Abstract: Modern artificial intelligence (AI) architectures use a mixture of problem-specific heuristics and approximation techniques in order to scale to high-dimensional problems and large datasets. A common paradigm for deep learning is to stack several problem-specific encoding (i.e., representation learning) layers to embed the problem into a lower-dimensional latent space, followed by a heuristic piecewise-linear approximation technique (i.e., fully-connected ReLU layers). In this talk, I consider the challenges of replacing the fully-connected ReLU layers with Delaunay interpolation in order to perform a principled piecewise-linear interpolation instead of regression. Advantages of this approach include improved verifiability and interpretability, and tight error bounds under certain conditions.I begin by analyzing the similarities between Delaunay interpolants and fully-connected ReLU multi-layer perceptrons (MLPs). Then I present some advantages and disadvantages of using Delaunay interpolants from both an approximation theory and practical perspective. Finally, I present several novel algorithms that allow us to work with Delaunay interpolants in high dimensions. I will conclude by discussing how these techniques could be merged into a typical deep learning pipeline and the work that is required to achieve scalability in these settings.
Bio: Tyler Chang is a postdoc in the MCS Division at Argonne. Prior to joining Argonne, he was the Cunningham doctoral fellow at Virginia Tech, where he completed his Ph.D. in Computer Science, with a specialization in numerical analysis. His research interests include approximation theory, blackbox optimization, computational geometry, and open-source software.