# Decentralized SGD with Controlled Disagreement Finds Flatter Minima

arXiv: https://arxiv.org/abs/2602.02899 · HTML: https://mlsanity.com/paper/2602.02899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 2 Feb 2026.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [The Road Less Scheduled](https://mlsanity.com/paper/2405.15682/) (2024)
- [Stochastic Gradient Push for Distributed Deep Learning](https://mlsanity.com/paper/1811.10792/) (2018)
- [SlowMo: Improving Communication-Efficient Distributed SGD with Slow Momentum](https://mlsanity.com/paper/1910.00643/) (2019)
- [Distributed Stochastic Gradient Tracking Methods](https://mlsanity.com/paper/1805.11454/) (2018)
- [Quasi-Global Momentum: Accelerating Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2102.04761/) (2021)
- [The alignment property of SGD noise and how it helps select flat minima: A stability analysis](https://mlsanity.com/paper/2207.02628/) (2022)
- [Exponential Graph is Provably Efficient for Decentralized Deep Training](https://mlsanity.com/paper/2110.13363/) (2021)
- [Friendly Sharpness-Aware Minimization](https://mlsanity.com/paper/2403.12350/) (2024)
- [Analytic Insights into Structure and Rank of Neural Network Hessian Maps](https://mlsanity.com/paper/2106.16225/) (2021)
- [Consensus Control for Decentralized Deep Learning](https://mlsanity.com/paper/2102.04828/) (2021)
- [A Unified and Refined Convergence Analysis for Non-Convex Decentralized Learning](https://mlsanity.com/paper/2110.09993/) (2021)
- [DecentLaM: Decentralized Momentum SGD for Large-batch Deep Training](https://mlsanity.com/paper/2104.11981/) (2021)
- [Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape](https://mlsanity.com/paper/2201.08025/) (2022)
- [Topology-aware Generalization of Decentralized SGD](https://mlsanity.com/paper/2206.12680/) (2022)
- [Does SGD really happen in tiny subspaces?](https://mlsanity.com/paper/2405.16002/) (2024)
- [Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization](https://mlsanity.com/paper/2501.12666/) (2025)
- [Momentum Tracking: Momentum Acceleration for Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2209.15505/) (2022)
- [Decentralized Learning Made Easy with DecentralizePy](https://mlsanity.com/paper/2304.08322/) (2023)
- [Decentralized SGD and Average-direction SAM are Asymptotically Equivalent](https://mlsanity.com/paper/2306.02913/) (2023)
- [Revisiting Random Weight Perturbation for Efficiently Improving Generalization](https://mlsanity.com/paper/2404.00357/) (2024)
- [DIGEST: Fast and Communication Efficient Decentralized Learning with Local Updates](https://mlsanity.com/paper/2307.07652/) (2023)
- [Improved Stability and Generalization Guarantees of the Decentralized SGD Algorithm](https://mlsanity.com/paper/2306.02939/) (2023)

## Abstract (arXiv)

Decentralized training is often regarded as inferior to centralized training because the consensus errors between workers are thought to undermine convergence and generalization. This work challenges this view by introducing decentralized SGD with Adaptive Consensus (DSGD-AC), which uses a time-dependent scaling mechanism to maintain consensus errors throughout the training. We show that adaptive consensus changes the stationary variance of disagreement modes by balancing two effects: it preserves consensus-error magnitude through weaker graph damping while still allowing curvature-dependent damping to shape the disagreement directions. This balance can produce a stronger Hessian-weighted loss-envelope penalty around the deployed model, even when normalized Hessian alignment is weaker than in standard DSGD. Empirical results on image classification show that DSGD-AC reaches flatter solutions and higher test accuracy than standard DSGD and even centralized SGD. Together, these results support consensus errors as a useful implicit regularizer and open a new perspective on the design of decentralized learning algorithms.