EQ-CBM: A Probabilistic Concept Bottleneck with Energy-based Models and Quantized Vectors

TL;DR

EQ-CBM is proposed, a novel framework that enhances CBMs through probabilistic concept encoding using energy-based models (EBMs) with quantized concept activation vectors (qCAVs) with quantized concept activation vectors (qCAVs), thereby improving prediction reliability and accuracy.

Abstract

The demand for reliable AI systems has intensified the need for interpretable deep neural networks. Concept bottleneck models (CBMs) have gained attention as an effective approach by leveraging human-understandable concepts to enhance interpretability. However, existing CBMs face challenges due to deterministic concept encoding and reliance on inconsistent concepts, leading to inaccuracies. We propose EQ-CBM, a novel framework that enhances CBMs through probabilistic concept encoding using energy-based models (EBMs) with quantized concept activation vectors (qCAVs). EQ-CBM effectively captures uncertainties, thereby improving prediction reliability and accuracy. By employing qCAVs, our method selects homogeneous vectors during concept encoding, enabling more decisive task performance and facilitating higher levels of human intervention. Empirical results using benchmark datasets demonstrate that our approach outperforms the state-of-the-art in both concept and task accuracy.

Figures (11)

• Figure 1: Comparison of concept encoding methods: (a) Deterministic concept encoding, and (b) probabilistic concept encoding using qCAVs.
• Figure 2: Overall architecture of the EQ-CBM. The input image $x$ is processed by the backbone network $f$ to generate a latent vector $z$. This latent vector is fed into probabilistic concept encoders $g_\mathrm{\Omega}$, which use variational inference techniques to infer $v_k$. The energy function $E_\theta$ evaluates the compatibility of $v_k$ with the qCAVs. Exponential Moving Average (EMA) updates each vector pair. The sampling module selects the concept vectors having lowest energy scores, which are then used for the final task.
• Figure 3: Integration of EBM in the concept encoder. The output is processed through softmax for concept prediction $c_k$ and LogSumExp (LSE) for composed energy score $\bar{e}_k$. The backward pass using SGLD updates $v_k$ based on the joint energy-concept landscape.
• Figure 3: Impact of model components on concept and task accuracy on the CUB dataset.
• Figure 4: Task accuracy under varying levels of human intervention in concept predictions for different models.