Research map / 3D vision / Face and shape
Manifold Learning in Quotient Spaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace vanilla autoencoding with quotient loss and rotation orbit pooling | 3D shape autoencoding · ShapeNet planes, chairs, and cars (2D depth maps and 3D voxels) | reconstruction error: AE 2 -> QAE: planes 2D 0.12 -> 0.10; planes 3D 0.44 -> 0.36; chairs 2D 0.28 -> 0.22; chairs 3D 2.0 -> 1.9; cars 2D 0.52 | Helped |
| Add orbit pooling over all rotations (ablation) | QAE · ShapeNet chairs 2D depth maps validation | reconstruction error: 0.28 -> 0.21 | Helped |
| Pool over 12 random rotations instead of all 36 (ablation) | QAE · ShapeNet chairs 2D depth maps validation | reconstruction error: 0.21 -> 0.24 | Hurt |
| Remove orbit pooling (ablation) | QAE · ShapeNet chairs 2D depth maps | reconstruction error | Hurt |
| Pretrain on aligned examples before fine-tuning on misaligned data (ablation) | QAE · ShapeNet 3D co-alignment | co-alignment error: chairs 20% -> 1.8%; cars 13% -> 2.8%; planes 28% -> 6.8% | Helped |
| Use Gauss-Newton instead of gradient descent to optimize the continuous transformation (ablation) | Continuous QAE · ShapeNet chairs depth maps validation | reconstruction error: 0.60 -> 0.41 | Helped |
Closest papers by meaning
- Learning Manifold Patch-Based Representations of Man-Made Shapes (ICLR 2021 · similarity 0.88)
- Isometric Quotient Variational Auto-Encoders for Structure-Preserving Representation Learning (NeurIPS 2023 · similarity 0.88)
- Neural Isometries: Taming Transformations for Equivariant ML (NeurIPS 2024 · similarity 0.87)
- Graph Geometry-Preserving Autoencoders (ICML 2024 · similarity 0.86)
- LaGeM: A Large Geometry Model for 3D Representation Learning and Diffusion (ICLR 2025 · similarity 0.86)
- The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws (NeurIPS 2026 · similarity 0.86)
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