LU Factorization of Discrete Random Matrices

What the math gives to ML

The paper gives probabilistic guarantees that iid discrete random matrices can be simultaneously pivot-safe for every leading principal block, while controlling the LU growth factor. This is potentially useful for neural architectures that require invertible or triangular linear maps, where a bad random initialization can create zero pivots or severe finite-precision amplification before learning can correct it. The most direct transfer is a discrete, bounded initialization scheme for LU-parameterized layers, combined with an explicit growth-factor check and resampling rather than relying on Gaussian initialization. The result is most relevant to invertible networks, normalizing flows, reversible sequence models, and learned linear preconditioners, not ordinary dense layers.