Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable approaches to representation learning, dynamical systems, and partial differential equations (PDEs). In this paper, we revisit a classical optimization framework from the computational physics literature known as the *orbital minimization method* (OMM), originally proposed in the 1990s for solving eigenvalue problems in computational chemistry. We provide a simple linear-algebraic proof of the consistency of the OMM objective, and reveal connections between this method and several ideas that have appeared independently across different domains. Our primary goal is to justify its broader applicability in modern learning pipelines. We adapt this framework to train neural networks to decompose positive semidefinite operators, and demonstrate its practical advantages across a range of benchmark tasks. Our results highlight how revisiting classical numerical methods through the lens of modern theory and computation can provide not only a principled approach for deploying neural networks in numerical simulation, but also effective and scalable tools for machine learning.

This paper introduces a novel application of IBR technology for efficient rendering of high quality CG and live action stereoscopic sequences. Traditionally, IBR has been applied to render novel views using image and depth based representations of the plenoptic functions. In this work, we present a restricted form of IBR in which lower resolution images for the views to be generated at a very high resolution are assumed to be available. Specifically, the paper addresses the problem of synthesizing stereo IMAX(R)1 3D motion picture images at a standard resolution of 4-6K. At such high resolutions, producing CG content is extremely time consuming and capturing live action requires bulky cameras. We propose a Hybrid Stereo Camera concept in which one view is rendered at the target high resolution but the other is rendered at a much lower resolution. Methods for synthesizing the second view sequence at the target resolution using image analysis and IBR techniques are the focus of this work. The high quality results from the techniques presented in this paper have been visually evaluated in the IMAX 3D large screen projection environment. The paper also highlights generalizations and extensions of the hybrid stereo camera concept.