# Learning to Detect Symbolic Failure: Machine Learning and the Limits of Black-Scholes

> Source: <https://www.machinebrief.com/news/learning-to-detect-symbolic-failure-machine-learning-and-the-8glu>
> Published: 2026-09-24 04:00:00+00:00

arXiv:2609.27764v1 Announce Type: new 
Abstract: We treat options pricing as a representation problem: can machine learning detect systematic deviations from Black-Scholes using 2.6M real option contracts? We compare three regimes: learned abstract embeddings (Kernel PCA), preserved domain structure (tree-based ensembles), and neural network validation. Tree-based methods outperform kernel dimensionality reduction by 21.5 percentage points (93.8% vs 72.3%), and domain-expert features (Greeks, moneyness) outperform engineered features. NN-based and BS-based deviation labels agree 99.9974% of the time, suggesting deviations reflect market structure rather than model artifact. We conclude that in domains with expert-designed symbolic features, preserving structure beats learning abstractions. We make no claim of exploitable mispricings.