# Predicting Company Growth using Scaling Theory informed Machine Learning

arXiv: https://arxiv.org/abs/2410.17587 · HTML: https://mlsanity.com/paper/2410.17587/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 6 of 6)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [A high-bias, low-variance introduction to Machine Learning for physicists](https://mlsanity.com/paper/1803.08823/) (2018)
- [Machine Learning Advances for Time Series Forecasting](https://mlsanity.com/paper/2012.12802/) (2020)
- [Interpretable Neural Networks for Panel Data Analysis in Economics](https://mlsanity.com/paper/2010.05311/) (2020)
- [Using Machine Learning to Forecast Future Earnings](https://mlsanity.com/paper/2005.13995/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Survey of Physics-Informed AI for Complex Urban Systems](https://mlsanity.com/paper/2506.13777/) (2025)

## Abstract (arXiv)

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth trend with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning (STIML) framework that integrates a scaling-based growth model to capture the mechanism-driven average trend, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat annual financial statement data (1950--2019) for 31,553 North American companies, we extend the growth model beyond assets to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth exhibits a clear separation between trend-driven predictability and fluctuation-driven predictability, with their relative importance depending strongly on company size and volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond simple autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic models.