Research Paper#Neural Networks, Conformal Field Theory, Physics🔬 ResearchAnalyzed: Jan 3, 2026 09:29
Virasoro Symmetry in Neural Networks
Published:Dec 30, 2025 19:00
•1 min read
•ArXiv
Analysis
This paper presents a novel approach to constructing Neural Network Field Theories (NN-FTs) that exhibit the full Virasoro symmetry, a key feature of 2D Conformal Field Theories (CFTs). The authors achieve this by carefully designing the architecture and parameter distributions of the neural network, enabling the realization of a local stress-energy tensor. This is a significant advancement because it overcomes a common limitation of NN-FTs, which typically lack local conformal symmetry. The paper's construction of a free boson theory, followed by extensions to Majorana fermions and super-Virasoro symmetry, demonstrates the versatility of the approach. The inclusion of numerical simulations to validate the analytical results further strengthens the paper's claims. The extension to boundary NN-FTs is also a notable contribution.
Key Takeaways
- •Introduces a method to build NN-FTs with full Virasoro symmetry.
- •Achieves this by carefully designing network architecture and parameter distributions.
- •Demonstrates the approach with free boson, Majorana fermion, and super-Virasoro examples.
- •Includes numerical simulations to validate analytical results.
- •Extends the framework to boundary NN-FTs.
Reference
“The paper presents the first construction of an NN-FT that encodes the full Virasoro symmetry of a 2d CFT.”