# FIRMA: FIbonacci Ring Model Aggregation for Privacy-preserving Federated Learning

arXiv: https://arxiv.org/abs/2605.22898 · HTML: https://mlsanity.com/paper/2605.22898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 27 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Think Locally, Act Globally: Federated Learning with Local and Global Representations](https://mlsanity.com/paper/2001.01523/) (2020)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Decentralized Federated Learning: A Segmented Gossip Approach](https://mlsanity.com/paper/1908.07782/) (2019)

## Abstract (arXiv)

Federated learning protocols face a structural trilemma: canonical server-based aggregation~citemcmahan2017 creates a single point of failure and gradient inversion risk; decentralised ring-gossip alternatives~citehu2019segmented expose classification heads to semi-honest peers via uninformed uniform weights; and personalised methods~citecollins2021exploiting reintroduce central aggregation. No existing protocol simultaneously achieves server-free operation, permanently private heads, ring topology, and principled asymmetric neighbour weighting. We propose FIRMA (FIbonacci Ring Model Aggregation), a family of three progressively enhanced federated learning protocols: 1) fibfl establishes the foundation: server-free ring aggregation with Fibonacci-weighted neighbour blending and permanently private classification heads. 2) fibflp augments this with accuracy-gated neighbour suppression, selectively down-weighting poorly-converged peers while preserving the Fibonacci directional bias. 3) fibflpp, the full system, completes the family with a 2-opt ring permutation that maximises adjacent-client class diversity, global ring coverage via Kg=lceil N/2rceil gossip passes, and cosine-annealed self-retention calibration. We establish a convergence rate bound and three supporting propositions governing normalisation, coverage, retention, and diversity optimality. Systematic experiments across 28 configurations -- four benchmarks crossed with seven heterogeneity regimes -- demonstrate that fibflpp surpasses fedavg in all 12 label-skew configurations, with a peak advantage of +20.7,pp on CIFAR-10 at K=1. Under Dirichlet heterogeneity, fibflpp is the Pareto-dominant method among all server-free protocols, achieving the highest accuracy in 17 of 28 configurations.