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

arXiv: https://arxiv.org/abs/2603.12276 · HTML: https://mlsanity.com/paper/2603.12276/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 22 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [SGD Learns the Conjugate Kernel Class of the Network](https://mlsanity.com/paper/1702.08503/) (2017)
- [Convolutional Kernel Networks](https://mlsanity.com/paper/1406.3332/) (2014)
- [Deep kernel processes](https://mlsanity.com/paper/2010.01590/) (2020)
- [Universal Approximation with Quadratic Deep Networks](https://mlsanity.com/paper/1808.00098/) (2018)
- [Quadratic Neuron-empowered Heterogeneous Autoencoder for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2204.01707/) (2022)

## Abstract (arXiv)

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.