{"ID":2824106,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24420","arxiv_id":"2512.24420","title":"Virasoro Symmetry in Neural Network Field Theories","abstract":"Neural Network Field Theories (NN-FTs) typically describe Generalized Free Fields that lack a local stress-energy tensor in two dimensions, obstructing the realization of Virasoro symmetry. We present the ``Log-Kernel'' (LK) architecture, which enforces local conformal symmetry via a specific rotation-invariant spectral prior $p(k) \\propto |k|^{-2}$. We analytically derive the emergence of the Virasoro algebra from the statistics of the neural ensemble. We validate this construction through numerical simulation, computing the central charge $c_{exp} = 0.9958 \\pm 0.0196$ (theoretical $c=1$) and confirming the scaling dimensions of vertex operators. Furthermore, we demonstrate that finite-width corrections generate interactions scaling as $1/N$. Finally, we extend the framework to include fermions and boundary conditions, realizing the super-Virasoro algebra. We verify the $\\mathcal{N}=1$ super-Virasoro algebra by measuring the supercurrent correlator to $96\\%$ accuracy. We further demonstrate conformal boundary conditions on the upper half-plane, achieving 99\\% agreement for boundary fermion and boson propagators.","short_abstract":"Neural Network Field Theories (NN-FTs) typically describe Generalized Free Fields that lack a local stress-energy tensor in two dimensions, obstructing the realization of Virasoro symmetry. We present the ``Log-Kernel'' (LK) architecture, which enforces local conformal symmetry via a specific rotation-invariant spectra...","url_abs":"https://arxiv.org/abs/2512.24420","url_pdf":"https://arxiv.org/pdf/2512.24420v3","authors":"[\"Brandon Robinson\"]","published":"2025-12-30T19:00:01Z","proceeding":"hep-th","tasks":"[\"hep-th\",\"cs.LG\"]","methods":"[]","has_code":false}