From 9f5601e65fd952e1588977686e4bfb1d05a0c28a Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 2 Sep 2022 17:46:20 +0200 Subject: Added first draft popular summary. --- popular summary.txt | 5 +++++ 1 file changed, 5 insertions(+) create mode 100644 popular summary.txt diff --git a/popular summary.txt b/popular summary.txt new file mode 100644 index 0000000..8829dcf --- /dev/null +++ b/popular summary.txt @@ -0,0 +1,5 @@ +Understanding the stationary points of a function can tell you a lot about the function. From these points (where the function's derivative vanishes) you can infer topological and geometric properties and, when the function is an energy landscape, these inferences can provide physical insight. For complex energy landscapes in high dimensions, physical insight is often sorely lacking. Our work extends existing methods to count stationary points to a broader class of complex landscapes. Namely, this encompasses landscapes whose equilibrium properties are described by the replica symmetry breaking (RSB) theory of Giorgio Parisi that won the Nobel Prize in physics last year. + +In the paper, we derive an expression for the typical number of stationary points in a class of complex random landscapes. In order to find the typical number rather than the mean number, which is biased by outliers, we use the replica method. We find a form for the solution inspired by Parisi's equilibrium solution, and show it is consistent with known properties at the very lowest energies. We then take the solution and apply it to two specific models with novel RSB structure in their energy landscapes. + +A correct accounting of stationary points for these and other complex landscapes promises to yield important insight into physics in many disciplines where such landscapes appear, from the condensed matter of glasses to the performance of machine learning algorithms. -- cgit v1.2.3-70-g09d2