# Byzantine Accountability Without Consensus: Strong Eventual Consistency for Non-Associative, Stochastic, Robust Aggregation

arXiv: https://arxiv.org/abs/2607.10305 · HTML: https://mlsanity.com/paper/2607.10305/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [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)
- [Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication](https://mlsanity.com/paper/1902.00340/) (2019)
- [DiLoCo: Distributed Low-Communication Training of Language Models](https://mlsanity.com/paper/2311.08105/) (2023)
- [Byzantine-Robust Decentralized Federated Learning](https://mlsanity.com/paper/2406.10416/) (2024)
- [Byzantine-Resilient Decentralized Stochastic Optimization with Robust Aggregation Rules](https://mlsanity.com/paper/2206.04568/) (2022)
- [Byzantine-Robust Aggregation for Securing Decentralized Federated Learning](https://mlsanity.com/paper/2409.17754/) (2024)
- [Byzantine-Robust Federated Learning over Ring-All-Reduce Distributed Computing](https://mlsanity.com/paper/2501.17392/) (2025)
- [Casper the Friendly Finality Gadget](https://mlsanity.com/paper/1710.09437/) (2017)
- [Delta State Replicated Data Types](https://mlsanity.com/paper/1603.01529/) (2016)
- [Krum Federated Chain (KFC): Using blockchain to defend against adversarial attacks in Federated Learning](https://mlsanity.com/paper/2502.06917/) (2025)
- [Merkle-CRDTs: Merkle-DAGs meet CRDTs](https://mlsanity.com/paper/2004.00107/) (2020)
- [The Blocklace: A Byzantine-repelling and Universal Conflict-free Replicated Data Type](https://mlsanity.com/paper/2402.08068/) (2024)
- [Conflict-Free Replicated Data Types for Neural Network Model Merging: A Two-Layer Architecture Enabling CRDT-Compliant Model Merging Across 26 Strategies](https://mlsanity.com/paper/2605.19373/) (2026)
- [Accountability and Reconfiguration: Self-Healing Lattice Agreement](https://mlsanity.com/paper/2105.04909/) (2021)
- [On Conflict-Free Replicated Data Types and Equivocation in Byzantine Setups](https://mlsanity.com/paper/2109.10554/) (2021)
- [A Composable CRDT Layer for Byzantine-Resilient Deterministic Reconstruction](https://mlsanity.com/paper/2606.18966/) (2026)
- [Decoupling Trust in Byzantine CRDTs: Fine-grained Post-Compromise Handling without Breaking Causality](https://mlsanity.com/paper/2606.31759/) (2026)

## Abstract (arXiv)

Byzantine-robust aggregation rules such as multi-Krum assume a central coordinator, and decentralising them is obstructed by the rules themselves: they are globally coupled, non-associative, and discontinuous, so an ulpscale perturbation can flip the selected subset, moving the output by a non-vanishing amount. None of this prevents coordinator-free replication, because a robust rule needs no agreed order of contributions, only an agreed set and an agreed exclusion predicate, both of which converge without consensus. ACFA (Accountable Consensus-Free Aggregation) replicates a content-addressed OR-Set of signed contributions and a grow-only set of self-authenticating equivocation proofs, offline-verifiable by anyone. Aggregation is a deterministic pure function of the converged product state: fixed-point integer arithmetic over a hash-canonical order, ties broken by content hash. We prove that any pure function of a converged product of CRDTs (non-monotone, non-associative, or stochastic) inherits Strong Eventual Consistency, together with its converse; the contribution is the composition of a data lattice with an evidence lattice applied to a robust selector, not the elementary lifting step. A prototype (10 nodes, 3 Byzantine) passes 16/16 falsification checks: byte-identical roots under adversarial gossip, deterministic re-convergence after late equivocation proofs, partition recovery, and three byte-identity-breaking ablations. The guarantee is consistency, not accuracy; robustness is imported, conditional on 2f + 3 admitted contributions (at most f Byzantine) and a stated quantisation-margin condition.