Related papers: Localization and landscape functions on quantum gr…
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the…
Characterizing the loss of a neural network with respect to model parameters, i.e., the loss landscape, can provide valuable insights into properties of that model. Various methods for visualizing loss landscapes have been proposed, but…
The core problem in optimal control theory applied to quantum systems is to determine the temporal shape of an applied field in order to maximize the expectation of value of some physical observable. The functional which maps the control…
Normal matrices, or matrices which commute with their adjoints, are of fundamental importance in pure and applied mathematics. In this paper, we study a natural functional on the space of square complex matrices whose global minimizers are…
An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal…
Loss landscape analysis is extremely useful for a deeper understanding of the generalization ability of deep neural network models. In this work, we propose a layerwise loss landscape analysis where the loss surface at every layer is…
The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback…
Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$. A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points…
Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed…
We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from…
In this paper, we consider the geometric landscape connection of the widely studied manifold and factorization formulations in low-rank positive semidefinite (PSD) and general matrix optimization. We establish a sandwich relation on the…
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…
Local optima networks (LONs) capture fitness landscape information. They are typically constructed in a black-box manner; information about the problem structure is not utilised. This also applies to the analysis of LONs: knowledge about…
It is known that, if a locally perturbed periodic self-adjoint operator on a combinatorial or quantum graph admits an eigenvalue embedded in the continuous spectrum, then the associated eigenfunction is compactly supported--that is, if the…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…
The localization subregions of stationary waves in continuous disordered media have been recently demonstrated to be governed by a hidden landscape that is the solution of a Dirichlet problem expressed with the wave operator. In this…
We investigate the rate of decrease at infinity of eigenfunctions of quantum graphs by using Agmon's method to prove $L^2$ and $L^\infty$ bounds on the product of an eigenfunction with the exponential of a certain metric. A generic result…
While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -- Localisation Landscape Theory (LLT) -- has unparalleled strengths and advantages, both…
Quantifying the flatness of the objective-function landscape associated with unstructured parameterized quantum circuits is important for understanding the performance of variational algorithms utilizing a "hardware-efficient ansatz",…
The hypergraph states are pure multipartite quantum states corresponding to a hypergraph. It is an equal superposition of the states belonging to the computational basis. Given any hypergraph, we can construct a hypergraph state determined…