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Classical artificial neural networks have witnessed widespread successes inmachine-learning applications. Here, we propose fermion neural networks (FNNs)whose physical properties, such as local density of states or conditionalconductance, serve as outputs, once the inputs are incorporated as an initiallayer. Comparable to back-propagation, we establish an efficient optimization,which entitles FNNs to competitive performance on challenging machine-learningbenchmarks. FNNs also directly apply to quantum systems, including hard oneswith interactions, and offer in-situ analysis without preprocessing orpresumption. Following machine learning, FNNs precisely determine topologicalphases and emergent charge orders. Their quantum nature also brings variousadvantages: quantum correlation entitles more general network connectivity andinsight into the vanishing gradient problem, quantum entanglement opens upnovel avenues for interpretable machine learning, etc.

Efficient and quantum-adaptive machine learning with fermion neural networks