The Triangle of Similarity: A Multi-Faceted Framework for Comparing Neural Network Representations

Comparing neural network representations is essential for understanding and validating models in scientific applications. Existing methods, however, often provide a limited view. We propose the Triangle of Similarity, a framework that combines three complementary perspectives: static representational similarity (CKA/Procrustes), functional similarity (Linear Mode Connectivity or Predictive Similarity), and sparsity similarity (robustness under pruning). Analyzing a range of CNNs, Vision Transformers, and Vision-Language Models using both in-distribution (ImageNetV2) and out-of-distribution (CIFAR-10) testbeds, our initial findings suggest that: (1) architectural family is a primary determinant of representational similarity, forming distinct clusters; (2) CKA self-similarity and task accuracy are strongly correlated during pruning, though accuracy often degrades more sharply; and (3) for some model pairs, pruning appears to regularize representations, exposing a shared computational core. This framework offers a more holistic approach for assessing whether models have converged on similar internal mechanisms, providing a useful tool for model selection and analysis in scientific research.