arXiv paper: From Classification to Regression: Using a Fruitfly to Solve Equations

arXiv ID: 2607.27196v1 Title: From Classification to Regression: Using a Fruitfly to Solve Equations Authors: Shady E. Ahmed, Panos Stinis Primary category: cs.LG Categories: cs.LG, math.NA Published: 2026-07-29T17:58:05Z Updated: 2026-07-29T17:58:05Z Abstract: We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data often occupy limited and recurring regions of the input space, we generate predictions by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. We apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, our offline-online workflow extracts patterns from data or governing equations during the offline phase, while online prediction requires only similarity evaluation and response aggregation. This structure helps us reduce computational and memory demands while providing explicit control over the trade-off among accuracy, storage, and inference cost. PDF: https://arxiv.org/pdf/2607.27196v1