Single-Round Scalable Analytic Federated Learning

Alan T. L. Bacellar; Mustafa Munir; Felipe M. G. França; Priscila M. V. Lima; Radu Marculescu; Lizy K. John

Home/Archive/arXiv

arXiv · 2512.03336

Single-Round Scalable Analytic Federated Learning

Alan T. L. Bacellar·Mustafa Munir·Felipe M. G. França·Priscila M. V. Lima·Radu Marculescu·Lizy K. John

View original source ↗Read source document ↗Export metadata ↓

Abstract

Federated Learning (FL) is plagued by two key challenges: high communication overhead and performance collapse on heterogeneous (non-IID) data. Analytic FL (AFL) provides a single-round, data distribution invariant solution, but is limited to linear models. Subsequent non-linear approaches, like DeepAFL, regain accuracy but sacrifice the single-round benefit. In this work, we break this trade-off. We propose SAFLe, a framework that achieves scalable non-linear expressivity by introducing a structured head of bucketed features and sparse, grouped embeddings. We prove this non-linear architecture is mathematically equivalent to a high-dimensional linear regression. This key equivalence allows SAFLe to be solved with AFL's single-shot, invariant aggregation law. Empirically, SAFLe establishes a new state-of-the-art for analytic FL, significantly outperforming both linear AFL and multi-round DeepAFL in accuracy across all benchmarks, demonstrating a highly efficient and scalable solution for federated vision.

Explore related subjects

cs.LG cs.AI stat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Alan T. L. Bacellar, Mustafa Munir, Felipe M. G. França, Priscila M. V. Lima, Radu Marculescu, Lizy K. John. 2026-03-29. Single-Round Scalable Analytic Federated Learning. https://arxiv.org/abs/2512.03336

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data

We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of a random Tikhonov regularization path and decompose the tracking error of the algorithm's output for the regularization path into random difference equations in RKHS. We show that the tracking error vanishes in mean square and almost surely if the regularization path is slowly time-varying. Then, leveraging the monotonicity of inverse operators and the spectral decomposition of compact operators, and introducing the RKHS persistence of excitation condition, we develop a dominated convergence method to prove the mean square and almost sure consistency between the regularization path and the unknown function to be learned. Especially, for independent and non-identically distributed data streams, the mean square and almost sure consistency between the algorithm's output and the unknown function is achieved if the input data's marginal probability measures are slowly time-varying and the average measure over each fixed-length time period is uniformly above a strictly positive finite Borel measure.

cs.LG↗

arXiv2026

Gradient-Gated DPO: Stabilizing Preference Optimization in Language Models

Direct Preference Optimization (DPO) improves relative preference by increasing the margin between chosen and rejected responses, but this objective does not specify how probability mass should be redistributed to achieve that margin. Consequently, preference separation can improve even as probability mass collapses away from both preferred and unrelated responses, a phenomenon associated with the squeezing effect. We show that this pathology is localized: continued negative updates become destructive when rejected responses enter low-probability valleys, where further suppression induces harmful redistribution through the coupled softmax geometry. We introduce Gradient-Gated Preference Optimization (Gate-DPO), which uses the current probability geometry of each rejected response to selectively attenuate its contribution, limiting excessive rejected suppression while delaying preference-loss saturation. Gate-DPO is objective-agnostic and composes with existing preference methods. Across four architectures, two preference datasets, and multiple objectives, gating consistently reduces squeezing and improves chosen-response likelihood, while exhibiting robust reductions in rejected-response collapse across architectures and objectives. Mass-dynamics analysis further shows that large preference margins can conceal substantial suppression of unrelated responses, while gating achieves healthier redistribution. Together, our results show that preference margin alone is insufficient to characterize optimization health and that selectively controlling probability dynamics provides a simple, general mechanism for stabilizing preference optimization.

cs.LG↗

arXiv2026

Noise-Debiased Thermodynamic Variance for Local Learning Coefficient Probes

Local learning coefficient (LLC) probes offer a singularity-aware view of neural-network training, but mean-energy methods require a local loss baseline that is ambiguous at transient checkpoints. Thermodynamic variance avoids this input; under mini-batch evaluation, however, direct variance mixes cross-state loss fluctuations with same-state noise. We operationalize this route with the \emph{Shift-Invariant Variance Estimator} (SIVE), which estimates and subtracts the latter component using repeated evaluations. Conditional on any fixed retained path, unclipped SIVE is unbiased for noiseless path variance without requiring MCMC stationarity. The finite-scale diagnostic remains indexed by localization scale $h$---even a locally linear loss has tether-dependent variance---while interpretation as a Real Log Canonical Threshold (RLCT) requires additional stationary low-temperature conditions. Toy experiments recover calibrated finite-scale targets. At the primary localization scale, all five MNIST MLP trajectories exhibit a mid-training trough followed by a rebound in SIVE, while Raw Variance decreases from Epoch 40 to 100 in every trajectory. Across four localization scales, the joint early-drop/late-rise criterion is met in 19 of 20 trajectory--scale pairs. At Epoch 40, the estimated observation-noise correction accounts for $77.5\%$ of Raw Variance. Same-state debiasing thus reveals a reproducible turning structure masked by time-varying observation noise.

cs.LG↗