Verifiable Deep Quantitative Group Testing

2025-12-08

AI Summary

Quantitative Group Testing (QGT) aims to identify a small number of defective items among $N$ items using $M ll N$ pooled tests, where each test returns the count of defectives in a subset. This paper proposes an end-to-end decoding framework based on a multilayer perceptron (MLP) that maps noisy quantitative measurements to binary defect indicators. We establish, for the first time, that feedforward neural networks can implicitly learn—and provably recover—the underlying test-item incidence structure. By analyzing the Jacobian matrix of the trained network, we explicitly extract this combinatorial structure, thereby ensuring both output interpretability and structural verifiability of the decoder. Under sparse and bounded measurement perturbations, the model achieves high-accuracy, robust defective identification and faithful incidence-matrix reconstruction. To our knowledge, this is the first deep learning framework for QGT with certified structural interpretability and verifiable recovery guarantees.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Identify defective items using fewer pooled tests
• Achieve accurate recovery under noisy measurements
• Learn and verify underlying combinatorial pooling structure

Innovation

• Neural network maps measurements to defect indicators accurately
• Network's Jacobian recovers underlying pooling structure implicitly
• Feedforward architecture learns verifiable inverse combinatorial mappings