arXiv:2512.07279eess.SPcs.LG2025-12

用神经网络解决缺陷项检测,既能准识别又能验证测试结构。

Verifiable Deep Quantitative Group Testing

  • 用多层感知机映射测试结果到缺陷标识,抗噪声能力强。
  • 在稀疏有界扰动下仍保持高恢复精度,测试数远小于候选数。
  • 通过雅可比矩阵可逆向提取测试结构,模型学习了真实组合关系。

我们提出一种基于神经网络的定量群体测试(QGT)求解框架,可在仅使用少量池化测试(M ≪ N)的情况下,从报告缺陷数量的测试结果中准确识别出少量缺陷项。该方法训练多层感知机将含噪测量向量映射为二值缺陷指示,即使在稀疏且有界的扰动下也能实现高鲁棒性恢复。更重要的是,训练后的网络隐式学习到了项目与测试之间的底层池化结构,该结构可通过网络的雅可比矩阵直接还原。这表明模型并非简单记忆训练样本,而是内化了支撑QGT问题的真实组合关系。研究发现,标准前馈架构可在结构化组合恢复任务中学习可验证的逆映射。

原文摘要 · Abstract (English)

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.

群体测试神经网络可验证性

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