Related papers: Dynamic Operads, Dynamic Categories: From Deep Lea…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
We introduce the concept of a dendroidal set. This is a generalization of the notion of a simplicial set, specially suited to the study of operads in the context of homotopy theory. We define a category of trees, which extends the category…
A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…
Object-based approaches for learning action-conditioned dynamics has demonstrated promise for generalization and interpretability. However, existing approaches suffer from structural limitations and optimization difficulties for common…
We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
The purpose of this paper is to study the derived category of simplicial multicategories with arbitrary sets of objects (also known as, colored operads in simplicial sets). Our main result is a derived Morita theory for operads-where we…
We introduce a framework that represents a dynamic program as a family of operators acting on a partially ordered set. We provide an optimality theory based only on order-theoretic assumptions and show how applications across almost all…
Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework (Sutton et…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
This is the first paper of a series which aims to set up the cornerstones of Koszul duality for operads over operadic categories. To this end we single out additional properties of operadic categories under which the theory of quadratic…
We present categories of open dynamical systems with general time evolution as categories of coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such…
A model of an organism as an autonomous intelligent system has been proposed. This model was used to analyze learning of an organism in various environmental conditions. Processes of learning were divided into two types: strong and weak…
Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…