2025/12/22 by Yuriy N. Bakhvalov, Bakhvalov, Yuriy N.
Computer Science · Engineering · #41A15 #62M45 #65D05 #65D07 #68T05 #Advanced Neural Network Applications #FOS: Computer and information sciences #FOS: Mathematics #Ferroelectric and Negative Capacitance Devices #G.1.2 #I.2.6 #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Parallel Computing and Optimization Techniques
paper · doi:10.48550/arxiv.2512.19524
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.