learning](https://mlsanity.com/paper/1903.03825/) (2019)
- [Semi-Supervised Learning of Visual Features by Non-Parametrically Predicting View Assignments with Support Samples](https://mlsanity.com/paper/2104.13963/) (2021)
- [Dual Student: Breaking the Limits of the Teacher in Semi-supervised Learning](https://mlsanity.com/paper/1909.01804/) (2019)
- [There Are Many Consistent Explanations of Unlabeled Data: Why You Should Average](https://mlsanity.com/paper/1806.05594/) (2018)
- [SimPLE: Similar Pseudo Label Exploitation for Semi-Supervised Classification](https://mlsanity.com/paper/2103.16725/) (2021)
- [Smooth Neighbors on Teacher Graphs for Semi-supervised Learning](https://mlsanity.com/paper/1711.00258/) (2017)

## Built on by (most cited first, 5 of 5)

- [Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning](https://mlsanity.com/paper/2210.15786/) (2022)
- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)
- [NorMatch: Matching Normalizing Flows with Discriminative Classifiers for Semi-Supervised Learning](https://mlsanity.com/paper/2211.09593/) (2022)
- [CRTrack: Low-Light Semi-Supervised Multi-object Tracking Based on Consistency Regularization](https://mlsanity.com/paper/2502.16809/) (2025)
- [Topology-Aware Active Learning on Graphs](https://mlsanity.com/paper/2510.25892/) (2025)

## Abstract (arXiv)

Semi-supervised learning has received a lot of recent attention as it alleviates the need for large amounts of labelled data which can often be expensive, requires expert knowledge and be time consuming to collect. Recent developments in deep semi-supervised classification have reached unprecedented performance and the gap between supervised and semi-supervised learning is ever-decreasing. This improvement in performance has been based on the inclusion of numerous technical tricks, strong augmentation techniques and costly optimisation schemes with multi-term loss functions. We propose a new framework, LaplaceNet, for deep semi-supervised classification that has a greatly reduced model complexity. We utilise a hybrid approach where pseudolabels are produced by minimising the Laplacian energy on a graph. These pseudo-labels are then used to iteratively train a neural-network backbone. Our model outperforms state-of-the art methods for deep semi-supervised classification, over several benchmark datasets. Furthermore, we consider the application of strong-augmentations to neural networks theoretically and justify the use of a multi-sampling approach for semi-supervised learning. We demonstrate, through rigorous experimentation, that a multi-sampling augmentation approach improves generalisation and reduces the sensitivity of the network to augmentation.