Kolmogorov-Arnold Networks and Evolutionary Game Theory for More Personalized Cancer Treatment

TL;DR

Addresses the need for interpretable, generalizable predictive tools in personalized cancer treatment. Proposes a hybrid framework that combines Kolmogorov-Arnold Networks (KANs) with Evolutionary Game Theory (EGT), including a KAN-ODE formulation $du/dt = \text{KAN}(u(t), \theta)$ to model dynamic cancer progression. Key contributions include leveraging the Kolmogorov-Arnold representation $f(\mathbf{x}) = \sum_{q=1}^{2n+1} \Phi_q (\sum_{p=1}^n \phi_{q,p}(x_p))$ and integrating edge-based learnable functions with game-theoretic dynamics to capture adaptive responses. The work highlights potential clinical impact and emphasizes the need for scalable validation, regulatory alignment, and cross-domain applicability.

Abstract

Personalized cancer treatment is revolutionizing oncology by leveraging precision medicine and advanced computational techniques to tailor therapies to individual patients. Despite its transformative potential, challenges such as limited generalizability, interpretability, and reproducibility of predictive models hinder its integration into clinical practice. Current methodologies often rely on black-box machine learning models, which, while accurate, lack the transparency needed for clinician trust and real-world application. This paper proposes the development of an innovative framework that bridges Kolmogorov-Arnold Networks (KANs) and Evolutionary Game Theory (EGT) to address these limitations. Inspired by the Kolmogorov-Arnold representation theorem, KANs offer interpretable, edge-based neural architectures capable of modeling complex biological systems with unprecedented adaptability. Their integration into the EGT framework enables dynamic modeling of cancer progression and treatment responses. By combining KAN's computational precision with EGT's mechanistic insights, this hybrid approach promises to enhance predictive accuracy, scalability, and clinical usability.

Figures (3)

• Figure 1: Multi-Layer Perceptrons (MLPs) vs. Kolmogorov-Arnold Networks (KANs), Figure from kan_survey2.
• Figure 2: Progression of KAN advancements in 2024, Figure from kan_survey2.
• Figure 3: Kolmogorov-Arnold Networks (KANs) and Evolutionary Game Theory (EGT) Modeling intergradation for better personalized cancer treatment, KAN Figure from kan_ode.