# On the Reconstruction of Training Data from Group Invariant Networks

arXiv: https://arxiv.org/abs/2411.16458 · HTML: https://mlsanity.com/paper/2411.16458/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning](https://mlsanity.com/paper/1702.07464/) (2017)
- [Gradient Descent Maximizes the Margin of Homogeneous Neural Networks](https://mlsanity.com/paper/1906.05890/) (2019)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [Directional convergence and alignment in deep learning](https://mlsanity.com/paper/2006.06657/) (2020)
- [Reconstructing Training Data from Trained Neural Networks](https://mlsanity.com/paper/2206.07758/) (2022)
- [Adapting Membership Inference Attacks to GNN for Graph Classification: Approaches and Implications](https://mlsanity.com/paper/2110.08760/) (2021)
- [GraphMI: Extracting Private Graph Data from Graph Neural Networks](https://mlsanity.com/paper/2106.02820/) (2021)
- [Deconstructing Data Reconstruction: Multiclass, Weight Decay and General Losses](https://mlsanity.com/paper/2307.01827/) (2023)
- [Reconstructing Training Data From Real World Models Trained with Transfer Learning](https://mlsanity.com/paper/2407.15845/) (2024)

## Abstract (arXiv)

Reconstructing training data from trained neural networks is an active area of research with significant implications for privacy and explainability. Recent advances have demonstrated the feasibility of this process for several data types. However, reconstructing data from group-invariant neural networks poses distinct challenges that remain largely unexplored. This paper addresses this gap by first formulating the problem and discussing some of its basic properties. We then provide an experimental evaluation demonstrating that conventional reconstruction techniques are inadequate in this scenario. Specifically, we observe that the resulting data reconstructions gravitate toward symmetric inputs on which the group acts trivially, leading to poor-quality results. Finally, we propose two novel methods aiming to improve reconstruction in this setup and present promising preliminary experimental results. Our work sheds light on the complexities of reconstructing data from group invariant neural networks and offers potential avenues for future research in this domain.