Topological data analysis (TDA) has achieved remarkable success in molecular sciences over the past decade. Integrating TDA with deep learning has led to advances in drug design, materials discovery, protein engineering, and COVID‑19 research. However, many TDA tools rely heavily on persistent homology, which captures only limited aspects of the underlying algebraic and geometric structures. To move beyond these limitations, we develop new mathematical foundations that bridge pure mathematics with modern AI. Recently, we introduced a multiscale commutative algebra embedding that captures intrinsic physical and chemical interactions in molecular systems for the first time. Using Persistent Stanley–Reisner Theory, we extract algebraic invariants—including facet ideals and $f$‑vectors—to construct a Commutative Algebra Neural Network (CANet). Our approach integrates deep learning with rich algebraic information, producing AI models that are mechanistic, interpretable, and highly generalizable. I will present the mathematical framework of CANet and show how these descriptors reveal structural patterns underlying genetic disease–causing mutations, pushing TDA beyond persistent homology.