Towards Compositionality in Concept Learning (2406.18534v1)

Abstract: Concept-based interpretability methods offer a lens into the internals of foundation models by decomposing their embeddings into high-level concepts. These concept representations are most useful when they are compositional, meaning that the individual concepts compose to explain the full sample. We show that existing unsupervised concept extraction methods find concepts which are not compositional. To automatically discover compositional concept representations, we identify two salient properties of such representations, and propose Compositional Concept Extraction (CCE) for finding concepts which obey these properties. We evaluate CCE on five different datasets over image and text data. Our evaluation shows that CCE finds more compositional concept representations than baselines and yields better accuracy on four downstream classification tasks. Code and data are available at https://github.com/adaminsky/compositional_concepts .

• The paper introduces Compositional Concept Extraction (CCE), a new method that learns orthogonal subspaces to capture compositional concept representations.
• The paper demonstrates that CCE outperforms traditional methods like PCA, ACE, and NMF on datasets such as CLEVR, CUB, and Truth in terms of MAP and compositionality scores.
• The paper shows that enforcing compositionality improves model debugging and downstream classification performance, offering enhanced transparency in AI systems.

Towards Compositionality in Concept Learning

In the evolving landscape of foundation models, interpretability remains a critical challenge. Stein et al.'s paper, "Towards Compositionality in Concept Learning," ventures into enhancing the interpretability of these models through the lens of concept compositionality. The authors propose a novel method, Compositional Concept Extraction (CCE), which aims to identify compositional concept representations without supervision, addressing the inadequacies of existing methods in capturing compositionality.

Problem Statement

Foundation models, although powerful across varied domains, tend to operate as black boxes, impairing our ability to debug, control, and trust their outputs. Concept-based interpretability methods have emerged as a promising way to decompose model embeddings into high-level, human-interpretable concepts. However, the utility of these concepts is maximal when they are compositional—when individual concepts can be combined to explain the full sample. Existing unsupervised methods for concept extraction, notably PCA and KMeans, often fail to discover compositional concepts. This paper bridges this gap by introducing CCE, designed to find and enforce more compositional concept representations.

Key Contributions

The paper offers four key contributions:

1. Analysis of Existing Methods: The authors critically evaluate current unsupervised concept extraction methods, demonstrating their failure to ensure the compositionality of discovered concepts.
2. Validation of Ground-Truth Compositionality: They show that models are indeed capable of representing compositional concepts, validated through controlled experiments on datasets like CLEVR, CUB, and Truth.
3. Identification of Salient Properties: The paper identifies two properties essential for compositionality in concept representations: orthogonality between different attributes and non-orthogonality within the same attribute.
4. Novel Method - CCE: CCE is introduced as a method that enforces these properties by searching for subspaces of concepts rather than individual concepts, improving the compositionality and downstream utility of the concepts extracted.

Methodology

The central insight behind CCE is to extract concepts within orthogonal subspaces, ensuring that concepts from different attributes (e.g., color vs shape) remain orthogonal while those within the same attribute may be correlated. CCE operates in a two-step process within an attribute:

• LearnSubspace: This step learns a subspace where the data is well-clustered according to current centroids.
• LearnConcepts: This step performs spherical KMeans clustering on the data projected into the learned subspace.

By iteratively refining these steps until convergence and projecting data out of subspaces associated with discovered concepts, CCE ensures the orthogonality and compositionality of the resulting concepts.

Evaluation and Results

Compositionality in Controlled Settings

CCE was evaluated on compositionality using MAP scores and compositionality scores across controlled settings:

• MAP Scores: CCE consistently outperformed PCA, ACE, NMF, and other baselines, showing higher accuracy in predicting the composition of concepts on datasets like CLEVR and Truth-sub.
• Compositionality Scores: CCE's scores were comparable to those of ground-truth representations, underscoring its efficacy in capturing compositionality.

Qualitative Analysis in Real Data Settings

CCE demonstrated its ability to discover and properly compose meaningful concepts in real-world datasets such as CUB and News. The qualitative results showed that CCE could identify both known and novel concepts, correctly combining them in logically consistent ways.

Downstream Performance

When assessing downstream classification tasks using the concept scores:

• Classification Accuracy: Models leveraging CCE-derived concepts often matched or exceeded the performance of models using original embeddings or other unsupervised concept extraction methods.
• Concept Supervision: CCE showed competitive performance even against Concept Transformer (a method using additional supervision), highlighting its robustness.

Implications and Future Directions

The theoretical insights and empirical results showcase CCE's potential in providing more interpretable and modular foundation models. These compositional concepts could simplify model debugging, refinement, and controlled modifications, fostering trust and reliability in AI systems.

Future research could further explore non-compositional and hierarchical concept structures, refine the automatic naming of concepts possibly through integration with vision-LLMs, and extend the methodology to cover broader types of models and data modalities.

Conclusion

Stein et al.'s paper represents a meaningful step towards making foundation models more interpretable through robust, compositional concept extraction. By validating the compositional nature of learned representations and proposing an effective method to discover them, this research bridges critical gaps in unsupervised concept learning, setting the stage for more transparent and manageable AI systems.