Beyond the Markovian Assumption: Robust Optimization via Fractional Weyl Integrals in Imbalanced Data

TL;DR

This paper introduces a fractional calculus-based optimization method that enhances robustness against noise and class imbalance, significantly improving performance in financial fraud detection and medical diagnostics.

Contribution

It proposes a novel optimization algorithm using Fractional Weyl Integrals to incorporate memory effects, reducing overfitting and improving accuracy in imbalanced datasets.

Findings

40% improvement in PR-AUC for fraud detection

Prevents overfitting in medical diagnostics

Provides a new regularization technique via fractional calculus

Abstract

Standard Gradient Descent and its modern variants assume local, Markovian weight updates, making them highly susceptible to noise and overfitting. This limitation becomes critically severe in extremely imbalanced datasets such as financial fraud detection where dominant class gradients systematically overwrite the subtle signals of the minority class. In this paper, we introduce a novel optimization algorithm grounded in Fractional Calculus. By isolating the core memory engine of the generalized fractional derivative, the Weighted Fractional Weyl Integral, we replace the instantaneous gradient with a dynamically weighted historical sequence. This fractional memory operator acts as a natural regularizer. Empirical evaluations demonstrate that our method prevents overfitting in medical diagnostics and achieves an approximately 40 percent improvement in PR-AUC over classical optimizers in financial fraud detection, establishing a robust bridge between pure fractional topology and applied Machine Learning.