Riemannian Structure and Optimization for a Class of Low-Parametric Orthogonal Matrices

arXiv:2609.27982 · cs.LG, cs.AI, cs.NA, math.DG, math.NA · Submitted 2026-09-23 · Read on arXiv

cs.LG, cs.AI, cs.NA, math.DG, math.NA

Submitted: 2026-09-23

Updated: 2026-09-23

Code: https://github.com/alialiev78/torchgs

Terminology

• Riemannian optimization — 30× in this paper · explained in 2 episodes
• Automatic Differentiation — 10× in this paper
• Fine-Tuning — 5× in this paper · explained in 5 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Accuracy — 3× in this paper · explained in 1 episode
• Objective Function — 3× in this paper · explained in 2 episodes
• AdamW Optimizer — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• International Conference on Machine Learning — 2× in this paper
• Parameter-Efficient Fine-Tuning — 2× in this paper · explained in 2 episodes
• Riemannian Gradient Descent — 2× in this paper
• Trace — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Alternation — 1× in this paper · explained in 1 episode
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Fast Fourier Transform — 1× in this paper
• Parameter-Efficient Fine-Tuning (PEFT) — 1× in this paper · explained in 4 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Projective product spaces

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