An Algebraic Approach to Learning and Grounding

TL;DR

This paper introduces a flexible algebraic framework for learning the semantics of composite expressions from examples, applicable to tasks like grammatical inference and scene description grounding.

Contribution

It presents a novel abstract framework for learning algebraic operations and grounding variables simultaneously from examples, unifying various learning tasks.

Findings

Framework successfully applied to grammatical inference

Effective in grounding logic scene descriptions

Versatile for multiple learning scenarios

Abstract

We consider the problem of learning the semantics of composite algebraic expressions from examples. The outcome is a versatile framework for studying learning tasks that can be put into the following abstract form: The input is a partial algebra $\alg$ and a finite set of examples $(\varphi_1, O_1), (\varphi_2, O_2), \ldots$, each consisting of an algebraic term $\varphi_i$ and a set of objects~$O_i$. The objective is to simultaneously fill in the missing algebraic operations in $\alg$ and ground the variables of every $\varphi_i$ in $O_i$, so that the combined value of the terms is optimised. We demonstrate the applicability of this framework through case studies in grammatical inference, picture-language learning, and the grounding of logic scene descriptions.