The role of modes in nonlinear fiber optical computing.

We investigate the nonlinear propagation of light in graded-index multimode fiber, utilizing it as an optical computing unit, and quantify how it employs waveguide modes to process information. Using a time-dependent spatiotemporal propagation model with modal decomposition, we evaluate several benchmark regression and classification tasks and study the modal content of the generated speckles, which couples with a simple digital layer to perform optical computing. Analysis of modal entropy and energy-based mode counts reveals that effective computation is confined to a low-dimensional modal subspace, whose identity depends on the task and propagation regime. This also sets a trade-off between modal richness and nonlinear beam self-cleaning. These results establish modal statistics as practical design metrics for fiber-based optical computers.