TY - JOUR
TI - Category Theory for Genetics
AU - Tuyéras, Rémy
T2 - arXiv:1708.05255 [math]
AB - We introduce a categorical language in which it is possible to talk about DNA sequencing, alignment methods, CRISPR, homologous recombination, haplotypes, and genetic linkage. This language takes the form of a class of limit-sketches whose categories of models can model different concepts of Biology depending on what their categories of values are. We discuss examples of models in the category of sets and in the category of modules over the Boolean semi-ring $\{0,1\}$. We identify a subclass of models in sets that models the genetic material of living beings and another subclass of models in modules that models haplotypes. We show how the two classes are related via a universal property.
DA - 2018/05/17/
PY - 2018
DP - arXiv.org
UR - http://arxiv.org/abs/1708.05255
Y2 - 2019/11/28/23:35:38
KW - Biology
ER -
TY - JOUR
TI - Category theory for genetics I: mutations and sequence alignments
AU - Tuyéras, Rémy
T2 - arXiv:1805.07002 [math]
AB - The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a class of limit-sketches and their associated models. While our program will aim to show that different phenomena of genetics can be modeled by changing the category in which the models take their values, in this paper, we study models in the category of sets to capture mutation mechanisms such as insertions, deletions, substitutions, duplications and inversions. We show how the proposed formalism can be used for constructing multiple sequence alignments with an emphasis on mutation mechanisms.
DA - 2018/12/13/
PY - 2018
DP - arXiv.org
ST - Category theory for genetics I
UR - http://arxiv.org/abs/1805.07002
Y2 - 2019/11/28/23:36:03
KW - Biology
ER -
TY - JOUR
TI - Category theory for genetics II: genotype, phenotype and haplotype
AU - Tuyéras, Rémy
T2 - arXiv:1805.07004 [math]
AB - In this paper, we use the language of pedigrads, introduced in previous work, to formalize the relationship between genotypes, phenotypes and haplotypes. We show how this formalism can help us localize the variations in the genotype that cause a given phenotype. We then use the concept of haplotype to formalize the process of predicting a certain phenotype for a given set of genotypes.
DA - 2018/08/01/
PY - 2018
DP - arXiv.org
ST - Category theory for genetics II
UR - http://arxiv.org/abs/1805.07004
Y2 - 2019/11/28/23:36:18
KW - Biology
ER -
TY - JOUR
TI - Backprop as Functor: A compositional perspective on supervised learning
AU - Fong, Brendan
AU - Spivak, David I.
AU - Tuyéras, Rémy
T2 - arXiv:1711.10455 [cs, math]
AB - 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 updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.
DA - 2019/05/01/
PY - 2019
DP - arXiv.org
ST - Backprop as Functor
UR - http://arxiv.org/abs/1711.10455
Y2 - 2019/11/23/14:42:07
KW - Categorical ML
KW - Machine learning
KW - Purely theoretical
ER -