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This paper investigates the resilience of decentralized training models against backdoor attacks by analyzing continuous optimization dynamics under adversarial conditions. By formalizing the injection-absorption dynamic through a Discrete-Time Markov Chain (DTMC), the authors quantify the minimum auditing overhead necessary to limit attack success rates when a fraction of trainers are compromised. The proposed defense strategy, which integrates natural absorption, a randomized scheduler, and a lazy verification oracle, effectively suppresses backdoor attacks without degrading model utility, achieving significant results with minimal computational overhead.
Adversarial backdoor attacks can be mitigated with a defense strategy that ensures attack success probabilities asymptotically approach zero, even with minimal auditing efforts.
Backdoor attacks severely threaten large-scale AI models. When model owners delegate training to external compute providers within a decentralized training paradigm, adversaries can craft stealthy, low-frequency triggers to inject malicious behavior while evading standard audits. Traditionally, detecting these attacks requires a full re-computation of the training steps--a prohibitive overhead that directly contradicts the owner's resource constraints. To address this, we investigate the resilience of continuous optimization dynamics under Byzantine perturbations, where adversaries are forced to compete against a continuous influx of honest updates. Under a threat model where an adversary compromises f out of n total trainers, we quantify the minimum auditing overhead required by the model owner to probabilistically bound the attack success rate. We formalize this injection-absorption dynamic as a Discrete-Time Markov Chain (DTMC). Using this framework, we prove that the success probability of any bounded adversary asymptotically collapses to zero under a defense strategy combining natural absorption, a randomized scheduler, and lazy verification oracle. Empirical results demonstrate significant backdoor suppression with zero utility degradation even when invoking the verification oracle on merely 10% of the total training steps. This approach yields a provably sound and computationally efficient defense for safety-critical AI.
