Efficient and quantum-adaptive machine learning with fermion neural networks

The application of machine learning to quantum data and models has been held back by the lack of adaptability of classical artificial neural networks and efficiency in present-day quantum neural networks. 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 apply directly to quantum systems, including complex ones with interactions, and offer in situ analysis without preprocessing or presumption. Following machine learning, FNNs precisely determine topological phases and emergent charge orders. FNNs' quantum nature also brings various advantages and insights: quantum correlation entitles more general network connectivity and insight into the vanishing gradient problem, quantum entanglement opens up alternative avenues for interpretable machine learning, etc.