6 papers
Stationary point complexity via minimal supersymmetry breaking
Jaron Kent-Dobias
The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding techni…
Very persistent random walkers reveal transitions in landscape topology
Jaron Kent-Dobias
We study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at…
Structure of solutions to continuous constraint satisfaction problems through the statistics of wedged and inscribed spheres
Jaron Kent-Dobias
The study of random landscapes has long relied on counting stationary points: metastable states and the barriers between them. However, this method is useless for describing flat r…
On the topology of solutions to random continuous constraint satisfaction problems
Jaron Kent-Dobias
We consider the set of solutions to random polynomial equations whose variables are restricted to the -sphere. Each equation has independent Gaussian coefficients an…
Conditioning the complexity of random landscapes on marginal optima
Jaron Kent-Dobias
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical d…
Algorithm-independent bounds on complex optimization through the statistics of marginal optima
Jaron Kent-Dobias
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algo…