Examining Data Representations to Expand the Theory of Learning Metrics

This thesis aims to examine case studies of data representation in artificial in- telligence in order to generate insights regarding model behavior and efficacy. Our first case study concerns neural networks and presents results detailing the concept of their mathematical equivalence. We demonstrate that the class of net- works equivalent to a given feedforward neural network with piecewise linear activation functions can be represented as a semi-algebraic set on the network coefficients. The second major exploration of data representation utilizes interdis- ciplinary techniques in order to qualitatively describe natural and synthetic hierar- chies in the image domain. We find that our approach predicts model performance in domain generalization (DG) tasks. The core thread throughout this work is a philosophy that emphasizes taking new vantages on popular AI data representa- tions and leveraging the resulting insights in order to lay the groundwork for new metrics of learning.