Structural Causality-based Generalizable Concept Discovery Models

TL;DR

This paper proposes a disentanglement mechanism utilizing a variational autoencoder (VAE) for learning mutually independent generative factors for a given dataset and subsequently learning task-specific concepts using a structural causal model (SCM).

Abstract

The rising need for explainable deep neural network architectures has utilized semantic concepts as explainable units. Several approaches utilizing disentangled representation learning estimate the generative factors and utilize them as concepts for explaining DNNs. However, even though the generative factors for a dataset remain fixed, concepts are not fixed entities and vary based on downstream tasks. In this paper, we propose a disentanglement mechanism utilizing a variational autoencoder (VAE) for learning mutually independent generative factors for a given dataset and subsequently learning task-specific concepts using a structural causal model (SCM). Our method assumes generative factors and concepts to form a bipartite graph, with directed causal edges from generative factors to concepts. Experiments are conducted on datasets with known generative factors: D-sprites and Shapes3D. On specific downstream tasks, our proposed method successfully learns task-specific concepts which are explained well by the causal edges from the generative factors. Lastly, separate from current causal concept discovery methods, our methodology is generalizable to an arbitrary number of concepts and flexible to any downstream tasks.

Figures (9)

• Figure 1: BOTTOM LEFT: Target image in question. Schematic figure to demonstrate why task-specific concepts are required. Even though the generative factors are known for the image, the concepts pertinent for correct classification can be causally related to multiple generative factors.
• Figure 2: Schematic diagram of the proposed approach to learn task-specific concepts from disentangled independent representations (generative factors). Our proposed approach utilizes a variational autoencoder to learn representations of mutually independent generative factors ($\mathbf{z}$). The generative factors are transformed into concepts $\mathbf{c}$ by the Structural Causal Matrix $\mathbf{A}$. Finally, task prediction is performed by the weighted sum of the concepts $c$ and Weight Matrix $W$. $\hat{x}$ represents the reconstructed $x$. The exact formulation is detailed in Appendix. Green blocks represent exogenous variables, i.e., variables that can be observed and are provided as input to the model. Blue blocks represent endogenous variables, i.e., variables learned from the model. Red blocks represent learnable parameters of the model. (Best viewed in color)
• Figure 3: Visualized graphical structure for mapping generative factors to task-specific concepts. The generated concepts are child terminal nodes of parent nodes corresponding to independent generative factors. The sets $Z \in\{z_i \}^N_1$ and $C \in\{c_i \}^K_1$ form a bipartite graph $\Gamma(Z,C)$ with directed edges from $Z$ to $C$. The edges from $Z$ to $C$ are modelled by the Causal Matrix $A$ which captures the edge transitions.
• Figure 4: TOP: Original test set images and their associated reconstructions from the d-Sprites dataset. BOTTOM: Original test set images and their associated reconstructions from the Shapes3D dataset. As can be seen, the reconstruction quality is perceptibly similar.
• Figure 5: Visualizations of the learned edge weight matrices $\mathbf{W}$ and causal matrices $\mathbf{A}$ for 2 binary tasks for the d-Sprites dataset. Note that we plot the transpose of both matrices. The lighter the color, the higher the weight assigned to the edge is (Best viewed in color). Similar visualizations for the Shapes3D dataset can be found in Appendix.