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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…
To deal with global problems we suggest to consider complex systems not in space and time, but in a possible deeper reality, i.e., the hierarchical network of prime integer relations. Encoded by arithmetic through the self-organization…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…
The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding…
Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated…
Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior…
We give two low-complexity algorithms, one for dimensionality reduction and one for dimensionality increase, which are applicable to any dataset, regardless of whether the set has an intrinsic dimension or not. The corresponding methods…
The physical processes that determine the properties of our everyday world, and of the wider cosmos, are determined by some key numbers: the 'constants' of micro-physics and the parameters that describe the expanding universe in which we…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
The last two decades have seen the emergence and steady development of tangible user interfaces. While most of these interfaces are applied for input - with output still on traditional computer screens - the goal of programmable matter and…
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
A new method is proposed to improve the numeri- cal simulation of time dependent problems when the initial and boundary data are not compatible. Unlike earlier methods limited to space dimension one, this method can be used for any space…
Recently, a measure has been put forward which allows for the quantification of the degree of reality of an observable for a given preparation [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. Here we employ this…
Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…
Identifying model parameters from observed configurations poses a fundamental challenge in data science, especially with limited data. Recently, diffusion models have emerged as a novel paradigm in generative machine learning, capable of…
Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…
The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…
Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of…