Representational Geometry as a Diagnostic for Adversarial Robustness

Adversarial training is a common technique for making neural networks more robust to small, intentionally crafted input perturbations, and robustness is commonly measured through accuracy under attack. By exploring inter-network representations across different adversarial training objectives, we can analyze whether multiple networks organize their latent representations similarly. We study Multilayer Perceptrons trained on MNIST under three adversarial training regimes and compare the resulting population training dynamics and geometry to those of a vanilla network. We use M-PHATE to embed data samples across training epochs and examine how the geometry of the data changes during training under adversarial objectives. On penultimate-layer representations we measure displacement between clean and perturbed points, distributional distance through maximum mean discrepancy, and nearest-neighbor recovery. Our visualizations and quantitative analyses show that adversarial training leads to structural changes in how networks organize internal data representations, and robust accuracy and representational stability can rank the same defenses in opposite ways. These findings support a discussion of re-evaluating how practitioners approach the auditing of model robustness by treating latent representations and their training trajectories as diagnostic artifacts across sets of networks.