# From Classification to Regression: Using a Fruitfly to Solve Equations

arXiv: https://arxiv.org/abs/2607.27196 · HTML: https://mlsanity.com/paper/2607.27196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Can a Fruit Fly Learn Word Embeddings?](https://mlsanity.com/paper/2101.06887/) (2021)
- [An Intuitive Tutorial to Gaussian Process Regression](https://mlsanity.com/paper/2009.10862/) (2020)
- [A multifidelity approach to continual learning for physical systems](https://mlsanity.com/paper/2304.03894/) (2023)
- [A Multifidelity deep operator network approach to closure for multiscale systems](https://mlsanity.com/paper/2303.08893/) (2023)
- [Ensemble and Mixture-of-Experts DeepONets For Operator Learning](https://mlsanity.com/paper/2405.11907/) (2024)
- [Probabilistic partition of unity networks for high-dimensional regression problems](https://mlsanity.com/paper/2210.02694/) (2022)
- [Enhancing classification accuracy through chaos](https://mlsanity.com/paper/2603.15299/) (2026)

## Abstract (arXiv)

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.