Related papers: Localization and landscape functions on quantum gr…
A quantum control landscape is defined as the physical objective as a function of the control variables to be optimized. Analyzing the topology of these landscapes is important for understanding the origins of the increasing number of…
We show how the localization landscape, originally introduced to bound low energy eigenstates of disordered wave media and many-body quantum systems, can form the basis for hardware-efficient quantum algorithms for solving binary…
The control of quantum systems has been proven to possess trap-free optimization landscapes under the satisfaction of proper assumptions. However, many details of the landscape geometry and their influence on search efficiency still need to…
We study localization properties of low-lying eigenfunctions $$(-\Delta +V) \phi = \lambda \phi \qquad \mbox{in}~\Omega$$ for rapidly varying potentials $V$ in bounded domains $\Omega \subset \mathbb{R}^d$. Filoche & Mayboroda introduced…
A recent theoretical breakthrough has brought a new tool, called \emph{localization landscape}, to predict the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures…
We investigate the validity of the assertion that eternal inflation populates the landscape of string theory. We verify that bubble solutions do not satisfy the Klein Gordon equation for the landscape potential. Solutions to the landscape…
In machine learning, a loss function measures the difference between model predictions and ground-truth (or target) values. For neural network models, visualizing how this loss changes as model parameters are varied can provide insights…
Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
We show that learning can be improved by using loss functions that evolve cyclically during training to emphasize one class at a time. In underparameterized networks, such dynamical loss functions can lead to successful training for…
Visual representations can be defined as the activations of neuronal populations in response to images. The activation of a neuron as a function over all image space has been described as a "tuning landscape". As a function over a…
We give a delocalization estimate for eigenfunctions of the discrete Laplacian on large $d+1$-regular graphs, showing that any subset of the graph supporting $\epsilon$ of the $L^2$ mass of an eigenfunction must be large. For graphs…
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval $I$, in…
Optimization is ubiquitous in quantum information science and technology, however, the corresponding optimization landscape can encounter false traps, i.e., local but not global optima, likely to prevent used optimizers from finding optimal…
In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and…
Overparameterization is central to the success of deep learning, yet the mechanisms by which it improves optimization remain incompletely understood. We analyze weight-space symmetries in neural networks and show that overparameterization…
A basic issue in optimization, inverse theory,neural networks, computational chemistry and many other problems is the geometrical characterization of high dimensional functions. In inverse calculations one aims to characterize the set of…