Verifiable Deep Quantitative Group Testing

TL;DR

This work tackles quantitative group testing by learning a non-adaptive neural decoder that maps pooled test counts to defect indicators while also inferring the underlying pooling design for verifiability. An MLP is trained with a balanced loss on synthetic data and evaluated against AMP baselines, demonstrating robust recovery under sparse, bounded noise and sparsity-agnostic performance. A Jacobian-based verifiability analysis reveals that the trained model implicitly captures the true pooling structure, enabling reconstruction of the forward design from local network behavior. The results suggest that standard feedforward architectures can perform verifiable inverse mappings in structured combinatorial recovery problems and point to future extensions to real-valued signals and theoretical guarantees.

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.

Figures (2)

• Figure 1: Decoding performance versus the number of measurements $M$ for the proposed MLP decoder and AMP baselines. Each curve shows the average measure value as a function of $M$, with all other parameters fixed ($N = 100$, $K/N = 0.06$, $S/N = 0.1$, $D = 1$). The MLP achieves performance comparable to AMP (Oracle-$K$) without requiring knowledge of sparsity and remains robust across different measurement regimes.
• Figure 2: Decoding performance versus noise sparsity $S$ for the proposed MLP decoder and AMP baselines. Each curve shows the average measure value as a function of $S$, with all other parameters fixed ($N = 100$, $K/N = 0.06$, $M = 35$, $D = 1$). The MLP matches or surpasses AMP (Oracle-$K$) across all tested noise levels, demonstrating strong robustness to sparse measurement noise.