Quotient geometry of tensor ring decomposition

arXiv:2601.21874 · math.NA, cs.NA, math.OC, quant-ph · Submitted 2026-01-29 · Read on arXiv

math.NA, cs.NA, math.OC, quant-ph

Submitted: 2026-01-29

Updated: 2026-09-23

Code: https://github.com/JimmyPeng1998/LRTCTR

Terminology

• Core — 29× in this paper · explained in 2 episodes
• Riemannian optimization — 5× in this paper · explained in 2 episodes
• Redundancy — 4× in this paper · explained in 2 episodes
• Tucker Decomposition — 4× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Matrix Product States (MPS) — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• Desingularization of bounded-rank tensor sets
• Tensor network ranks
• Tensor Ring Decomposition

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