Related papers: Neural category

This PhD thesis is focused on the central idea that single neurons in the brain should be regarded as temporally precise and highly complex spatio-temporal pattern recognizers. This is opposed to the prevalent view of biological neurons as…

Many monoidal-type objects are known to be classified by maps from the Catalan simplicial set $\mathbb{C}$ to various nerves of categories and higher categories. There are, for example, three different nerves of the 2-category of categories…

This paper proposes a generalized framework for cellular automata using the language of category theory, extending the classical definition beyond set-theoretic constraints. For an arbitrary category $\mathscr{C}$ with products, we define…

A compact closed bicategory is a symmetric monoidal bicategory where every object is equipped with a weak dual. The unit and counit satisfy the usual "zig-zag" identities of a compact closed category only up to natural isomorphism, and the…

In humans and other animals, category learning enhances discrimination between stimuli close to the category boundary. This phenomenon, called categorical perception, was also empirically observed in artificial neural networks trained on…

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

It is well-known that small categories have equivalent descriptions as partial monoids. We provide a formulation of partial monoid and partial monoid homomorphism involving $s$ and $t$ instead of identities and then following a recent…

Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of 'what' and…

A major challenge in cognitive neuroscience is to evaluate the ability of the human brain to categorize or group visual stimuli based on common features. This categorization process is very fast and occurs in few hundreds of millisecond…

We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of $(\infty,1)$-categories (and more generally of category-objects in an $\infty$-category), as a version of factorization…

The subject of this paper is a nerve construction for bicategories introduced by Leinster, which defines a fully faithful functor from the category of bicategories and normal pseudofunctors to the category of presheaves over Joyal's…

In this paper we study a 2-dimensional version of Quillen's homotopy category construction. Given a category $\mathscr{A}$ and a class of morphisms $\Sigma \subset \mathscr{A}$ containing the identities, we construct a 2-category…

In a recent article, Brette argues that coding as a concept is inappropriate for explanations of neurocognitive phenomena. Here, we argue that Brette's conceptual analysis mischaracterizes the structure of causal claims in coding and other…

Neural Collapse (NC) gives a precise description of the representations of classes in the final hidden layer of classification neural networks. This description provides insights into how these networks learn features and generalize well…

For most models of $(\infty,2)$-categories an embedding of the $\infty$-category of 2-categories into that of $(\infty,2)$-categories has been constructed in the form of a nerve construction of some flavor. We prove that all those nerve…

We propose a neuropsychological approach to the explainability of artificial neural networks, which involves using concepts from human cognitive psychology as relevant heuristic references for developing synthetic explanatory frameworks…

Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding combinatorial criteria on codes that can be used to classify…

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…

The cerebral cortex is composed of multiple cortical areas that exert a wide variety of brain functions. Although human brain neurons are genetically and areally mosaic, the three-dimensional structural differences between neurons in…

We use techniques from relative algebraic geometry and homotopical algebraic geometry in order to construct several categories of schemes defined "under Spec Z". We define this way the categories of N-schemes, F_1-schemes, S-schemes,…