Related papers: A General Notion of Useful Information

Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…

A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…

This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…

In this paper I will discuss the properties of the Algorithmic Complexity, presenting the most relevant properties. The related concept of logical depth is also introduced. These properties will be used to study the problem of learning from…

Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…

We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

Compositional generalization is the capacity to recognize and imagine a large amount of novel combinations from known components. It is a key in human intelligence, but current neural networks generally lack such ability. This report…

With the increasing application of deep learning algorithms to time series classification, especially in high-stake scenarios, the relevance of interpreting those algorithms becomes key. Although research in time series interpretability has…

We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…

We show how it is possible to define and study black holes of arbitrary shapes in the framework of Newtonian mechanics.

This study is a preliminary exploration of the concept of informativeness -how much information a sentence gives about a word it contains- and its potential benefits to building quality word representations from scarce data. We propose…

In an earlier paper, the notion of integrality known from algebraic number fields and fields of algebraic functions has been extended to D-finite functions. The aim of the present paper is to extend the notion to the case of P-recursive…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…

With the growth of deep learning, how to describe deep neural networks unifiedly is becoming an important issue. We first formalize neural networks mathematically with their directed graph representations, and prove a generation theorem…

This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…

Many abstract interpretation frameworks and analyses for Prolog have been proposed, which seek to extract information useful for program optimization. Although motivated by practical considerations, notably making Prolog competitive with…