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Pantypes: Diverse Representatives for Self-Explainable Models
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Introduces pantypes, prototypes learned with a DPP-inspired volumetric loss inside a VAE-based prototypical self-explainable classifier (PanVAE, built on ProtoVAE) to improve data-space coverage, diversity and fairness.
Problem
Prototypical self-explainable classifiers often learn prototypes that cover only small regions of the input distribution, leading to representation bias and poor coverage of low-density regions.
Approach
Replace ProtoVAE's orthonormality diversity loss with a volumetric loss based on the Gram determinant of prototype vectors (a DPP-inspired linear-kernel volume), which pushes prototypes apart to span more of the latent space and allows pruning of prototypes that are not needed.
Key results
- PanVAE achieves the best Davies-Bouldin scores on all four datasets, e.g. 1.09 vs 1.35 (ProtoVAE) on FMNIST and 1.82 vs 2.57 on QuickDraw.
- On UTK Face, PanVAE reduces the White male vs Black female accuracy gap from 4.69 to 0.32 points, with overall accuracy 95.42 vs 95.08 for ProtoVAE.
- PanVAE's sample convex hull covers 77% of the full class convex hull for the FMNIST bag class versus 33% for ProtoVAE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · MNIST | Davies-Bouldin index: 1.21 $\pm$ 0.00 -> 1.13 $\pm$ 0.03 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · FMNIST | Davies-Bouldin index: 1.35 $\pm$ 0.01 -> 1.09 $\pm$ 0.01 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · QDraw | Davies-Bouldin index: 2.57 $\pm$ 0.01 -> 1.82 $\pm$ 0.01 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · CelebA | Davies-Bouldin index: 1.58 $\pm$ 0.15 -> 1.37 $\pm$ 0.01 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · MNIST | accuracy: 99.3 $\pm$ 0.1 -> 99.4 $\pm$ 0.1 | No clear effect |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · FMNIST | accuracy: 91.6 $\pm$ 0.1 -> 92.2 $\pm$ 0.1 | No clear effect |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · QDraw | accuracy: 85.6 $\pm$ 0.1 -> 85.5 $\pm$ 0.1 | No clear effect |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · CelebA | accuracy: 98.6 $\pm$ 0.0 -> 98.6 $\pm$ 0.0 | No clear effect |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · UTK Face | accuracy gap: 4.69 $\pm$ 0.24 -> 0.32 $\pm$ 0.15 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · UTK Face | accuracy (Black Female): 91.67 $\pm$ 0.53 -> 94.90 $\pm$ 0.39 | Helped |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · UTK Face | accuracy (White Male): 96.35 $\pm$ 0.31 -> 95.21 $\pm$ 0.33 | Hurt |
| Replace class-wise orthonormality loss with volumetric loss | ProtoVAE (PanVAE) · UTK Face | demographic diversity: 1.26 $\pm$ 0.06 -> 1.43 $\pm$ 0.07 | Helped |
Surprising findings
- Scaling ProtoVAE's orthonormality loss does not significantly change prototype diversity, whereas scaling the volumetric loss gives direct diversity control.
- The accuracy gain for Black females comes at the cost of lower accuracy on White males compared with ProtoVAE (95.21 vs 96.35).
Limitations
- Volumetric loss only enforces geometric (visual) diversity, which may not align with demographic diversity when background and pose vary.
- Demographic fairness gains come with reduced accuracy on the majority group.
- Pruning is a heuristic based on maximal similarity scores.
Experimental setup
Datasets: FashionMNIST MNIST QuickDraw CelebA UTK Face
Benchmarks: MNIST FashionMNIST QuickDraw CelebA UTK Face
Metrics: accuracy Davies-Bouldin index convex hull data coverage accuracy gap information entropy demographic diversity
Baselines: ProtoPNet ProtoVAE
Builds on: ProtoVAE ProtoPNet Determinantal Point Process
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