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Found 12 papers, 3 papers with code
Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets
Natural organized systems adapt to internal and external pressures and this happens at all levels of the abstraction hierarchy.
Deep neural networks as nested dynamical systems
Since the "neurons" in deep neural networks are managing the changing weights, they are more akin to the synapses in the brain; instead, it is the wires in deep neural networks that are more like nerve cells, in that they are what cause the information to flow.
Learners' Languages
In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)$\to$Learn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation.
Monitoring and Diagnosability of Perception Systems
The resulting temporal diagnostic graphs (i) provide a framework to reason over the consistency of perception outputs -- across modules and over time -- thus enabling fault detection, (ii) allow us to establish formal guarantees on the maximum number of faults that can be uniquely identified in a given perception system, and (iii) enable the design of efficient algorithms for fault identification.
Monitoring and Diagnosability of Perception Systems
Towards this goal, we draw connections with the literature on self-diagnosability for multiprocessor systems, and generalize it to (i) account for modules with heterogeneous outputs, and (ii) add a temporal dimension to the problem, which is crucial to model realistic perception systems where modules interact over time.
A Compositional Sheaf-Theoretic Framework for Event-Based Systems (Extended Version)
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented.
Categorical Data Integration for Computational Science
Categorical Query Language is an open-source query and data integration scripting language that can be applied to common challenges in the field of computational science.
Databases
Graphical Regular Logic
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment.
Category Theory Logic in Computer Science Logic 18B10, 03G30
Behavioral Mereology
Mereology is the study of parts and the relationships that hold between them.
Logic Category Theory 03B45, 18B25, 03A10
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples.
Category Theory 18-01
Backprop as Functor: A compositional perspective on supervised learning
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$.
Simplicial Databases
Along the way we give a precise formulation of the category of relational databases, and prove that it is a full subcategory of DB.
Databases Information Retrieval
