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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Routing on the Stiefel Manifold: When Does Adaptive Subsp...
Isabella Costa Maia, Pedro L. C. Rodrigues, Salem Said, Marco Co · 2026-05-29 · via stat updates on arXiv.org

Cross-domain EEG decoding remains challenging despite advances in Riemannian deep learning: covariance matrices from different subjects occupy systematically distinct regions of the SPD manifold, yet existing domain adaptation methods either require target-domain calibration data or learn subject-specific components that cannot generalise across domains. We propose dynamic Stiefel routing: a pool of $K$ expert projection filters on the Stiefel manifold, each specialised for a different region of the SPD manifold, with each input covariance routed to the most appropriate filter via cross-attention, adapting the subspace projection per sample. A central finding is that this approach, implemented naively, provably collapses to ensemble averaging: when routing weights are uniform, the adaptive filter reduces exactly to an equal-contribution combination of experts, indistinguishable from a single fixed filter. Three structural properties break this degeneracy: a symmetric anchor $W_{\mathrm{base}} \in \mathrm{St}(n,k)$ that removes proximity bias among experts; a frozen domain-discriminative query encoder that decouples routing from task optimisation; and a decoupled key alignment loss that trains expert keys toward stable domain attractors. Together they produce the first genuinely committed and domain-structured routing on SPD manifolds, with consistent gains across three datasets: balanced accuracy improves from $0.773\to 0.823$, $0.757\to 0.809$, and $0.801\to 0.839$, with the alignment strategy determined automatically by a single data-driven rule and no dataset-specific hyperparameter search.