Verifiable Deep Quantitative Group Testing

TL;DR

This paper introduces a neural network approach for quantitative group testing that achieves accurate, robust identification of defective items while also enabling verification of the underlying pooling structure through the network's Jacobian.

Contribution

The work demonstrates that neural networks can learn verifiable inverse mappings in structured combinatorial problems like QGT, combining accuracy with structural interpretability.

Findings

High decoding accuracy under noisy conditions

The network's Jacobian reveals the pooling structure

Standard architectures can learn verifiable inverse mappings

Abstract

We present a neural network-based framework for solving the quantitative group testing (QGT) problem that achieves both high decoding accuracy and structural verifiability. In QGT, the objective is to identify a small subset of defective items among $N$ candidates using only $M \ll N$ pooled tests, each reporting the number of defectives in the tested subset. We train a multi-layer perceptron to map noisy measurement vectors to binary defect indicators, achieving accurate and robust recovery even under sparse, bounded perturbations. Beyond accuracy, we show that the trained network implicitly learns the underlying pooling structure that links items to tests, allowing this structure to be recovered directly from the network's Jacobian. This indicates that the model does not merely memorize training patterns but internalizes the true combinatorial relationships governing QGT. Our findings reveal that standard feedforward architectures can learn verifiable inverse mappings in structured combinatorial recovery problems.