An Enriched Category Theory of Language: From Syntax to Semantics

Bradley, Tai-Danae; Terilla, John; Vlassopoulos, Yiannis

doi:10.1007/s44007-022-00021-2

Cited by 4 publications

(7 citation statements)

References 24 publications

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“…In this section, we review what has been attempted to explain how or what a neural network learns. For that, we analyze the structure of the learning algorithm (see [FST19]) and of the studied dataset (see [BTV22]). The study of the structure of these elements is carried by the same theoretical means, yet these are two separate approaches.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…That being said, the data does pertain to a set with added structure, usually an Euclidean vector space. As exemplified by [BTV22] if the data is semantical, we can consider the structure of a [0, 1]-enriched category. That is, each object in the category is a string of words, that is, a sentence.…”

Section: Definition 25 ([Fst19 Definition Iii1])mentioning

confidence: 99%

“…As hinted in [BTV22], learning algorithms do not invent new properties: they merely learn to recognize properties of the data. That means that considering the data as a dataset, that is, just a set of data loses information.…”

Section: Introductionmentioning

confidence: 99%

“…That means that considering the data as a dataset, that is, just a set of data loses information. In [BTV22], the authors propose to model the data consisting of text with the language of enriched categories. In particular, they construct a category whose objects are strings of text and whose morphisms are inclusions of one string into the other.…”

Section: Introductionmentioning

confidence: 99%

“…We believe that understanding the structure of the elements involved, the dataset and algorithm, and how it propagates information is a step to shed some light on the explainability issue. For that, we propose to unify the approaches of [FST19,BTV22] by means of the enriched version of the Yoneda embedding. This will allow us to keep track of the relationship between points in the dataset (input) and the results (output) of the algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Exploring explainable AI: category theory insights into machine learning algorithms

Fabregat-Hernández,

Palanca,

Botti

2023

Mach. Learn.: Sci. Technol.

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Explainable artificial intelligence (XAI) is a growing field that aims to increase the transparency and interpretability of machine learning (ML) models. The aim of this work is to use the categorical properties of learning algorithms in conjunction with the categorical perspective of the information in the datasets to give a framework for explainability. In order to achieve this, we are going to define the enriched categories, with decorated morphisms, L e a r n L e a r n , P a r a P a r a and M N e t M N e t of learners, parameterized functions, and neural networks over metric spaces respectively. The main idea is to encode information from the dataset via categorical methods, see how it propagates, and lastly, interpret the results thanks again to categorical (metric) information. This means that we can attach numerical (computable) information via enrichment to the structural information of the category. With this, we can translate theoretical information into parameters that are easily understandable. We will make use of different categories of enrichment to keep track of different kinds of information. That is, to see how differences in attributes of the data are modified by the algorithm to result in differences in the output to achieve better separation. In that way, the categorical framework gives us an algorithm to interpret what the learning algorithm is doing. Furthermore, since it is designed with generality in mind, it should be applicable in various different contexts. There are three main properties of category theory that help with the interpretability of ML models: formality, the existence of universal properties, and compositionality. The last property offers a way to combine smaller, simpler models that are easily understood to build larger ones. This is achieved by formally representing the structure of ML algorithms and information contained in the model. Finally, universal properties are a cornerstone of category theory. They help us characterize an object, not by its attributes, but by how it interacts with other objects. Thus, we can formally characterize an algorithm by how it interacts with the data. The main advantage of the framework is that it can unify under the same language different techniques used in XAI. Thus, using the same language and concepts we can describe a myriad of techniques and properties of ML algorithms, streamlining their explanation and making them easier to generalize and extrapolate.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Definition 25 ([Fst19 Definition Iii1])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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