No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation

• URL: http://arxiv.org/abs/2603.12276v1
• Date: Sun, 22 Feb 2026 01:09:31 GMT
• Title: No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation
• Abstract summary: We introduce the yat-product, a kernel operator combining quadratic alignment with inverse-square proximity.<n>We prove it is a Mercer kernel, analytic, Lipschitz on bounded domains, and self-regularizing.<n> Neural Matter Networks (NMNs) use yat-product as the sole non-linearity, replacing conventional linear-activation-normalization blocks with a single geometrically-grounded operation.
• Score: 0.42303492200814446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the yat-product, a kernel operator combining quadratic alignment with inverse-square proximity. We prove it is a Mercer kernel, analytic, Lipschitz on bounded domains, and self-regularizing, admitting a unique RKHS embedding. Neural Matter Networks (NMNs) use 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. Empirically, NMN-based classifiers match linear baselines on MNIST while exhibiting bounded prototype evolution and superposition robustness. In language modeling, Aether-GPT2 achieves lower validation loss than GPT-2 with a comparable parameter budget while using yat-based attention and MLP blocks. Our framework unifies kernel learning, gradient stability, and information geometry, establishing NMNs as a principled alternative to conventional neural architectures.

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