An arXiv preprint compares how much of an update is retained for transmission. QEF-GT-AdamW approaches the accuracy of a full-precision reference at about 30% Top-K density on MNIST and 35% on CIFAR-10. QGT-AdamW, another method in the comparison, requires around 90%. Top-K density is the share of update coordinates retained for transmission.
Those density figures come from an accuracy comparison. In a separate reported compression setting used across the methods, Top-K sparsification retained 10% of coordinates, described as a 90% message reduction. The 30%, 35% and 90% figures therefore describe the density comparison, while the 10% figure describes the fixed compression setup.
The question behind the test
The paper addresses decentralized learning over wireless networks where local data are heterogeneous and communication is constrained and unreliable. It asks how QEF-GT-AdamW performs compared with representative decentralized-learning baselines under those conditions.
QEF-GT-AdamW combines gradient tracking, AdamW-based adaptive optimization, dual-stream biased quantization with error feedback, and a local fallback after an unsuccessful packet reception.
A deliberately uneven setting
The evaluation used a simulated network of 15 nodes, with directed links within 750 metres and default transmit power of 0.2 watts. The experiments used logistic regression on MNIST and CIFAR-10, each with 50,000 training samples and standard test sets, over 1,000 epochs.
The local data mixes were non-identical. MNIST used a pathological label-skew split that gave each node two to five labels, while CIFAR-10 used a Dirichlet concentration of 0.5. In plain terms, the nodes did not receive identical data mixes.
The packet curves
For unquantized GT-AdamW, average packet drops were approximately 100% at 0.05, 0.1 and 0.2 MHz. The reported figures were about 83% at 0.5 MHz, around 28% at 1 MHz, about 4% at 2 MHz and nearly 0% at 10 MHz.
In the transmit-power comparison for unquantized GT-AdamW, drops were about 96% at 0.005 watts, 91% at 0.01 watts, 82% at 0.02 watts and 63% at 0.05 watts. The reported rate was about 28% at 0.2 watts, 9% at 0.75 watts and 4% at 2 watts.
The curves for QGT-AdamW and QEF-GT-AdamW were reported together. Their packet-drop rates were about 67% at 0.05 MHz, roughly 10% at 0.1 MHz and essentially zero from 0.2 MHz onward. Against transmit power, the reported rates were about 8% at 0.005 watts, around 1% at 0.01 watts and nearly zero at 0.02 watts and above. These rates were much lower than those reported for unquantized GT-AdamW across the listed settings.
What the accuracy gap may mean
At the same Top-K sparsification, QEF-GT-AdamW produced uniformly lower loss than QGT-AdamW. The authors attribute QEF-GT-AdamW's accuracy gain over QGT-AdamW to error-feedback optimization rather than to a lower transmission-failure probability. This is an author attribution from simulation comparisons, not an independently isolated causal estimate.
Across the reported comparisons, the authors describe QEF-GT-AdamW as offering a more favorable trade-off among communication efficiency, robustness to wireless impairments and learning effectiveness under heterogeneous data. That conclusion is limited to the decentralized-learning baselines and simulated settings examined in the paper.
Theory does not remove the practical limits
The theoretical analysis is conditional. It covers smooth convex objectives under compression and unreliable communication, with a stronger linear-rate characterization under an additional gradient-dominance condition. When perturbations vanish, the paper reports recovery of the standard O(1/K) convex convergence rate. In ordinary language, that notation describes a bound that decreases in inverse proportion to the number of iterations.
The guarantees rely on assumptions about convexity, smoothness, compression, random mixing and bounded state, and the stated standard rate requires vanishing perturbations. The empirical evidence is simulation-based: packet-delivery and channel behavior are modeled, and no physical wireless deployment or real-device experiment is reported.
Exact plotted accuracy and loss values, uncertainty intervals and the number of simulation repetitions are not reported in the supplied analysis. The accuracy thresholds and packet-drop figures are approximate descriptive reports, so the numerical comparisons should be read as reported simulation results rather than estimates with reported uncertainty.
The analysis leaves open how the method would perform on larger networks, additional tasks, more diverse non-IID distributions, real wireless traces and physical-device constraints. It also identifies repeated runs, alternative compressors and different fallback policies as questions for reproducibility and further comparison.
A preprint, not a deployment result
The document is arXiv version 1, dated 26 August 2026, and is a preprint. It reports support from the Luxembourg National Research Fund through the CHIST-ERA SHIELD project and the FNR AFR program via the FULFIL project.
Paper data and sources
Original title: Resilient Decentralized Wireless Federated Learning via Gradient Tracking with AdamW
Authors: Nguyen Van Thieu, Ti Ti Nguyen, Ons Aouedi et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text