Infinite-Width Neural Networks as Kernel Machines, the Continuum Hypothesis, and Liouville Quantum Gravity
The abstract theory establishes that infinite-width deep neural networks are mathematically equivalent to kernel machines operating in high-dimensional spaces through linear parameterization. Furthermore, the resolution of chaotic Liouville field dynamics demonstrates a rigorous equivalence between probabilistic path integrals and bootstrap representation theories for quantum gravity models. These concepts fundamentally redefine the theoretical boundaries of machine learning optimization, statistical mechanics, and set theory regarding the continuum hypothesis.
Kernel Machines in Deep Learning Theory
The abstract theory establishes that infinite-width deep neural networks are mathematically equivalent to kernel machines operating in high-dimensional spaces through linear parameterization. Further…