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Learning a Gradient-free Riemannian Optimizer on Tangent Spaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the learned gradient-free tangent-space optimizer instead of Gao et al.'s manifold optimizer | Riemannian optimization · YaleB face recognition | accuracy (%): 89.0 -> 90.2 | Helped |
| Use the learned gradient-free tangent-space optimizer instead of Gao et al.'s manifold optimizer | Riemannian optimization · Kylberg texture clustering | accuracy (%): 85.2 -> 86.1 | Helped |
| Use the learned tangent-space optimizer rather than hand-designed Riemannian optimizers | Riemannian optimization · YaleB face recognition | accuracy (%): 78.0 -> 90.2 | Helped |
| Use the learned tangent-space optimizer rather than hand-designed Riemannian optimizers | Riemannian optimization · Kylberg texture clustering | accuracy (%): 80.3 -> 86.1 | Helped |
| Learn updates on tangent spaces and avoid differentiating through manifold optimization | Riemannian meta-optimizer · PCA on MNIST | training time (seconds): 1876.6 -> 208.4 | Helped |
| Learn updates on tangent spaces and avoid differentiating through manifold optimization | Riemannian meta-optimizer · YaleB face recognition | training time (seconds): 2508.6 -> 272.8 | Helped |
| Learn updates on tangent spaces and avoid differentiating through manifold optimization | Riemannian meta-optimizer · Kylberg texture clustering | training time (seconds): 11979.2 -> 1419.0 | Helped |
| Increase the inner-loop steps from 5 to 20 (ablation) | Ours optimizer · Kylberg texture clustering | meta-gradient mean: 0.92 -> 2.13 × 10^1 | Mixed |
| Increase the inner-loop steps from 5 to 20 (ablation) | Ours optimizer · Kylberg texture clustering | meta-gradient variance: 1.10 -> 1.25 × 10^3 | Mixed |
| Increase the inner-loop steps from 5 to 20 (ablation) | Ours optimizer · PCA on MNIST | training time (seconds): 61.3 -> 208.4 | Hurt |
| Increase the inner-loop steps from 5 to 20 (ablation) | Ours optimizer · YaleB face recognition | training time (seconds): 71.5 -> 272.8 | Hurt |
| Increase the inner-loop steps from 5 to 20 (ablation) | Ours optimizer · Kylberg texture clustering | training time (seconds): 1365.6 -> 1419.0 | Hurt |
Closest papers by meaning
- Learning-Rate-Free Stochastic Optimization over Riemannian Manifolds (ICML 2024 · similarity 0.92)
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- Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method (ICML 2025 · similarity 0.89)
- Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space (NeurIPS 2025 · similarity 0.88)
- An Adaptive Algorithm for Bilevel Optimization on Riemannian Manifolds (NeurIPS 2025 · similarity 0.88)
- Riemannian Geometric-based Meta Learning (AAAI 2025 · similarity 0.88)
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