Taylor Mode AD in Practice: Experiments with Mixed-Partial Computation

Speaker: Tim Siebert, Humboldt-Universität zu Berlin / Zuse Institute Berlin

Abstract

Higher-order Taylor mode AD admits several mathematically equivalent ways to compute mixed partial derivatives. Univariate Taylor propagation combined with polarization reconstructs tensor entries from directional derivatives, whereas multivariate Taylor mode propagates all mixed-partials directly. We present an experimental study of dense and derivative-aware multivariate jets, univariate polarization, and hybrid methods such as bivariate Taylor propagation with blockwise polarization. The study compares runtime, storage footprint, numerical agreement of the result, and propagated coefficient counts. Compiler- optimization ablations and profiling instrumentation are used to distinguish structural cost proxies from implementation bottlenecks. Our initial results show that reducing the number of directional propagations does not necessarily lower runtime: the shape of the propagated coefficient set and the generated code can dominate. We discuss the resulting practical trade-offs and limitations of the evaluated implementations.