Related papers: Compositional Exploration of Combinatorial Scienti…
Learning compact and interpretable representations is a very natural task, which has not been solved satisfactorily even for simple binary datasets. In this paper, we review various ways of composing experts for binary data and argue that…
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…
The category of I-spaces is the diagram category of spaces indexed by finite sets and injections. This is a symmetric monoidal category whose commutative monoids model all E-infinity spaces. Working in the category of I-spaces enables us to…
Discovering new drug molecules is a pivotal yet challenging process due to the near-infinitely large chemical space and notorious demands on time and resources. Numerous generative models have recently been introduced to accelerate the drug…
Drawing from research on computational models of argumentation (particularly the Carneades Argumentation System), we explore the graphical representation of arguments in a dispute; then, comparing two different traditions on the limits of…
The study of complex networks has been historically based on simple graph data models representing relationships between individuals. However, often reality cannot be accurately captured by a flat graph model. This has led to the…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…
We introduce the first work to tackle the image retrieval problem as a continuous operation. While the proposed approaches in the literature can be roughly categorized into two main groups: category- and instance-based retrieval, in this…
Combinatorial optimization augmented machine learning (COAML) has recently emerged as a powerful paradigm for integrating predictive models with combinatorial decision-making. By embedding combinatorial optimization oracles into learning…
Computer models are used to model complex processes in various disciplines. Often, a key source of uncertainty in the behavior of complex computer models is uncertainty due to unknown model input parameters. Statistical computer model…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model…
The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
Sequence modeling with neural networks has lead to powerful models of symbolic music data. We address the problem of exploiting these models to reach creative musical goals, by combining with human input. To this end we generalise previous…