Related papers: Self-Referential Order
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
We consider self-organization and memory formation in a mesoscopic model of an amorphous solid subject to a random shear strain protocol confined to a strain range $\pm \varepsilon_{\rm max}$. We develop proper read-out protocols to show…
In supervised learning, we typically leverage a fully labeled dataset to design methods for function estimation or prediction. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is…
The work is devoted to study of the following problem: can we use any qualitative criteria for realization of such universal phenomenon as self-organization in open systems? We have defined values of information at fixed points of…
We review recent progress in applying information- and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…
Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking…
Items in many datasets can be arranged to a natural order. Such orders are useful since they can provide new knowledge about the data and may ease further data exploration and visualization. Our goal in this paper is to define a…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
Crystals are a state of matter characterised by periodic order. Yet crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular…
Learning from the multidimensional data has been an interesting concept in the field of machine learning. However, such learning can be difficult, complex, expensive because of expensive data processing, manipulations as the number of…
Artificial intelligence has shown remarkable success in materials discovery and property prediction, particularly for crystalline and polymer systems where material properties and structures are dominated by discrete graph representations.…
This paper extends the class of ordinal regression models with a structured interpretation of the problem by applying a novel treatment of encoded labels. The net effect of this is to transform the underlying problem from an ordinal…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
This thesis details a class of partial orders on the space of probability distributions and the space of density operators which capture the idea of information content. Some links to domain theory and computational linguistics are also…
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…
Sequential self-attention models usually rely on additive positional embeddings, which inject positional information into item representations at the input. In the absence of positional signals, the attention block is…
Structure-property relationships in ordered materials have long been a core principle in materials design. However, the intentional introduction of disorder into materials provides structural flexibility and thus access to material…