FedSQ: Optimized Weight Averaging via Fixed Gating

Federated Learning (FL) must balance training efficiency and model accuracy across heterogeneous clients. Post-training quantization (PTQ) avoids the extra computation of quantization-aware training (QAT), but can incur greater accuracy loss. We propose FedHQ, a hybrid quantization framework that assigns PTQ or QAT according to clients' hardware and data characteristics. Hardware-based speed estimates and local data-distribution indicators guide coarse-grained global initialization, followed by fine-grained training-based adjustment of selected client strategies. Experiments on three image-classification datasets show that FedHQ achieves up to 2.47x training speedup over FedAQT and up to 11.15 percentage points higher accuracy than FedFQ.

Federated learning (FL) must serve devices with varying computational capabilities. A fixed model cannot suit all devices, while training one model per deployment limit is costly. Federated supernet training instead learns one elastic model with differently sized subnetworks, then deploys a suitable one to each device. When client inference budgets differ, however, parameters exclusive to high-cost subnetworks are reachable by fewer clients. We propose FEAST, a federated shared-space training framework that counters this imbalance by jointly training multiple subnetworks within each client's limit. Budget-tailored sub-supernet routing sends only the relevant supernet portion, and sparse aggregation merges the returned parameter slices. The trained supernet directly serves the subnetworks used during federation and supports post-hoc extraction of additional subnetworks without federated retraining. We further show that independently assigning clients' training-data volumes and inference budgets can distort accuracy--inference-cost comparisons in heterogeneous FL simulations, and introduce a one-parameter $γ$-allocation protocol to control this coupling. In our experimental setup, the SuperFedNAS and DeepFedNAS supernet training procedures remain near chance at 25M and reach at most $17.09\%$ at $596$M inference MACs; FEAST reaches $71.06\%$ at $596$M, $2.4$ points above the strongest model-heterogeneous weight-sharing baseline at its largest tier. Across CIFAR-100, CINIC-10, and TinyImageNet-200, FEAST achieves the highest population-averaged accuracy among the evaluated weight-sharing methods when each client receives its largest affordable subnetwork. Sub-supernet routing reduces aggregate model-parameter traffic by $6.8\times$ relative to full-supernet transmission.

Federated fine-tuning is bottlenecked by communication: FedAvg and pseudo-gradient schemes transmit a payload that scales with the model, and gradient compression shrinks it by only a constant factor. We take a different lever. Mapping networks generate a network's weights from a small trainable latent through a frozen affine projection; because the map is shared and affine, averaging latents is exactly averaging the generated weights. We turn this into a practical low-bandwidth federated channel with two changes: a low-rank, seed-regenerable factorisation of the projection (cutting generator memory from ~80 GB to ~10 MB), and a delta formulation $θ= θ^{\mathrm{pre}} + U V^{\top} z$ that learns an additive correction around a shared centrally-pretrained base -- federated fine-tuning, which is what makes the method work at scale. A frozen orthogonal classifier head further removes the head from the payload while improving accuracy. On CIFAR-100 with ResNet-18+GroupNorm, our method (FLITE, Federated Low-rank Iterative Training Engine) communicates 1,280 floats (~5 KB) per client per round -- an 8718x reduction -- and reaches 74.67%, within ~0.5 pp of full-weight FedAvg. The averaging identity holds to floating-point precision ($6 \times 10^{-8}$); the method sits one to two orders of magnitude below PowerSGD and top-k on the bandwidth-accuracy Pareto; it matches or exceeds full-weight FedAvg under strong non-IID skew. int4 latents reach 648 bytes per round at unchanged accuracy, whereas int4 full-weight FedAvg collapses to chance.