Stiefel Attention: When the Geometry of Transformer Projection Matrices Dominates Optimizer Choice---and When It Does Not

arXiv:2609.19363 · cs.LG, cs.NA, math.NA · Submitted 2026-09-16 · Read on arXiv

cs.LG, cs.NA, math.NA

Submitted: 2026-09-16

Updated: 2026-09-27

Comments: 16 pages, 2 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Adam — 30× in this paper · explained in 2 episodes
• Accuracy — 23× in this paper · explained in 1 episode
• Benchmark — 15× in this paper · explained in 2 episodes
• Ablation — 12× in this paper · explained in 1 episode
• Transformer — 11× in this paper · explained in 2 episodes
• Stiefel manifold — 8× in this paper · explained in 2 episodes
• Riemannian optimization — 5× in this paper · explained in 2 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Regularization — 4× in this paper · explained in 3 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Redundancy — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Homogeneity — 2× in this paper · explained in 2 episodes
• AdamW Optimizer — 1× in this paper · explained in 1 episode
• Attention Entropy — 1× in this paper · explained in 2 episodes
• Attention Mechanism — 1× in this paper · explained in 3 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Entropy Collapse — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• In International Conference on Learning Representations — 1× in this paper
• International Conference on Machine Learning — 1× in this paper

Sources

• Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks