Query languages for neural networks

TL;DR

This paper introduces a formal framework for querying neural networks using logic-based languages inspired by databases, comparing black-box and white-box approaches, and demonstrating their relative expressive powers.

Contribution

It develops a formal foundation for neural network query languages, analyzing their expressive capabilities and showing white-box approaches can subsume black-box methods under certain conditions.

Findings

White-box query language can express more than black-box language.

Main result: white-box approach subsumes black-box approach for certain neural networks.

Proved for linear constraint queries over piecewise linear neural networks.

Abstract

We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic, that mainly differ in their access to the neural network model. First-order logic over the reals naturally yields a language which views the network as a black box; only the input--output function defined by the network can be queried. This is essentially the approach of constraint query languages. On the other hand, a white-box language can be obtained by viewing the network as a weighted graph, and extending first-order logic with summation over weight terms. The latter approach is essentially an abstraction of SQL. In general, the two approaches are incomparable in expressive power, as we will show. Under natural circumstances, however, the white-box approach can subsume the black-box approach; this is our main result. We prove the result concretely for linear constraint queries over real functions definable by feedforward neural networks with a fixed number of hidden layers and piecewise linear activation functions.