Pantypes: Diverse Representatives for Self-Explainable Models
Rune Kjærsgaard
Ahcène Boubekki
Line Clemmensen
DTU, Denmark
PTB, Germany
DTU, Denmark
Motivation
Improve prototypes' diversity
Motivation
What is Diversity?
Geometric diversity
In the embedding
Combinatorial diversity
In terms of attributes
High Geometric
Low Combinatorial
Low Geometric
High Combinatorial
High Geometric
High Combinatorial
Celis, L. Elisa, et al. "How to be fair and diverse?." arXiv:1610.07183 (2016)
Pantypes
Pantypes
Pantypes builds upon ProtoVAE
Gautam, Srishti, et al. "Protovae: A trustworthy self-explainable prototypical variational model." Neurips (2022)
⊕ Robust
⊕ Reconstruct prototypes
⊖ Slow training
⊖ Sensitive hyper-tuning
Pantypes
ProtoVAE loss function:
\mathcal{L}_{\mathrm{ProtoVAE}}=\mathcal{L}_{\mathrm{pred}} + \mathcal{L}_{\mathrm{VAE}} + \mathcal{L}_{\mathrm{orth}}
\mathcal{L}_{\mathrm{ProtoVAE}}=\mathcal{L}_{\mathrm{pred}} + \mathcal{L}_{\mathrm{VAE}} + \sum_{k} || \mathbf{\Phi}_k^T \mathbf{\Phi}_k - \mathbf{I}_M||_F^2
Explicit constraints on rank and norm.
Let's make these constraints implicit!
Orthonormal prototypes
Pantypes
Pantypes
Pantypes loss function:
\mathcal{L}_{\mathrm{Pantypes}}=\mathcal{L}_{\mathrm{pred}} + \mathcal{L}_{\mathrm{VAE}} + \frac{1}{K} \sum_{k} \frac{1}{|\mathbf{G}_k|^\frac{1}{2}}
\text{with} \: \mathbf{G}_k = \mathbf{\Phi}^T_k \mathbf{\Phi}_k
Maximize the volume
of the prototypical Gram matrix.
⇝ Maximize norm and rank of .
\mathbf{\Phi}_k
IF USED!
Regularized by the VAE loss
Maximize the volume
of the prototypical Gram matrix.
⇒ Maximize norm and rank of .
\mathbf{G}_k
"Unused" prototypes diverge out-of-distribution
maximizes the norm and rank of the prototypes
\mathcal{L}_\mathrm{vol}
regularizes the norm of "used" prototypes
\mathcal{L}_\mathrm{VAE}
\mathcal{L}_{\mathrm{Pantypes}}=\mathcal{L}_{\mathrm{pred}} + \mathcal{L}_{\mathrm{VAE}} + \mathcal{L}_{\mathrm{vol}}
Pantypes
Norm constraint
too strong
Missing
OOD prototype
Evaluation
Geometric Diversity
Evaluation: Geometric Diversity
Davies-Bouldin Index
\operatorname{DB} = \frac{1}{K}\sum_k \max_{l \neq k} \frac{s_k+s_l}{d_{kl}}
The better the lower which indicates dense and well separated clusters
The better the lower which indicates dense and well separated clusters
Pantypes
converge faster
Evaluation: Geometric Diversity
⏺ Data of class "bags"
⏹ Prototypes/Pantypes
⏺ 100 most similar points to each prototypes
━ Class' convex hull
━ Prototypes' convex hull
━ Subset's convex hull
\frac{\operatorname{Volume}(\hspace{2.5cm})}{\operatorname{Volume}(\hspace{2.5cm})}
Class' convex hull
Subset's convex hull
\text{Pantypes}:77\%
\text{ProtoVAE}:33\%
Evaluation
Combinatorial Diversity
Evaluation: Combinatorial Diversity
Visual inspection:
UTKFace Large Scale Face Dataset https://susanqq.github.io/UTKFace/
Evaluation: Combinatorial Diversity
Diversity Index
\begin{split}
\operatorname{DI} & = H\left( \begin{array}{c} \text{probability an attribute} \\ \text{is captured by a prototype} \end{array} \right) \\
& = \sum_{a\in \operatorname{\tiny Attributes}} -p_a \log(p_a)
\end{split}
A high entropy equates to a more diverse (fair) representation, which is not particularly biased towards any demographic group.
Higher
Diversity Index
Smaller
accuracy gap
\operatorname{Attributes} = \{ \mathrm{White}, \mathrm{Black}, \mathrm{Asian}, \mathrm{Indian}, \mathrm{Others} \} \times \{\mathrm{Female}, \mathrm{Male}\}.
UTKFace Large Scale Face Dataset https://susanqq.github.io/UTKFace/
Summary
Summary
- build upon a robust backbone.
- maximize the volume of the prototypical Gram matrix.
- enforce implicitly a constraint on rank and norm.
- select automatically the prototypes.
- Smaller Davies-Bouldin index that converges faster.
- Smaller accuracy gap between White Male and Black Female.
- Larger diversity index.
⇒ Better geometric and combinatorial diversity.
Pantypes
Evaluation
Pantypes: Diverse Representatives for Self-Explainable Models
Rune Kjærsgaard
Ahcène Boubekki
Line Clemmensen
DTU, Denmark
PTB, Germany
DTU, Denmark
Pantypes
By ahcene
Pantypes
AAAI24 Presentation
