提出可扩展的去中心化联邦学习抗拜占庭攻击方法，利用随机矩阵理论检测异常梯度。
Spectral Sentinel: Scalable Byzantine-Robust Decentralized Federated Learning via Sketched Random Matrix Theory on Blockchain
- 基于随机矩阵理论，通过协方差谱分布差异识别恶意更新
- 支持15亿参数模型，内存开销仅O(k²)，k远小于维度d
- 在144种攻击配置下平均准确率达78.4%，显著优于基线方法
去中心化联邦学习（DFL）可在无中心信任前提下协同训练模型，但面临非独立同分布（Non-IID）数据下拜占庭客户端污染梯度的问题。现有防御方法存在可扩展性三难：基于距离的过滤（如Krum）可能误拒合法更新，几何中位数方法计算成本高达O(n²d)，许多认证防御仅在参数量低于1亿的模型上验证。本文提出Spectral Sentinel，一种基于随机矩阵理论的检测与聚合框架：诚实的非独立同分布梯度其协方差特征谱的主体部分符合Marchenko-Pastur定律，而拜占庭扰动会引发可检测的尾部异常。算法结合频繁方向压缩与数据依赖的MP追踪，在模型规模达15亿参数时，仅需O(k²)内存（k≪d）。在(σ, f)威胁模型下，假设坐标级真实方差上限为σ²，且恶意节点占比f < 1/2，证明了(ε, δ)-拜占庭鲁棒性，收敛速率可达O(σf / √T + f² / T)，并给出匹配的信息论下界Ω(σf / √T)，实现极小极大最优。系统集成区块链，部署于Polygon网络，共验证144种攻击-聚合组合，平均准确率达78.4%，基线方法仅为48–63%。
原文摘要 · Abstract (English)
Decentralized federated learning (DFL) enables collaborative model training without centralized trust, but it remains vulnerable to Byzantine clients that poison gradients under heterogeneous (Non-IID) data. Existing defenses face a scalability trilemma: distance-based filtering (e.g., Krum) can reject legitimate Non-IID updates, geometric-median methods incur prohibitive $O(n^2 d)$ cost, and many certified defenses are evaluated only on models below 100M parameters. We propose Spectral Sentinel, a Byzantine detection and aggregation framework that leverages a random-matrix-theoretic signature: honest Non-IID gradients produce covariance eigenspectra whose bulk follows the Marchenko-Pastur law, while Byzantine perturbations induce detectable tail anomalies. Our algorithm combines Frequent Directions sketching with data-dependent MP tracking, enabling detection on models up to 1.5B parameters using $O(k^2)$ memory with $k \ll d$. Under a $(σ,f)$ threat model with coordinate-wise honest variance bounded by $σ^2$ and $f < 1/2$ adversaries, we prove $(ε,δ)$-Byzantine resilience with convergence rate $O(σf / \sqrt{T} + f^2 / T)$, and we provide a matching information-theoretic lower bound $Ω(σf / \sqrt{T})$, establishing minimax optimality. We implement the full system with blockchain integration on Polygon networks and validate it across 144 attack-aggregator configurations, achieving 78.4 percent average accuracy versus 48-63 percent for baseline methods.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。