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Hammer and Anvil: Toward a Theory of Backdoors in Federated Learning

arXiv 2509.08089 ↗First posted 9 Sep 2025cs.LG cs.CRcited by 0

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Abstract (arXiv)

Federated Learning (FL) enables distributed model training but is vulnerable to backdoor attacks, where malicious clients embed attacker-controlled behaviors into the global model. Existing defenses fail against adaptive adversaries. In this paper, we present "Hammer and Anvil", a principled theoretical framework that categorizes backdoors by the deviation, δ, of their updates to the mean of the updates. We identify two fundamental defense types: "Type 1 (The Anvil)", comprising outlier detection and robust aggregation effective against large-deviation attacks, and "Type 2 (The Hammer)", consisting of removal-based defenses effective against small-deviation attacks. We demonstrate that defenses of a single type and non-principled combined defenses inherently leave an exploitable gap for adaptive attackers. To bridge this gap, we propose the principled combination of Type 1 and Type 2 defenses. We evaluate our framework against a new, worst-case, full-information adaptive adversary that knows the benign updates, the aggregation algorithm, and its parameters, and yet this adversary fails against our combined defenses. Our empirical evaluation across various datasets and settings shows that single-typed and non-principled combined defenses are easily broken, often by a single malicious client. In contrast, our best combined defense variants, HAFlameCSFT, HAKrumCSFT, and HAMulti-MetricsCSFT, remain undefeated even in the most adversarial settings. Our results provide a principled approach for research on backdoors in federated learning.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 28 of its 62 references that are in the map. First posted on arXiv 9 Sep 2025.

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28 of 62 references.

References · 28

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2016Communication-Efficient Learning of Deep Networks from Decentralized Datacited by 7,592
  3. 2018Byzantine-Robust Distributed Learning: Towards Optimal Statistical Ratescited by 698
  4. 2018Analyzing Federated Learning through an Adversarial Lenscited by 346
  5. 2019Differential Privacy Has Disparate Impact on Model Accuracycited by 316
  6. 2020Attack of the Tails: Yes, You Really Can Backdoor Federated Learningcited by 307
  7. 2019A Little Is Enough: Circumventing Defenses For Distributed Learningcited by 285
  8. 2020Data Poisoning Attacks Against Federated Learning Systemscited by 266
  9. 2018Mitigating Sybils in Federated Learning Poisoningcited by 158
  10. 2022FLDetector: Defending Federated Learning Against Model Poisoning Attacks via Detecting Malicious Clientscited by 119
  11. 2021CRFL: Certifiably Robust Federated Learning against Backdoor Attackscited by 91
  12. 2018D"IoT: A Federated Self-learning Anomaly Detection System for IoTcited by 89
16 more
  1. 2020Learning to Detect Malicious Clients for Robust Federated Learningcited by 86
  2. 2020Defending against Backdoors in Federated Learning with Robust Learning Ratecited by 82
  3. 2022DeepSight: Mitigating Backdoor Attacks in Federated Learning Through Deep Model Inspectioncited by 78
  4. 2019Byzantine-Robust Federated Machine Learning through Adaptive Model Averagingcited by 70
  5. 2021FL-WBC: Enhancing Robustness against Model Poisoning Attacks in Federated Learning from a Client Perspectivecited by 35
  6. 2022Fine-Tuning Is All You Need to Mitigate Backdoor Attackscited by 35
  7. 2023Backdoor Attacks and Defenses in Federated Learning: Survey, Challenges and Future Research Directionscited by 33
  8. 2023On the Vulnerability of Backdoor Defenses for Federated Learningcited by 27
  9. 2023FreqFed: A Frequency Analysis-Based Approach for Mitigating Poisoning Attacks in Federated Learningcited by 25
  10. 2023BayBFed: Bayesian Backdoor Defense for Federated Learningcited by 23
  11. 2023Multi-metrics adaptively identifies backdoors in Federated learningcited by 23
  12. 2023Data and Model Poisoning Backdoor Attacks on Wireless Federated Learning, and the Defense Mechanisms: A Comprehensive Surveycited by 17
  13. 2022Semi-Targeted Model Poisoning Attack on Federated Learning via Backward Error Analysiscited by 9
  14. 2023G2uardFL: Safeguarding Federated Learning Against Backdoor Attacks through Attributed Client Graph Clusteringcited by 9
  15. 2023A Survey on Vulnerability of Federated Learning: A Learning Algorithm Perspectivecited by 9
  16. 2024Identify Backdoored Model in Federated Learning via Individual Unlearningcited by 4

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