Related papers: Information loss under coarse-graining: a geometri…
Diffusion models transform noise into data by injecting information that was captured in their neural network during the training phase. In this paper, we ask: \textit{what} is this information? We find that, in pixel-space diffusion…
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…
Diffusion-based generative models represent a forefront direction in generative AI research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight…
In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information…
Granular materials such as sand, powders, and grains are omnipresent in daily life, industrial applications, and earth-science [1]. When unperturbed, they form stable structures that resemble the ones of other amorphous solids like metallic…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
The continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will…
Mutual information between particle positions before and after mixing provides a universal assumption-free measure of mixing efficiency at low Reynolds number which accounts for the kinematic reversibility of the Stokes equation. For a…
Some basic questions about the hydrodynamical approach to relativistic heavy ion collisions are discussed aiming to clarify how far we can go with such an approach to extract useful information on the properties and dynamics of the QCD…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
Gravity-driven flows of granular matter are involved in a wide variety of situations, ranging from industrial processes to geophysical phenomena, such as avalanches or landslides. These flows are characterized by the coexistence of solid…
Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been…
We derive constraints on renormalization group (RG) flows and stability of phases in nonequilibrium systems using quantum information inequalities. These constraints involve conditional mutual information (CMI), which quantifies…
Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to…
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…
Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…
We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples…