# SWB-DM: A Calibrated Sliced-Wasserstein-Barycenter Aggregator with Delayed-Momentum Caching for Byzantine-Robust Federated Learning under Partial Participation

arXiv: https://arxiv.org/abs/2609.16099 · HTML: https://mlsanity.com/paper/2609.16099/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 12 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 8 of 8)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [FLTrust: Byzantine-robust Federated Learning via Trust Bootstrapping](https://mlsanity.com/paper/2012.13995/) (2020)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation](https://mlsanity.com/paper/1903.03936/) (2019)
- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Delayed Momentum Aggregation: Communication-efficient Byzantine-robust Federated Learning with Partial Participation](https://mlsanity.com/paper/2509.02970/) (2025)

## Abstract (arXiv)

Robust aggregation methods for federated learning quietly rest on a fragile assumption: that whoever shows up in a given round is a fair sample of the full population. In practice, they rarely are. When only a handful of clients participate per round, even a modest fraction of adversaries can dominate that sample and silently invalidate the finite-sample guarantees that coordinate-wise median, Krum, Bulyan, and trimmed mean all depend on. We introduce SWB-DM to address this directly. SWB treats each slice of a client update as a one-dimensional distribution, computes a trimmed Wasserstein barycenter across clients, and recovers coordinate identity via a medoid-based gauge-fixing step -- a heuristic we developed and do not claim it belongs to standard optimal-transport theory. DeMoA-style delayed momentum then caches updates across the full client population each round, decoupling robustness from whoever happened to be sampled. Trim ratio calibration is not cosmetic: under-trimming causes collapse at corruption levels a properly calibrated model survives. Across 448 CIFAR-10 configurations, plus CIFAR-100, FEMNIST, and a 500-client scalability run, we find several mechanistically distinct failure modes. Even-sample coordinate-wise median degrades to a deterministic wrong answer. Krum silently violates its own n greater than 2f+2 precondition and diverges without warning. Bulyan's n greater than or equal to 4f+3 threshold produces a sharp pass/fail boundary. On attacks, IPM defeats order-statistic defenses -- including SWB -- more reliably than ALIE, confirmed through delta-space measurements against a convergence bound. SWB-DM's cache carries a real warm-up cost, but extending all baselines to the same round budget shows its CIFAR-10 gains are disproportionately large. On CIFAR-100, FLTrust benefits more -- for reasons entirely unrelated to caching.