Concept Attribution

The foundational technique for concept attribution. TCAV quantifies a model's sensitivity to a user-defined concept by measuring the directional derivative of a class prediction toward a Concept Activation Vector (CAV).

• Produces a score indicating how strongly a concept influences a class
• Uses statistical significance testing with random vectors to validate results
• Operates on any layer of a neural network without modifying the architecture

The fundamental building block of concept-based explanations. A CAV is a vector in a neural network's activation space that represents a human-understandable concept. It is derived by training a linear classifier to distinguish between examples of the concept and random counterexamples. The direction of this vector encodes the concept's semantic meaning, enabling quantitative testing of how strongly a model responds to it.

A technique that quantifies a model's sensitivity to a user-defined concept by measuring the directional derivative of a class prediction towards the Concept Activation Vector. TCAV produces a score called the TCAV score, which represents the fraction of inputs for which the model's prediction increases along the concept direction. Statistical significance testing with two-sided t-tests against random vectors ensures the concept is not an artifact.

An extension of Layer-wise Relevance Propagation that decomposes a model's decision not just by input features but also through higher-level latent concepts. CRP traces the flow of relevance through the network's layers, attributing importance to specific filters, channels, or neurons that encode semantic concepts. This provides a fine-grained, heatmap-style explanation of which concepts drove a prediction.

A method that applies Shapley values from cooperative game theory to quantify the importance of individual concepts for a model's prediction. ConceptSHAP treats each concept as a player in a coalition and computes its marginal contribution to the prediction across all possible concept subsets. This provides a game-theoretic attribution with axiomatic guarantees of fairness and consistency.

An inherently interpretable architecture that first predicts a set of predefined human-understandable concepts from the input and then uses only those concept scores to make the final prediction. This creates a strict information bottleneck that forces the model to reason through explicit concepts. Key metrics include:

• Concept Completeness Score: How sufficient the concepts are for the task
• Concept Purity: How well concept representations cluster together
• Concept Separability: How distinct different concepts are in activation space

Techniques for causally testing concept influence by directly manipulating activations during inference. Concept Intervention modifies internal activations to increase or decrease a concept's presence and observes the output change. Concept Erasure removes a concept's information by projecting activations onto a subspace orthogonal to the concept vector. These methods establish causal relationships rather than mere correlations.