Explain Like I'm 5
We made a new kind of LEGO brick! ๐งฑโจ
- ๐ฏ It works just as well as the old bricks (sometimes better!)
- ๐ง It's easier to understand what it's doing inside
- ๐ And there's SO MUCH MORE we can build with it!
We're excited to see what amazing things people will create! ๐
๐ Summary of Contributions
Theoretical Foundation
Mercer kernel properties, universal approximation, self-regulation, stable gradients, and Lipschitz continuity.
Architecture Design
NMN layers, โต-Convolution, โต-Attention, AetherResNet, and AetherGPT implementations.
Empirical Validation
Improvements across vision (CIFAR, ImageNet), language (GPT-2), and geometric reasoning (XOR).
Geometric Interpretability
Vortex decision boundaries, prototype learning, and information-theoretic connections.
๐ Future Research Directions
Systematic investigation of computational trade-offs and optimization dynamics at billion-parameter scales. How do NMN layers behave in models like GPT-4 or Llama-70B?
The interpretability framework enables principled analysis of learned representations. Can we visualize and understand what large NMN models have learned about the world?
The connection to physical laws (inverse-square, field interactions) suggests applications in Physics-Informed Neural Networks (PINNs) and molecular dynamics simulations.
Custom CUDA kernels and potential TPU/NPU implementations could exploit the specific computational patterns of the โต-product for better efficiency.
๐ฏ The Vision
๐ค Get Involved
Try the Package
pip install nmn
Drop-in replacement for Linear + ReLU!
Contribute
GitHub: azettaai/nmn
Issues, PRs, discussions welcome!
Read the Paper
Full theoretical analysis and proofs available in the research paper.
Discuss
Share your experiments, questions, and ideas with the community!
๐ Acknowledgments
This work draws inspiration from physics, kernel methods, and decades of neural network research. We thank the open-source community for tools like PyTorch, JAX, and the many researchers whose work laid the foundation for geometric deep learning.