Query Languages for Machine-Learning Models

TL;DR

This paper explores two logical frameworks, FO(SUM) and IFP(SUM), as query languages for neural networks modeled as weighted graphs, analyzing their expressiveness and computational complexity.

Contribution

It introduces the application of FO(SUM) and IFP(SUM) logics as query languages for neural networks, extending foundational logic work to machine learning models.

Findings

Queries to neural networks can be expressed in these logics.

Fundamental results on expressiveness of the logics.

Analysis of computational complexity for query evaluation.

Abstract

In this paper, I discuss two logics for weighted finite structures: first-order logic with summation (FO(SUM)) and its recursive extension IFP(SUM). These logics originate from foundational work by Gr\"adel, Gurevich, and Meer in the 1990s. In recent joint work with Standke, Steegmans, and Van den Bussche, we have investigated these logics as query languages for machine learning models, specifically neural networks, which are naturally represented as weighted graphs. I present illustrative examples of queries to neural networks that can be expressed in these logics and discuss fundamental results on their expressiveness and computational complexity.