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Finding Low-Rank Matrix Weights in DNNs via Riemannian Optimization: RAdaGrad and RAdamW
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Proposes Riemannian adaptive optimizers (RAdaGrad, RAdamW) that optimize low-rank matrix weights directly on the fixed-rank manifold, avoiding non-unique factorizations and ill-conditioning slowdowns.
Problem
Finding low-rank matrix weights for large DNNs to reduce memory and compute; existing factorization-based methods are redundant and converge slowly when target low-rank matrices are ill-conditioned.
Approach
Treats low-rank weight matrices as points on a Riemannian manifold and applies adaptive gradient methods (AdaGrad- and AdamW-style) directly in that geometry, avoiding factorization and its Jacobian condition-number dependence.
Experimental setup
Baselines: factorization-based low-rank methods
Builds on: AdaGrad AdamW LoRA
Closest papers by meaning
- A Riemannian Network for SPD Matrix Learning (AAAI 2017 · similarity 0.88)
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- Riemannian Multinomial Logistics Regression for SPD Neural Networks (CVPR 2024 · similarity 0.87)
- Riemannian coordinate descent algorithms on matrix manifolds (ICML 2024 · similarity 0.87)
- From Low Rank Gradient Subspace Stabilization to Low-Rank Weights: Observations, Theories, and Applications (ICML 2025 · similarity 0.86)
- Matrix Manifold Neural Networks++ (ICLR 2024 · similarity 0.86)
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