arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.
This review discusses how neuroimaging data can be represented as symmetric positive-definite (SPD) matrices and analyzed using the Riemannian geometry of the SPD manifold. It surveys the evolution from modality-specific SPD representations to geometric shallow and deep learning methods, emphasizing how these approaches maintain structural constraints while integrating modern AI techniques. The paper frames SPD matrix learning as a bridge between classical geometric statistics and contemporary machine learning in neuroimaging and brain‑computer interface research.
The paper introduces a personalised federated learning approach for EEG decoding, applying it to both a Riemannian SPDNet and a Euclidean EEGNet. In this scheme, all subjects share a common trunk that learns a latent representation, while each subject retains a private head for classification, thereby addressing inter‑subject variability. Experiments on three motor‑imagery datasets show that personalised SPDNet outperforms standard federated learning and centralised training, converges faster, and communicates fewer parameters, and it also surpasses all EEGNet variants on two of the datasets.
The paper explores personalised federated learning for EEG decoding using two lightweight models: the Riemannian SPDNet and the Euclidean EEGNet. In the personalised approach, all subjects share a common trunk while keeping individual heads, which improves accuracy and reduces communication compared to standard federated learning and centralised training. Experiments on three motor‑imagery datasets show that personalised SPDNet outperforms both standard FL and centralised training, and beats EEGNet on two datasets, though centralised EEGNet remains superior to centralised SPDNet.
arXiv:2610.33712v1 Announce Type: new Abstract: Federated learning trains a shared model across clients without exchanging their data, yet the updates they transmit still leak information about indiv...
arXiv:2607. 08368v1 Announce Type: new Abstract: With the widespread deployment of basic models in edge intelligence, communication bandwidth has become a core bottleneck restricting the scalability of federated learning.
arXiv:2604. 24012v3 Announce Type: replace Abstract: Federated learning enables a population of clients to collaboratively train machine learning models without exchanging their raw data, but standard algorithms such as FedAvg suffer from slow convergence and high communication and memory costs in heterogeneous, resource-constrained environments.
With the widespread deployment of basic models in edge intelligence, communication bandwidth has become a core bottleneck restricting the scalability of federated learning. Although one-shot federated learning alleviates this problem by minimizing communication rounds, existing iterative fine-tuning or knowledge distillation methods still face challenges such as high server-side computational costs and hyperparameter sensitivity.
arXiv:2606. 00442v1 Announce Type: new Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks.
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
The paper introduces a new spectral federated learning method that combines local updates and communication compression, addressing key bottlenecks in FL such as data heterogeneity and high communication overhead. It builds on the spectral optimizer Muon, which has shown superiority over Adam-like methods in centralized training, and adapts it to the federated setting. The authors provide rigorous convergence guarantees without requiring the restrictive bounded heterogeneity assumption and validate their approach on standard image classification benchmarks.
arXiv:2606. 14416v1 Announce Type: new Abstract: Federated learning (FL) often struggles with generalization due to heterogeneous client data.