# Time-varying Mixing Matrix Design for Energy-efficient Decentralized Federated Learning

arXiv: https://arxiv.org/abs/2512.24069 · HTML: https://mlsanity.com/paper/2512.24069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Builds on (most cited first, 30 of 32)

- [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)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [D2: Decentralized Training over Decentralized Data](https://mlsanity.com/paper/1803.07068/) (2018)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [Communication Compression for Decentralized Training](https://mlsanity.com/paper/1803.06443/) (2018)
- [Distributed optimization over time-varying directed graphs](https://mlsanity.com/paper/1303.2289/) (2013)
- [Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGD](https://mlsanity.com/paper/1810.08313/) (2018)
- [Optimal Complexity in Decentralized Training](https://mlsanity.com/paper/2006.08085/) (2020)
- [Decentralized Federated Learning: Balancing Communication and Computing Costs](https://mlsanity.com/paper/2107.12048/) (2021)
- [Communication-Efficient Adaptive Federated Learning](https://mlsanity.com/paper/2205.02719/) (2022)
- [Can Federated Learning Save The Planet?](https://mlsanity.com/paper/2010.06537/) (2020)
- [Federated Learning over Wireless Device-to-Device Networks: Algorithms and Convergence Analysis](https://mlsanity.com/paper/2101.12704/) (2021)
- [DAdaQuant: Doubly-adaptive quantization for communication-efficient Federated Learning](https://mlsanity.com/paper/2111.00465/) (2021)
- [Asynchronous Decentralized SGD with Quantized and Local Updates](https://mlsanity.com/paper/1910.12308/) (2019)
- [Decentralized gradient methods: does topology matter?](https://mlsanity.com/paper/2002.12688/) (2020)
- [Refined Convergence and Topology Learning for Decentralized SGD with Heterogeneous Data](https://mlsanity.com/paper/2204.04452/) (2022)
- [SQuARM-SGD: Communication-Efficient Momentum SGD for Decentralized Optimization](https://mlsanity.com/paper/2005.07041/) (2020)
- [Beyond spectral gap: The role of the topology in decentralized learning](https://mlsanity.com/paper/2206.03093/) (2022)
- [Moniqua: Modulo Quantized Communication in Decentralized SGD](https://mlsanity.com/paper/2002.11787/) (2020)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Delay Analysis of Wireless Federated Learning Based on Saddle Point Approximation and Large Deviation Theory](https://mlsanity.com/paper/2103.16994/) (2021)
- [Optimal Complexity in Non-Convex Decentralized Learning over Time-Varying Networks](https://mlsanity.com/paper/2211.00533/) (2022)
- [Communication-Efficient Network-Distributed Optimization with Differential-Coded Compressors](https://mlsanity.com/paper/1912.03208/) (2019)
- [Decentralized Learning over Wireless Networks: The Effect of Broadcast with Random Access](https://mlsanity.com/paper/2305.07368/) (2023)
- [Faster Convergence with Less Communication: Broadcast-Based Subgraph Sampling for Decentralized Learning over Wireless Networks](https://mlsanity.com/paper/2401.13779/) (2024)

## Built on by (most cited first, 1 of 1)

- [Decentralised Federated Learning over Temporal Networks: The Role of Heterogeneities](https://mlsanity.com/paper/2607.03171/) (2026)

## Abstract (arXiv)

We consider the design of mixing matrices to minimize the operation cost for decentralized federated learning (DFL) in wireless networks, with focus on minimizing the maximum per-node energy consumption. As a critical hyperparameter for DFL, the mixing matrix controls both the convergence rate and the needs of agent-to-agent communications, and has thus been studied extensively. However, existing designs mostly focused on minimizing the communication time, leaving open the minimization of per-node energy consumption that is critical for energy-constrained devices. This work addresses this gap through a theoretically-justified solution for mixing matrix design that aims at minimizing the maximum per-node energy consumption until convergence, while taking into account the broadcast nature of wireless communications. Based on a novel convergence theorem that allows arbitrarily time-varying mixing matrices, we propose a multi-phase design framework that activates time-varying communication topologies under optimized budgets to trade off the per-iteration energy consumption and the convergence rate while balancing the energy consumption across nodes. Our evaluations based on real data have validated the efficacy of the proposed solution in combining the low energy consumption of sparse mixing matrices and the fast convergence of dense mixing matrices.