Dr Peter Braam is going to talk about; 'State time geometry: causal performance profiles and optimal data transport in parallel execution'
The increasing complexity of parallel architectures and heterogeneous microarchitectures makes predicting and optimising program performance notoriously difficult. For Optimal Data Transport, we present a discrete variant of the Wasserstein–Fisher–Rao metric that quantifies the true cost of data layout transformations and movement across memory hierarchies. For Causal Performance Profiles, we introduce the Lyons–Gregg Signature, which combines the ideas of Terry Lyons' rough path signatures with hardware performance counters (eBPF) to capture cross-correlated, causal bottlenecks in execution streams. Both arose from State Time Geometry (STG), a model for stateful program execution on computing infrastructure, first modelled as a dynamical system governing state-values over the space of memory addresses. The address space generalises to geometric objects defining infrastructure and leads to the metric. The state transitions of parallel executions become a Grothendieck quantum field theory over the infrastructure and carry the statistical model for the Lyons-Gregg Signature. The central theme is that an intuitive faithful model is not doomed by complexity but forms a geometric domain in which both theoretical and engineering perspectives are simplified.
(In a companion lecture in the Computing Laboratory at 11:00 on Nov 13, we will discuss STG's underlying categorical and geometric structure and its relationship to programming languages and formal methods)