Property Testing of Computational Networks

TL;DR

This paper introduces a framework for property testing of weighted computational networks, focusing on neural Boolean networks with ReLU activation, and demonstrates size-independent testability for near constant functions.

Contribution

It develops a novel property testing framework for computational networks and provides the first results on size-independent testability for certain neural network properties.

Findings

Near constant functions are testable with query complexity independent of network size.

The framework applies to neural Boolean networks with ReLU activation.

Size-independent testing is not possible in certain natural generalizations.

Abstract

In this paper we initiate the study of \emph{property testing of weighted computational networks viewed as computational devices}. Our goal is to design property testing algorithms that for a given computational network with oracle access to the weights of the network, accept (with probability at least $\frac23$) any network that computes a certain function (or a function with a certain property) and reject (with probability at least $\frac23$) any network that is \emph{far} from computing the function (or any function with the given property). We parameterize the notion of being far and want to reject networks that are \emph{$(\epsilon,\delta)$-far}, which means that one needs to change an $\epsilon$-fraction of the description of the network to obtain a network that computes a function that differs in at most a $\delta$-fraction of inputs from the desired function (or any function with a given property). To exemplify our framework, we present a case study involving simple neural Boolean networks with ReLU activation function. As a highlight, we demonstrate that for such networks, any near constant function is testable in query complexity independent of the network's size. We also show that a similar result cannot be achieved in a natural generalization of the distribution-free model to our setting, and also in a related vanilla testing model.