Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional conductance, serve as outputs, once the inputs are incorporated as an initial layer. Comparable to back-propagation, we establish an efficient optimization, which entitles FNNs to competitive performance on challenging machine-learning benchmarks. FNNs also directly apply to quantum systems, including hard ones with interactions, and offer in-situ analysis without preprocessing or presumption. Following machine learning, FNNs precisely determine topological phases and emergent charge orders. Their quantum nature also brings various advantages: quantum correlation entitles more general network connectivity and insight into the vanishing gradient problem, quantum entanglement opens up novel avenues for interpretable machine learning, etc.

翻译：经典人工神经网络在机器学习应用中取得了广泛成功。本文提出费米子神经网络（FNNs），其物理特性（如局域态密度或条件电导）在将输入作为初始层嵌入后直接作为输出。与反向传播算法类似，我们建立了一种高效优化方法，使FNNs在具有挑战性的机器学习基准测试中展现出竞争性性能。FNNs还可直接应用于量子系统（包括存在相互作用的复杂系统），无需预处理或预设假设即可实现原位分析。遵循机器学习范式，FNNs能够精确确定拓扑相和涌现电荷序。其量子本性还带来多重优势：量子关联赋予更通用的网络连接性，并对梯度消失问题提供新见解；量子纠缠为可解释机器学习开辟创新途径等。