# Bayes' capacity as a measure for reconstruction attacks in federated learning

arXiv: https://arxiv.org/abs/2406.13569 · HTML: https://mlsanity.com/paper/2406.13569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [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)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [R-GAP: Recursive Gradient Attack on Privacy](https://mlsanity.com/paper/2010.07733/) (2020)
- [Privacy Assessment on Reconstructed Images: Are Existing Evaluation Metrics Faithful to Human Perception?](https://mlsanity.com/paper/2309.13038/) (2023)

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

- [FedRP: A Communication-Efficient Approach for Differentially Private Federated Learning Using Random Projection](https://mlsanity.com/paper/2509.10041/) (2025)

## Abstract (arXiv)

Within the machine learning community, reconstruction attacks are a principal attack of concern and have been identified even in federated learning, which was designed with privacy preservation in mind. In federated learning, it has been shown that an adversary with knowledge of the machine learning architecture is able to infer the exact value of a training element given an observation of the weight updates performed during stochastic gradient descent. In response to these threats, the privacy community recommends the use of differential privacy in the stochastic gradient descent algorithm, termed DP-SGD. However, DP has not yet been formally established as an effective countermeasure against reconstruction attacks. In this paper, we formalise the reconstruction threat model using the information-theoretic framework of quantitative information flow. We show that the Bayes' capacity, related to the Sibson mutual information of order infinity, represents a tight upper bound on the leakage of the DP-SGD algorithm to an adversary interested in performing a reconstruction attack. We provide empirical results demonstrating the effectiveness of this measure for comparing mechanisms against reconstruction threats.