Technical Summary: Concept-Based Abductive and Contrastive Explanations for Behaviors of Vision Models

Problem Statement

Existing methods for explaining deep neural network (DNN) predictions face two primary limitations. First, concept-based explanations (ConXps) typically rely on sensitivity analysis or concept erasure to determine the impact of high-level semantic concepts on model outputs. However, these approaches often fail to establish rigorous causal connections, specifically lacking the ability to determine if a concept is necessary or sufficient for a prediction, or to handle scenarios where multiple concepts interact causally. Second, formal abductive and contrastive explanation methods provide mathematically rigorous guarantees of minimality and causality but are restricted to low-level features (e.g., pixels), which lack human interpretability. Furthermore, these formal methods struggle to scale to modern vision models due to the computational cost of constraint solving.

There is a gap in the literature for explanations that are simultaneously:

1. Concept-based: Expressed in terms of human-understandable semantic concepts.
2. Formal: Guaranteeing minimality and causal relevance (sufficiency/necessity).
3. Scalable: Applicable to state-of-the-art vision models and capable of explaining behaviors across collections of images, not just single instances.

Methodology

The authors propose Concept-based Abductive and Contrastive Explanations (ConAXps and ConCXps), a framework that merges formal explanation theory with concept-based interpretability.

1. Concept Representation and Erasure

To bridge the gap between vision models and human concepts, the authors leverage Vision-Language Models (VLMs), specifically CLIP, as a semantic lens.

• Concept Vectors: Concept vectors are extracted from CLIP's text encoder using descriptive captions. These vectors are mapped to the vision model's embedding space via a learned linear transformation.
• Concept Strength: The strength of a concept in an image embedding is calculated as the cosine similarity between the embedding and the concept vector.
• Concept Erasure: To establish causality, the method "erases" concepts from the embedding. The paper evaluates three erasure procedures:
  • Ortho (Proposed): A constrained optimization that projects the embedding to be orthogonal to the erased concept vectors while preserving the scalar projections of unerased concepts.
  • SPLiCE: Uses sparse non-negative decomposition to reconstruct embeddings without specific concepts.
  • LEACE: A closed-form linear transformation that removes linear correlations with a concept while minimally modifying the embedding.

2. Formal Definitions

The authors extend formal explanation definitions to the concept space:

• Concept-based Abductive Explanation (ConAXp): A minimal set of concepts such that retaining them (and erasing all others) is sufficient to maintain the model's prediction.
• Concept-based Contrastive Explanation (ConCXp): A minimal set of concepts such that erasing them (and retaining all others) is sufficient to change the model's prediction.

These definitions rely on a monotonicity assumption regarding the model head: adding a concept to a representation does not change the prediction away from the original class. The authors provide empirical evidence supporting this assumption.

3. Explanation Enumeration Algorithms

To compute these explanations, the paper presents three algorithms:

• NaiveEnum: A depth-bounded exhaustive search that enumerates concept sets starting from single concepts. It is computationally expensive for large vocabularies but guarantees finding all explanations within the depth bound.
• XpEnum: Adapted from formal explanation literature, this algorithm exploits the duality between abductive and contrastive explanations (hitting sets) to simultaneously enumerate both types. It uses a minimal hitting set approach to generate candidates.
• XpSatEnum: A novel algorithm designed to handle behaviors across image collections. It takes initial explanations from a budget-bounded enumerator and "saturates" them by checking if they are valid across other images in the behavior set, maximizing the overlap of explanations.

4. Aggregating for Behavior

Rather than explaining single images, the framework aggregates signed explanations (concepts with positive or negative activation) across a dataset subset (a "behavior") to produce a histogram of the most frequent explanations. This allows for the identification of general patterns driving model decisions or misclassifications.

Key Contributions

1. Novel Notion: The introduction of ConAXps and ConCXps, which provide minimal, causally grounded explanations in terms of high-level concepts rather than pixels.
2. Algorithmic Suite: The development of three enumeration algorithms (NaiveEnum, XpEnum, XpSatEnum) that balance computational tractability with the completeness of explanation discovery.
3. New Erasure Procedure: The proposal of the Ortho erasure method, which offers a closed-form solution for concept removal that preserves unerased concept strengths.
4. Behavioral Analysis: A methodology for aggregating per-image explanations to explain model behaviors (e.g., specific misclassification patterns) across collections of images, demonstrating that a small subset of explanations often covers the majority of cases.

Experimental Results

The approach was evaluated on three vision models (zero-shot CLIP, ResNet18, VGG19) and two datasets (RIVAL-10, EuroSAT) across various behaviors (correct classifications and misclassifications).

• Generalizability: The most frequent explanations (ConXps) remained stable across disjoint subsets of the same behavior, achieving high Intersection-over-Union (IoU) scores. This indicates that the explanations capture universal reasons for model behavior rather than image-specific noise.
• Coverage: Despite the potential for thousands of unique explanations, a very small subset (typically $K \le 10$) was sufficient to cover the majority of images in a behavior. In many cases, $K \le 5$ achieved full coverage.
• Parsimony: Shorter explanations (containing 1 or 2 concepts) consistently demonstrated higher individual coverage than longer explanations, supporting the principle of Occam's razor in this context.
• Plausibility: Using an LLM-as-a-judge (Gemini 3 Pro) to evaluate concept relevance, the study found that models generally rely on plausible (relevant) concepts. However, a significant portion of explanations were "partially plausible," indicating that models often rely on a mix of relevant features and spurious correlations (e.g., background textures).
• Efficiency: The XpEnum algorithm paired with Ortho or SPLiCE erasure proved to be the most efficient, computing explanations for 700 images in 5–10 minutes. LEACE was found to be computationally expensive due to the need for training data to compute affine transformations for each erasure.

Significance and Claims

The paper claims that its approach successfully bridges the gap between formal verification and semantic interpretability. By providing minimal sets of concepts that are causally sufficient or necessary, the method offers explanations that are both mathematically rigorous and human-understandable.

The authors emphasize that their method allows analysts to:

• Identify general, universal explanations for model behaviors rather than isolated observations.
• Detect spurious reasoning by identifying cases where model decisions rely on irrelevant concepts.
• Understand model decisions on collections of images, facilitating the debugging of systematic errors.

The work concludes that short, concept-based explanations are highly effective for understanding vision models and that the proposed framework offers a reasonable trade-off between scalability and explanation quality, making formal causal analysis feasible for modern deep learning systems. Future work is suggested to apply these methods to Large Language Models (LLMs) and Vision-Language Models (VLMs) to address sequential behaviors.