Virasoro Symmetry in Neural Network Field Theories

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 cexp = 0.9958 ± 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 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.