[P] Tridiagonal eigenvalue models in PyTorch: cheaper training/inference than dense spectral models

Researcher Alex Shtf has introduced a novel neural architecture in PyTorch that replaces traditional dense matrix operations with eigenvalue computations on symmetric tridiagonal matrices. The model family, defined as f(x) = λₖ(A₀ + ∑ᵢ xᵢAᵢ), uses constrained tridiagonal structure to dramatically accelerate training and inference. By wiring scipy.linalg.eigh_tridiagonal into PyTorch's autograd system, Shtf achieved 5-6x faster eigensolves on 100x100 batches compared to dense spectral models, making larger experiments computationally feasible.

This work represents a deliberate departure from transformer-dominated AI research, exploring what single "neurons" can achieve when nonlinearities come from matrix eigenvalues rather than activation functions. The tridiagonal constraint maintains adjacent latent-variable interactions while avoiding the computational explosion of dense matrices, creating models that sit between interpretable linear regression and opaque deep networks. Initial experiments on toy and tabular datasets demonstrate the approach's potential as a transparent alternative to black-box neural architectures.

The engineering-focused writeup details both the mathematical motivation and practical implementation, showing how diagonal structures collapse to piecewise-linear models while tridiagonal structures preserve valuable interactions. This research direction offers a fresh perspective on model interpretability in an era dominated by massive, uninterpretable transformer networks, providing tools for practitioners who need both expressivity and transparency in their AI systems.