不再幻想：基于物理的核网络用于几何基础的神经计算

This research introduces a novel kernel operator called the yat-product, which combines quadratic alignment with inverse-square proximity. It is proven to be a Mercer kernel, analytic, Lipschitz on bounded domains, and self-regularizing, allowing for a unique embedding in the Reproducing Kernel Hilbert Space (RKHS). Neural Matter Networks (NMNs) utilize the yat-product as the sole non-linearity, replacing conventional linear activation normalization blocks with a single geometrically grounded operation. This architectural simplification preserves universal approximation while shifting normalization into the kernel itself via the denominator, rather than relying on separate normalization layers. Empirical results show that NMN-based classifiers match linear baselines on the MNIST dataset while exhibiting bounded prototype evolution and robustness in superposition.