I am an independent researcher working on deriving deep learning architectures from first principles (Random Function Theory) rather than empirical heuristics.
The core idea: Instead of choosing kernels (like RBF) arbitrarily, I derive the optimal kernel analytically from symmetry postulates (translation, rotation, scale invariance). This leads uniquely to the Polyharmonic Spline.
Key features of this architecture:
1. No Gradient Descent: Training uses a synchronized global linear solver (Lagrange multipliers) to update function values.
2. Deep & Stable: Can scale to 500+ layers without skip connections or normalization, avoiding vanishing gradients.
3. Results: Achieves ~98.3% on MNIST (using flat vectors) and competitive results on HIGGS (11M examples), training very fast on GPU.
I’ve just released the full cycle of 4 papers on arXiv explaining the math and the algorithm.
Hi HN, I’m the author of this project.
I am an independent researcher working on deriving deep learning architectures from first principles (Random Function Theory) rather than empirical heuristics.
The core idea: Instead of choosing kernels (like RBF) arbitrarily, I derive the optimal kernel analytically from symmetry postulates (translation, rotation, scale invariance). This leads uniquely to the Polyharmonic Spline.
Key features of this architecture:
1. No Gradient Descent: Training uses a synchronized global linear solver (Lagrange multipliers) to update function values. 2. Deep & Stable: Can scale to 500+ layers without skip connections or normalization, avoiding vanishing gradients. 3. Results: Achieves ~98.3% on MNIST (using flat vectors) and competitive results on HIGGS (11M examples), training very fast on GPU. I’ve just released the full cycle of 4 papers on arXiv explaining the math and the algorithm.
Papers: https://arxiv.org/abs/2512.12731 (theory + 3 follow-ups)
The code is PyTorch-based. I’d love to hear your feedback on the math or the implementation!