VGG

Visual Geometry Group, Oxford

Structures found in this family (5)

Circle, Intrinsic-dimension profile across depth, Curvature profile of the representation manifold, Polytope (Simplex), Linear Separability

By model (1)

VGG (image classifier, various depths)

Circle, Intrinsic-dimension profile across depth, Curvature profile of the representation manifold, Polytope (Simplex), Linear Separability

Observations (7)

A persistent circle recurs in the convolutional filter weights of real trained CNNs across depths, datasets, and training runs, and fixing an idealized circle as the first layer causally improves cross-dataset generalization

CNN intrinsic dimension is hunchback-shaped; last-layer ID predicts accuracy

Latent-manifold principal curvature (MAPC) tracks CNN generalization

Penultimate-layer manifold geometry predicts OOD generalization failure

Last-layer class means converge to a Simplex Equiangular Tight Frame

Object manifolds untangle across CNN depth, causally driven by geometry

Object-manifold radius and dimension track memorization and double descent

Papers

Topological Approaches to Deep Learning (2018), Exposition and Interpretation of the Topology of Neural Networks (2019), Intrinsic Dimension of Data Representations in Deep Neural Networks (2019), Data Representations' Study of Latent Image Manifolds (2023), Diagnosing Generalization Failures from Representational Geometry Markers (2026), Prevalence of Neural Collapse during the terminal phase of deep learning training (2020), Are Neurons Actually Collapsed? On the Fine-Grained Structure in Neural Representations (2023), Separability and Geometry of Object Manifolds in Deep Neural Networks (2020), On the Geometry of Generalization and Memorization in Deep Neural Networks (2021)