Related papers: Dynamic Operads, Dynamic Categories: From Deep Lea…
In this dissertation we develop a new formal graphical framework for causal reasoning. Starting with a review of monoidal categories and their associated graphical languages, we then revisit probability theory from a categorical perspective…
Social order does not exist as a stable phenomenon, but can be considered as "an order of reproduced expectations." When anticipations operate upon one another, they can generate a non-linear dynamics which processes meaning. Although…
Given an operad $\mathcal{O}$, we define a notion of weak $\mathcal{O}$-monoids -- which we term $\mathcal{O}$-pseudomonoids -- in a 2-category. In the special case with the 2-category in question is the 2-category $\mathsf{Cat}$ of…
Disordered systems subject to a fluctuating environment can self-organize into a complex history-dependent response, retaining a memory of the driving. In sheared amorphous solids, self-organization is established by the emergence of a…
We are currently designing an object oriented model which describes static and dynamical knowledge in diff{\'e}rent domains. It provides a twin conceptual level. The internal level proposes: the object structure composed of sub-objects…
The multi-group learning model formalizes the learning scenario in which a single predictor must generalize well on multiple, possibly overlapping subgroups of interest. We extend the study of multi-group learning to the natural case where…
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 $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
It is shown how double categories provide a direct abstract approach to coloured operads; namely, product-preserving normal lax functors from (Pb C)^op (the opposite of the double category of pullback squares in C) to Cat (the double…
We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This…
We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…
This paper aims at providing a rigorous definition of self- organization, one of the most desired properties for dynamic systems (e.g., peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks). We characterize…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
We propose a general scenario to analyze social and economic changes in modern environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time,…
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative…
How do cognitive agents decide what is the relevant information to learn and how goals are selected to gain this knowledge? Cognitive agents need to be motivated to perform any action. We discuss that emotions arise when differences between…
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
We introduce unary operadic 2-categories as a framework for operadic Grothendieck construction for categorical $\mathbb{O}$-operads, $\mathbb{O}$ being a unary operadic category. The construction is a fully faithful functor…