# Range Penalization: Theoretical Insights with Applications in Federated Learning

arXiv: https://arxiv.org/abs/2606.10916 · HTML: https://mlsanity.com/paper/2606.10916/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 70 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Robust and Communication-Efficient Federated Learning from Non-IID Data](https://mlsanity.com/paper/1903.02891/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [FedPAQ: A Communication-Efficient Federated Learning Method with Periodic Averaging and Quantization](https://mlsanity.com/paper/1909.13014/) (2019)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (2018)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [ProxSkip: Yes! Local Gradient Steps Provably Lead to Communication Acceleration! Finally!](https://mlsanity.com/paper/2202.09357/) (2022)
- [Federated Learning with Partial Model Personalization](https://mlsanity.com/paper/2204.03809/) (2022)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [Personalized Federated Learning for Intelligent IoT Applications: A Cloud-Edge based Framework](https://mlsanity.com/paper/2002.10671/) (2020)
- [Motley: Benchmarking Heterogeneity and Personalization in Federated Learning](https://mlsanity.com/paper/2206.09262/) (2022)
- [Splitting Methods for Convex Clustering](https://mlsanity.com/paper/1304.0499/) (2013)
- [Towards Energy Efficient Federated Learning over 5G+ Mobile Devices](https://mlsanity.com/paper/2101.04866/) (2021)
- [FedHB: Hierarchical Bayesian Federated Learning](https://mlsanity.com/paper/2305.04979/) (2023)
- [On Cross-validation for Sparse Reduced Rank Regression](https://mlsanity.com/paper/1812.11555/) (2018)
- [Analysis of Generalized Bregman Surrogate Algorithms for Nonsmooth Nonconvex Statistical Learning](https://mlsanity.com/paper/2112.09191/) (2021)
- [Supervised Multivariate Learning with Simultaneous Feature Auto-grouping and Dimension Reduction](https://mlsanity.com/paper/2112.09746/) (2021)
- [Dual Seminorms, Ergodic Coefficients and Semicontraction Theory](https://mlsanity.com/paper/2201.03103/) (2022)

## Abstract (arXiv)

This paper introduces range regularization for federated learning with linear systematic components to enhance statistical accuracy and induce cross-client regularity conducive to quantization, coding, and resource efficiency. Our approach identifies features with shared weights across different clients and adaptively clusters the weights of personalized features at extreme values, a process we refer to as polar clustering. Theoretical analysis of the associated estimators poses significant challenges due to the seminorm nature and non-decomposability of the regularizer. We develop new proof techniques for the nonasymptotic analysis of statistical accuracy and faithful pattern recovery. Moreover, a fast optimization algorithm that leverages varying degrees of local strong convexity is proposed to reduce iteration complexity. Experiments support the efficacy and efficiency of the proposed approach.