# From Mean to Extreme: Formal Differential Privacy Bounds on the Success of Real-World Data Reconstruction Attacks

arXiv: https://arxiv.org/abs/2402.12861 · HTML: https://mlsanity.com/paper/2402.12861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Membership inference attacks, one of 12 directions in LLM safety and security.
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Placed in

- LLM safety and security / [Membership inference attacks](https://mlsanity.com/safety/membership-inference-attacks/)

## Builds on (most cited first, 9 of 9)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Unlocking High-Accuracy Differentially Private Image Classification through Scale](https://mlsanity.com/paper/2204.13650/) (2022)
- [Adversary Instantiation: Lower Bounds for Differentially Private Machine Learning](https://mlsanity.com/paper/2101.04535/) (2021)
- [Reconstructing Training Data with Informed Adversaries](https://mlsanity.com/paper/2201.04845/) (2022)
- [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)
- [Bounding Training Data Reconstruction in Private (Deep) Learning](https://mlsanity.com/paper/2201.12383/) (2022)
- [Bounding Training Data Reconstruction in DP-SGD](https://mlsanity.com/paper/2302.07225/) (2023)
- [Bounding data reconstruction attacks with the hypothesis testing interpretation of differential privacy](https://mlsanity.com/paper/2307.03928/) (2023)

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

- [Visual Privacy Auditing with Diffusion Models](https://mlsanity.com/paper/2403.07588/) (2024)

## Abstract (arXiv)

The gold standard for privacy in machine learning, Differential Privacy (DP), is often interpreted through its guarantees against membership inference. However, translating DP budgets into quantitative protection against the more damaging threat of data reconstruction remains a challenging open problem. Existing theoretical analyses of reconstruction risk are typically based on an "identification" threat model, where an adversary with a candidate set seeks a perfect match. When applied to the realistic threat of "from-scratch" attacks, these bounds can lead to an inefficient privacy-utility trade-off. This paper bridges this critical gap by deriving the first formal privacy bounds tailored to the mechanics of demonstrated Analytic Gradient Inversion Attacks (AGIAs). We first formalize the optimal from-scratch attack strategy for an adversary with no prior knowledge, showing it reduces to a mean estimation problem. We then derive closed-form, probabilistic bounds on this adversary's success, measured by Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR). Our empirical evaluation confirms these bounds remain tight even when the attack is concealed within large, complex network architectures. Our work provides a crucial second anchor for risk assessment. By establishing a tight, worst-case bound for the from-scratch threat model, we enable practitioners to assess a "risk corridor" bounded by the identification-based worst case on one side and our from-scratch worst case on the other. This allows for a more holistic, context-aware judgment of privacy risk, empowering practitioners to move beyond abstract budgets toward a principled reasoning framework for calibrating the privacy of their models.