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We introduce a hybrid quantum-classical neural network whose quantum layer is based on the paradigm of fermionic quantum computing. This model broadens the scope of fermionic machine learning (FermiML) introduced in [arXiv:2404.19032] by extending its applicability to a wider range of learning tasks. Since fermionic quantum circuits are efficiently simulable classically in polynomial time, our work introduces a scalable quantum-inspired benchmark for hybrid quantum machine learning models. We conduct a systematic evaluation of this model on supervised tasks such as classification, evaluating its performance against other hybrid quantum-classical neural networks. Our findings indicate that the proposed model performs competitively across multiple metrics, often outperforming existing architectures. Additionally, in the context of previously proposed hybrid neural networks, we observe that the inclusion of a fully-quantum layer offers no significant benefit to learning on most datasets. In contrast, incorporating fermionic layers tends to enhance accuracy and scalability, suggesting their potential value in hybrid architectures.