Linking Robustness and Generalization: A k* Distribution Analysis of Concept Clustering in Latent Space for Vision Models

Most evaluations of vision models use indirect methods to assess latent space quality. These methods often involve adding extra layers to project the latent space into a new one. This projection makes it difficult to analyze and compare the original latent space. This article uses the k* Distribution, a local neighborhood analysis method, to examine the learned latent space at the level of individual concepts, which can be extended to examine the entire latent space. We introduce skewness-based true and approximate metrics for interpreting individual concepts to assess the overall quality of vision models' latent space. Our findings indicate that current vision models frequently fracture the distributions of individual concepts within the latent space. Nevertheless, as these models improve in generalization across multiple datasets, the degree of fracturing diminishes. A similar trend is observed in robust vision models, where increased robustness correlates with reduced fracturing. Ultimately, this approach enables a direct interpretation and comparison of the latent spaces of different vision models and reveals a relationship between a model's generalizability and robustness. Results show that as a model becomes more general and robust, it tends to learn features that result in better clustering of concepts. Project Website is available online at https://shashankkotyan.github.io/k-Distribution/