Hammer and Anvil: Toward a Theory of Backdoors in Federated Learning
Why this work is in the frame
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Bibliographic record
Abstract
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, $HA_{Flame}^{CSFT}$, $HA_{Krum}^{CSFT}$, and $HA_{Multi-Metrics}^{CSFT}$, remain undefeated even in the most adversarial settings. Our results provide a principled approach for research on backdoors in federated learning.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it