CLIP-QDA: An Explainable Concept Bottleneck Model

TL;DR

This work addresses the opacity of large multimodal foundation models by proposing CLIP-QDA, a greybox CBM that models CLIP scores with a $Gaussian\ Mixture\ Model$ and uses a $Quadratic\ Discriminant\ Analysis$ head for classification. It provides both dataset-wide and sample-level explanations, augmenting with adapted CBM-specific LIME and SHAP methods, and introduces two evaluation metrics (Deletion and Detection) to quantify explanation faithfulness. Empirical results show that the Gaussian-prior assumption can hold on certain datasets with limited concept sets, yielding competitive accuracy and fast, interpretable explanations, while large concept sets challenge the approach, motivating future work on richer priors and latent-space guidance. Overall, CLIP-QDA offers a transparent, efficient alternative to fully black-box CLIP-based CBMs, with practical benefits for bias detection and explainability in vision tasks.

Abstract

In this paper, we introduce an explainable algorithm designed from a multi-modal foundation model, that performs fast and explainable image classification. Drawing inspiration from CLIP-based Concept Bottleneck Models (CBMs), our method creates a latent space where each neuron is linked to a specific word. Observing that this latent space can be modeled with simple distributions, we use a Mixture of Gaussians (MoG) formalism to enhance the interpretability of this latent space. Then, we introduce CLIP-QDA, a classifier that only uses statistical values to infer labels from the concepts. In addition, this formalism allows for both local and global explanations. These explanations come from the inner design of our architecture, our work is part of a new family of greybox models, combining performances of opaque foundation models and the interpretability of transparent models. Our empirical findings show that in instances where the MoG assumption holds, CLIP-QDA achieves similar accuracy with state-of-the-art methods CBMs. Our explanations compete with existing XAI methods while being faster to compute.

Figures (22)

• Figure 1: Overview of our modeling method. By considering the whole dataset CLIP scores ${\bm{z}}$ as class conditioned distributions ${\bm{Z}}=Z^{{1}}\ldotsZ^{{N}}$, we model the CLIP latent space as a mixture of Gaussians, allowing for mathematically grounded explanations.
• Figure 2: Training procedure of the general framework. First, CLIP scores ${\bm{z}}$ are computed for each of the concepts $\{{\bm{k}}^{j}\}_{j=1}^{N}$, then a classifier $h_{{\bm{\omega}}^h}(.)$, with parameters ${\bm{\omega}}^h$ is trained to classify the label from the concatenation of the CLIP scores.
• Figure 3: Normalized histogram of scores $Z^{j}$ specifically for the concept "Pointy-eared". On the left, we observe that the different classes can be modeled as weighted Gaussians. On the right, we show the resulting Gaussian mixture modeling.
• Figure 4: The different source of explanation of CLIP-QDA. Global (CLIP-QDA$^{global}$) vs. Local (CLIP-QDA$^{local}$) explanations offer insights into classifier behavior across the dataset and on individual samples, respectively. Post-hoc explanations with CLIP-SHAP and CLIP-LIME use traditional XAI techniques.
• Figure 5: Visualization of the counterfactuals in the two Gaussians toy example. Samples of the two distributions are plotted in blue and orange. The equiprobability line is plotted in black.

Theorems & Definitions (3)

• Proposition 1
• Proposition 2
• proof