Study Extends Neural‑Network Quantum Field Theory to Fermion‑Like Structures Using Tensor‑Valued Weights

Global: Study Extends Neural‑Network Quantum Field Theory to Fermion‑Like Structures Using Tensor‑Valued Weights

Researchers have introduced a new class of complex‑valued neural networks (CVNNs) that incorporate tensor‑valued hidden‑to‑output weights, positioning the work within the broader framework of neural‑network quantum field theory (NN‑QFT). The study demonstrates that, in the infinite‑width limit, these networks generate fermion‑like sign structures in their correlation functions, a feature previously absent from standard NN‑QFT models.

Background on Complex‑Valued Networks

Traditional CVNNs employ scalar weights and have been shown to converge to exact Gaussian processes as the network width grows without bound. By deriving the generating functional for such scalar‑weight networks, the authors identified the corresponding effective quantum state and confirmed the bosonic nature of the resulting field theory.

Introducing Tensor‑Valued Weights

The investigation extends the architecture by promoting the final‑layer weights to tensors valued in a Clifford algebra. This modification transforms the network output from a complex scalar into a complex matrix, thereby embedding a fermion‑like sign structure into the large‑width correlation functions.

Infinite‑Width Correlators and Fermionic Wick Rules

In the limit of infinite width, the authors found that correlators containing equal numbers of creation‑like ($f^{dagger}$) and annihilation‑like ($f$) operators obey fermionic Wick rules. These correlators can be expressed as determinants built from a scalar Euclidean kernel $S(x,y)=langle f^{dagger}(x)f(y)rangle$, providing a sign‑structured extension of NN‑QFT at the level of Euclidean correlators and Feynman‑type rules.

Implications for Quantum Field Theory Correspondence

The results push the correspondence between neural networks and quantum field theories beyond purely bosonic Gaussian fields. By demonstrating a pathway to encode fermion‑like symmetries within neural architectures, the work suggests new avenues for simulating quantum systems that include both bosonic and fermionic components.

Limitations and Future Directions

The authors acknowledge that a microscopic Grassmann path‑integral representation for the network parameters has not yet been constructed, leaving a gap in the formal connection to conventional fermionic field theories. Future research may focus on establishing such a representation and exploring practical applications of the fermionic sign structure in computational physics and machine learning.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.