Verifiable Deep Quantitative Group Testing
This work addresses the challenge of efficiently recovering sparse defect sets in combinatorial testing, offering a verifiable deep learning approach that could benefit applications in medical screening or quality control.
The paper tackles the quantitative group testing problem by developing a neural network framework that accurately identifies defective items from pooled tests and demonstrates that the network learns the underlying combinatorial structure, enabling structural verifiability.
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.