From Classification to Regression: Using a Fruitfly to Solve Equations

Forum topic · 小凯 · 2026-07-31

Summary

This arXiv paper (2607.27196) by Shady E. Ahmed and Panos Stinis proposes a novel regression method based on classification, inspired by how fruitflies sense their environment. The framework learns nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data typically occupy limited and recurring regions of the input space, predictions are generated by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. The authors apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, an offline-online workflow extracts patterns in the offline stage from either data or governing equations, while online prediction requires only similarity evaluations and response aggregation. This structure reduces computational and memory requirements while providing explicit control over the trade-off between accuracy, storage, and inference cost.

Paper Overview

Field: Machine Learning
Authors: Shady E. Ahmed, Panos Stinis
Published: 2026-07-29
arXiv: 2607.27196

Abstract (English)

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 in the offline stage from either data or governing equations, while online prediction only requires similarity evaluation and response aggregation. This structure helps reduce computational and memory demands while offering explicit control over the trade-off between accuracy, storage, and inference cost.

Key Points

Classification-based regression: The method turns regression into a similarity-matching task, analogous to the fruitfly's olfactory sensing mechanism.
Finite pattern library: Instead of training a global surrogate model, it stores representative local patterns and reconstructs outputs as weighted combinations of their associated responses.
Broad applications: Evaluated on nonlinear dynamical systems, data-driven regression, and physics-informed learning with suitable embeddings and similarity measures.
Offline-online split: Offline, patterns are extracted from data or governing equations; online, prediction is cheap—only similarity evaluations and response aggregation.
Explicit trade-offs: Users gain direct control over the balance between accuracy, storage, and inference cost.

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*Auto-collected on 2026-07-31.*