New Formalism Enables Conformal Defects in Neural Network Field Theories

Global: New Formalism Enables Conformal Defects in Neural Network Field Theories

A team of researchers including Pietro Capuozzo, Brandon Robinson, and Benjamin Suzzoni announced a new formalism for constructing conformally invariant defects within Neural Network Field Theories (NN-FTs). The study, first submitted on December 8, 2025 and revised on January 28, 2026, appears on the preprint server arXiv under identifier arXiv:2512.07946.

Background on Neural Network Field Theories

NN-FTs represent an emerging approach that translates the architecture and prior distribution of neural networks into the language of quantum field theory. By selecting appropriate network specifications, researchers can emulate a broad class of field theories, including those possessing conformal symmetry.

Formalism for Conformal Defects

The authors propose a systematic method to embed conformal defects—localized modifications that preserve conformal invariance—into NN-FTs. Their construction parallels the defect operator product expansion (defect OPE) used in traditional conformal field theory, adapting it to the neural network context.

Demonstrations in Toy Models

To illustrate the approach, the paper examines two simplified scalar NN-FT models. In each case, the authors derive an expansion resembling the defect OPE for two‑point correlation functions and interpret the coefficients in terms of neural network parameters.

Implications for Theory and Machine Learning

The work bridges techniques from high‑energy physics with modern machine‑learning frameworks, suggesting new avenues for studying non‑perturbative effects and defect dynamics using trainable models. It also provides a concrete example of how field‑theoretic concepts can be operationalized within neural architectures.

Future Directions

Capuozzo and co‑authors acknowledge that extending the formalism beyond toy examples will require addressing higher‑dimensional defects and incorporating training dynamics. They propose investigating more complex network architectures and exploring potential connections to holographic dualities.

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.