$α$-TCAV: A Unified Framework for Testing with Concept Activation Vectors

TCAV (Testing with Concept Activation Vectors) is an interpretability method that assesses the alignment between the internal representations of a trained neural network and human-understandable, high-level concepts. Though effective, TCAV suffers from significant computational overhead, inter-layer disagreement of TCAV scores, and statistical instability. This work takes a step toward addressing these challenges by introducing E-TCAV, a framework for efficient approximation of TCAV scores, which is based on extensive investigation into three key aspects of the TCAV methodology: 1) the effect of latent classifiers on the stability of TCAV scores, 2) the inter-layer agreement of TCAV scores, and 3) the use of the penultimate layer as a fast proxy for earlier layers for TCAV computation. To ensure a solid foundation for E-TCAV, we conduct extensive evaluations across four different architectures and five datasets, encompassing problems from both computer vision and natural language domains. Our results show that the layers in the final block of the neural network strongly agree with the penultimate layer in terms of the TCAV scores, and the commonly observed variance of the TCAV scores can be attributed to the choice of the latent classifier. Leveraging this inter-layer agreement and the degeneracy of directional sensitivities at the penultimate layer, E-TCAV guarantees linearly scaling speed-ups with respect to the network's size and the number of evaluation samples, marking a step towards efficient model debugging and real-time concept-guided training.

Class activation mapping (CAM) is one of the most widely used visual explanation families in explainable artificial intelligence. Its purpose is intuitive: it converts internal model evidence into a heatmap that highlights the image regions, convolutional channels, tokens, or patches that support a target class or concept. Since the first CAM formulation in 2016, the field has moved far beyond global-average-pooled CNN classifiers. CAM-style methods now include gradient-based post-hoc explanations, gradient-free score and ablation methods, high-resolution upscaling, weakly supervised localization and segmentation, transformer token attribution, causal and debiasing methods, and foundation-model-era approaches that use CLIP, DINO, SAM, or feature-distribution comparisons. This review synthesizes a strict corpus of 57 method-centered papers published from 2016 onward. The paper develops a taxonomy that separates methods by attribution mechanism, architectural dependence, and evaluation objective. It then reviews gradient-based CAMs, recent and hybrid CAM-style methods, and model-based or architecture-aware methods. Across the corpus, the main trend is clear: the field is shifting from explaining one class score in one low-resolution CNN layer toward comparative, multi-layer, probabilistic, token-aware, and foundation-model-aware explanations. At the same time, evaluation remains fragmented. Faithfulness, localization, robustness, computational cost, and human trust are often measured with different protocols. The review therefore emphasizes not only what each method contributes, but also which gap it leaves open and which later methods attempt to close that gap.

Image similarity underlies many computer vision applications, yet it is often unclear why two images receive a high or low similarity score. Existing explainability methods often rely on gradient-based attribution maps to provide local justifications for similarity. These approaches struggle to provide global insights into what specifically drives similarity in regions of an embedding space, such as texture, shape, or color. We introduce a model- and metric-agnostic framework that explains image similarity using Concept Activation Vectors (CAVs) extracted automatically via Sparse Autoencoders (SAEs). Given a pair of images, we perturb their embeddings along discovered concept directions and measure the resulting change in a chosen similarity function, yielding concept importances. For image pairs, we provide localization with concept attribution maps. We extend this procedure to group-level settings, explaining what drives similarity across a cluster of images rather than a single pair, and further, we introduce Exemplar Retrieval, aiming to recover samples with similar reasons contributing to similarity. Our experiments show that our latent perturbations are more faithful to the underlying data distribution than pixel-space baselines, and that concept importances linearly recover the true similarity score. Qualitative results further confirm the usefulness of our methods in understanding a model's individual and group similarity judgments.