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This paper introduces the Transformer Geometry Observatory-II (TGO-II), a framework for analyzing the geometric evolution of representations in Vision Transformers during supervised training. Using techniques like Centered Kernel Alignment (CKA) and Singular Vector Canonical Correlation Analysis (SVCCA), the authors reveal that representational specialization increases while intrinsic dimensionality expands, indicating a simultaneous emergence of complexity and layer specialization. Notably, the study challenges the notion that increased representational complexity stems from token independence, showing instead that strong token interactions persist throughout training.
Representation complexity in Vision Transformers grows through richer transformations while maintaining strong token interactions, reshaping our understanding of model training dynamics.
While Vision Transformers have achieved remarkable success across computer vision and language applications, the geometric evolution of their internal representations throughout training remains insufficiently understood. Existing analyses primarily focus on attention mechanisms and downstream performance, leaving the evolution of representation geometry largely unexplored. In this work, we present Transformer Geometry Observatory-II (TGO-II), a representation geometry analysis framework designed to investigate how Transformer representations evolve during supervised training. TGO-II analyzes Vision Transformer (ViT-Small/16) representations using Centered Kernel Alignment (CKA), Singular Vector Canonical Correlation Analysis (SVCCA), Two-Nearest Neighbor Intrinsic Dimensionality (TwoNN-ID), and token covariance analysis. Our experiments reveal three key observations. First, both CKA and SVCCA progressively decrease throughout training, indicating increasing representational specialization across Transformer layers. Second, intrinsic dimensionality consistently increases before stabilizing, suggesting progressive expansion of the representation manifold into a larger set of locally accessible degrees of freedom. Third, token covariance and coupling analyses demonstrate that strong token interaction structure persists throughout training, challenging the hypothesis that increasing representational complexity arises primarily from progressive token independence. These findings suggest that representation complexity and layer specialization emerge simultaneously during training. Manifold expansion appears to occur without token decoupling. Together, these observations motivate a new hypothesis in which Vision Transformers increase representational complexity through progressively richer transformations while preserving strong token interaction structure during learning.
