# OPFL: Optimistic Verification of Federated Learning via Empirical Boundary

arXiv: https://arxiv.org/abs/2609.37011 · HTML: https://mlsanity.com/paper/2609.37011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [FLTrust: Byzantine-robust Federated Learning via Trust Bootstrapping](https://mlsanity.com/paper/2012.13995/) (2020)
- [Proof-of-Learning: Definitions and Practice](https://mlsanity.com/paper/2103.05633/) (2021)
- [Free-rider Attacks on Model Aggregation in Federated Learning](https://mlsanity.com/paper/2006.11901/) (2020)
- [EIFFeL: Ensuring Integrity for Federated Learning](https://mlsanity.com/paper/2112.12727/) (2021)
- [RoFL: Robustness of Secure Federated Learning](https://mlsanity.com/paper/2107.03311/) (2021)
- [Backdoor Federated Learning by Poisoning Backdoor-Critical Layers](https://mlsanity.com/paper/2308.04466/) (2023)
- [Optimistic Verifiable Training by Controlling Hardware Nondeterminism](https://mlsanity.com/paper/2403.09603/) (2024)
- [Secure and Verifiable Data Collaboration with Low-Cost Zero-Knowledge Proofs](https://mlsanity.com/paper/2311.15310/) (2023)

## Abstract (arXiv)

Federated learning enables multiple clients to collaboratively train models without sharing their private data. However, the lack of visibility into local training makes it difficult to verify whether clients follow the prescribed training procedure or submit malicious updates, such as model poisoning. A natural approach is to replay client training for verification. However, privacy-preserving replay produces numerical results that cannot be directly matched with local client execution because the two run in different environments. We present OPFL, an optimistic verification framework for privacy-preserving federated learning. To protect data privacy, OPFL performs replay inside secure multi-party computation (MPC). Although gradients computed on MPC and local GPUs are not bitwise identical, we observe that their absolute differences are stable and bounded. OPFL therefore calibrates an empirical boundary offline and uses it to distinguish benign numerical deviations from malicious manipulation. To reduce the cost of expensive MPC replay, OPFL adopts optimistic verification by post auditing only sampled training steps. Experiments on LeNet, BERT, and Qwen show that the boundary generalizes across datasets, input lengths, and GPUs, while achieving 0% ASR against model poisoning and PGD-based attacks. On a LeNet workload, at p=0.01, OPFL is approximately 98.6× faster than full MPC-based FL and 625.5× faster than ZK-based approach.