Related papers: Information loss under coarse-graining: a geometri…
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
Coarse-graining (CG) of molecular simulations simplifies the particle representation by grouping selected atoms into pseudo-beads and drastically accelerates simulation. However, such CG procedure induces information losses, which makes…
In this brief article I show how the notion of coarse graining and the Renormalization Group enter naturally in the dynamics of genetic systems, in particular in the presence of recombination. I show how the latter induces a dynamics…
We use the method of maximum entropy to model physical space as a curved statistical manifold. It is then natural to use information geometry to explain the geometry of space. We find that the resultant information metric does not describe…
An important challenge in theoretical ecology is to find good, coarse-grained representations of complex food webs. Here we use the approach of generalized modeling to show that it may be possible to formulate a coarse-graining algorithm…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…
Separating relevant and irrelevant information is key to any modeling process or scientific inquiry. Theoretical physics offers a powerful tool for achieving this in the form of the renormalization group (RG). Here we demonstrate a…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry induced by the data? To answer this, we introduce a…
The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
Complex networks can model a range of different systems, from the human brain to social connections. Some of those networks have a large number of nodes and links, making it impractical to analyze them directly. One strategy to simplify…
Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations, and can…
The analysis of complex physical systems hinges on the ability to extract the relevant degrees of freedom from among the many others. Though much hope is placed in machine learning, it also brings challenges, chief of which is…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
The relationship between micro-structure and macro-structure of complex systems using information geometry has been dealt by several authors. From this perspective, we are going to apply it as a geometrical structure connecting both…
Complex fluids exhibit structure on a wide range of length and time scales, and hierarchical approaches are necessary to investigate all facets of their often unusual properties. The study of idealized coarse-grained models at different…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…