# Maximum Knowledge Orthogonality Reconstruction with Gradients in Federated Learning

arXiv: https://arxiv.org/abs/2310.19222 · HTML: https://mlsanity.com/paper/2310.19222/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 23 of 23)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Exploiting Unintended Feature Leakage in Collaborative Learning](https://mlsanity.com/paper/1805.04049/) (2018)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [Beyond Inferring Class Representatives: User-Level Privacy Leakage From Federated Learning](https://mlsanity.com/paper/1812.00535/) (2018)
- [Evaluating Gradient Inversion Attacks and Defenses in Federated Learning](https://mlsanity.com/paper/2112.00059/) (2021)
- [Protection Against Reconstruction and Its Applications in Private Federated Learning](https://mlsanity.com/paper/1812.00984/) (2018)
- [When the Curious Abandon Honesty: Federated Learning Is Not Private](https://mlsanity.com/paper/2112.02918/) (2021)
- [Robbing the Fed: Directly Obtaining Private Data in Federated Learning with Modified Models](https://mlsanity.com/paper/2110.13057/) (2021)
- [R-GAP: Recursive Gradient Attack on Privacy](https://mlsanity.com/paper/2010.07733/) (2020)
- [Provable Defense against Privacy Leakage in Federated Learning from Representation Perspective](https://mlsanity.com/paper/2012.06043/) (2020)
- [Fishing for User Data in Large-Batch Federated Learning via Gradient Magnification](https://mlsanity.com/paper/2202.00580/) (2022)
- [Auditing Privacy Defenses in Federated Learning via Generative Gradient Leakage](https://mlsanity.com/paper/2203.15696/) (2022)
- [Eluding Secure Aggregation in Federated Learning via Model Inconsistency](https://mlsanity.com/paper/2111.07380/) (2021)
- [GradViT: Gradient Inversion of Vision Transformers](https://mlsanity.com/paper/2203.11894/) (2022)
- [Gradient Disaggregation: Breaking Privacy in Federated Learning by Reconstructing the User Participant Matrix](https://mlsanity.com/paper/2106.06089/) (2021)
- [Privacy-preserving Collaborative Learning with Automatic Transformation Search](https://mlsanity.com/paper/2011.12505/) (2020)
- [User-Level Label Leakage from Gradients in Federated Learning](https://mlsanity.com/paper/2105.09369/) (2021)

## Built on by (most cited first, 4 of 4)

- [Exploring the Vulnerabilities of Federated Learning: A Deep Dive into Gradient Inversion Attacks](https://mlsanity.com/paper/2503.11514/) (2025)
- [Cutting Through Privacy: A Hyperplane-Based Data Reconstruction Attack in Federated Learning](https://mlsanity.com/paper/2505.10264/) (2025)
- [No More Guessing: a Verifiable Gradient Inversion Attack in Federated Learning](https://mlsanity.com/paper/2604.15063/) (2026)
- [On the Detectability of Active Gradient Inversion Attacks in Federated Learning](https://mlsanity.com/paper/2511.10502/) (2025)

## Abstract (arXiv)

Federated learning (FL) aims at keeping client data local to preserve privacy. Instead of gathering the data itself, the server only collects aggregated gradient updates from clients. Following the popularity of FL, there has been considerable amount of work, revealing the vulnerability of FL approaches by reconstructing the input data from gradient updates. Yet, most existing works assume an FL setting with unrealistically small batch size, and have poor image quality when the batch size is large. Other works modify the neural network architectures or parameters to the point of being suspicious, and thus, can be detected by clients. Moreover, most of them can only reconstruct one sample input from a large batch. To address these limitations, we propose a novel and completely analytical approach, referred to as the maximum knowledge orthogonality reconstruction (MKOR), to reconstruct clients' input data. Our proposed method reconstructs a mathematically proven high quality image from large batches. MKOR only requires the server to send secretly modified parameters to clients and can efficiently and inconspicuously reconstruct the input images from clients' gradient updates. We evaluate MKOR's performance on the MNIST, CIFAR-100, and ImageNet dataset and compare it with the state-of-the-art works. The results show that MKOR outperforms the existing approaches, and draws attention to a pressing need for further research on the privacy protection of FL so that comprehensive defense approaches can be developed.