We introduce effective field neural networks (EFNNs), a new architecture based on continued functions—mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical three-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: Trained on $10\times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training—and the accuracy improves with system size, with a computational time speedup of ${10}^3$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply.

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• Artificial neural networks
• Effective field theory
• Ising model
• Machine learning
• Quantum Monte Carlo
• Spin lattice models