The authors built a framework for discovering symbolic mathematical functions and their antiderivatives (integrals) simultaneously from data. The key insight is that the product and chain rules from calculus naturally generate function-derivative pairs that form a self-expanding library. They use two "primitives" (exponential-log and sine-cosine combinations) as seeds, then build "additive atomic forests"—sums of expression trees whose derivatives are fitted to data. Because derivatives are determined by construction, you automatically get both the function and its derivative without needing symbolic integration.
Main takeaways:
- Simultaneously discovers a function and its antiderivative from data using derivative algebra
- Self-expanding library grows via product rule and chain rule applied to elementary functions
- Two primitives (EML for e^u - ln v, SOL for sin u - cos v) seed the library efficiently
- "Additive atomic forests" are sums of expression trees fitted to data
- No symbolic integration step needed; derivatives determined by construction
- On 17 classification benchmarks, matches or exceeds XGBoost on 13 datasets while producing interpretable formulas