Iterative Methods for Computing the Moore--Penrose Inverse of Split-Quaternion Matrices with Applications
arXiv:2607.29270
2026
Architecture
1 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The transferable contribution is a representation-based pseudoinverse method with a polynomial inverse initialization, an explicit Newton–Schulz residual recursion, and a spectral acceptance test. This can replace repeated SVD pseudoinverses inside low-rank adapters, whitening layers, implicit modules, or matrix-compression blocks. The most practical adaptation is to compute a cheap polynomial start, verify contraction using an estimated residual norm, and fall back to a safe transpose-scaled start when the test fails.
Ideas from this paper
Unverified
2026
Replace an SVD-based pseudoinverse of a learned rectangular matrix with a low-degree polynomial initialization followed by a few Newton–Schulz iterations. The polynomial approximates the inverse Gram operator, while a cheap residual test accepts it only when the iteration is contractive and otherwise selects a conservative transpose-scaled initialization.
Useful6/10
Difficulty5/10
Novelty6/10