# Capacity Confounds and Coverage Guarantees in Adaptive Sub-model Federated Learning

arXiv: https://arxiv.org/abs/2608.07157 · HTML: https://mlsanity.com/paper/2608.07157/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 48 of its 65 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 30 of 48)

- [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)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (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)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients](https://mlsanity.com/paper/2010.01264/) (2020)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [Model Pruning Enables Efficient Federated Learning on Edge Devices](https://mlsanity.com/paper/1909.12326/) (2019)
- [FjORD: Fair and Accurate Federated Learning under heterogeneous targets with Ordered Dropout](https://mlsanity.com/paper/2102.13451/) (2021)
- [FedKD: Communication Efficient Federated Learning via Knowledge Distillation](https://mlsanity.com/paper/2108.13323/) (2021)
- [Federated Learning for Smart Healthcare: A Survey](https://mlsanity.com/paper/2111.08834/) (2021)

## Abstract (arXiv)

Sub-model federated learning lets resource-constrained clients train width-reduced versions of a global model, but existing methods allocate capacity by device resources alone. A natural next step, allocating capacity by each client's data heterogeneity as estimated from the updates the server already observes, is suggested by recent methods that size sub-models from training-derived signals. We ask whether that step is possible, using HAS-FL, an adaptive capacity-allocation framework, as a test case. First, validated against ground-truth label-distribution divergence on reproducible partitions, update-divergence estimates of client heterogeneity are dominated by capacity rather than data: on both image benchmarks and every seed, the estimates correlate strongly and negatively with device capacity, and once capacity is controlled for their association with data heterogeneity is near zero or negative. Any method estimating client statistics from sub-model updates is exposed to this previously undocumented confound. Second, adaptive allocation has a hidden failure mode: when every client is capped below full width, the uncovered parameters stay at random initialization and progressively corrupt the global model. A simple coverage guarantee removes the failure and explains why uniform allocation collapses. Third, a matched-budget control settles what adaptivity contributes: random allocation to the same average budget matches the adaptive policy to within seed-to-seed variation on both image benchmarks, and on the naturally partitioned text benchmark the adaptive policy is the weakest of the three strategies while consuming the most capacity. Sub-model training admits constrained clients at quadratically reduced cost but gives up substantial accuracy relative to full-model training, and what protects that accuracy is parameter coverage rather than allocation intelligence.