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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.12276 |
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| _version_ | 1866911509439840256 |
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| author | Bouhsine, Taha |
| author_facet | Bouhsine, Taha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12276 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation Bouhsine, Taha Machine Learning 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. |
| title | No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.12276 |