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A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…
In modern recommender systems, both users and items are associated with rich side information, which can help understand users and items. Such information is typically heterogeneous and can be roughly categorized into flat and hierarchical…
Much recent work in physics education research has focused on ontological metaphors for energy, particularly the substance ontology and its pedagogical affordances. The concept of negative energy problematizes the substance ontology for…
Effectful categories have two classes of morphisms: pure morphisms, which form a monoidal category; and effectful morphisms, which can only be combined monoidally with central morphisms (such as the pure ones), forming a premonoidal…
A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…
We offer a new approach to the information decomposition problem in information theory: given a 'target' random variable co-distributed with multiple 'source' variables, how can we decompose the mutual information into a sum of non-negative…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
The minimization of specific cases in binary classification, such as false negatives or false positives, grows increasingly important as humans begin to implement more machine learning into current products. While there are a few methods to…
Existing preference optimization methods often assume scenarios where paired preference feedback (preferred/positive vs. dis-preferred/negative examples) is available. This requirement limits their applicability in scenarios where only…
The information conveyed by a hierarchical attractor neural network is examined. The network learns sets of correlated patterns (the examples) in the lowest level of the hierarchical tree and can categorize them at the upper levels. A way…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering, learning systems. However, this paper aims to investigate whether the conventional proposition always holds. It begins with the definition of task…
Categorization is an important topic both for biological and artificial neural networks. Here, we take an information theoretic approach to assess the efficiency of the representations induced by category learning. We show that one can…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
In work of Fokkinga and Meertens a calculational approach to category theory is developed. The scheme has many merits, but sacrifices useful type information in the move to an equational style of reasoning. By contrast, traditional proofs…
Distributed representations of words have shown to be useful to improve the effectiveness of IR systems in many sub-tasks like query expansion, retrieval and ranking. Algorithms like word2vec, GloVe and others are also key factors in many…
Top-$N$ recommender systems typically utilize side information to address the problem of data sparsity. As nowadays side information is growing towards high dimensionality, the performances of existing methods deteriorate in terms of both…
The possibility of calculation of the conditional and unconditional complexity of description of information objects in the algorithmic theory of information is connected with the limitations for the set of the used languages of programming…
Our research explores the use of natural language processing (NLP) methods to automatically classify entities for the purpose of knowledge graph population and integration with food system ontologies. We have created NLP models that can…
This article presents the top-level of an ontology categorizing and generalizing best practices and quality criteria or measures for Linked Data. It permits to compare these techniques and have a synthetic organized view of what can or…