I am a Tenure-Track Assistant Professor in the Electrical Engineering Department at the University of Colorado Denver, and founder and director of the Abstract Signal Processing (ASP) Lab. My work is guided by a central thesis: that algebraic structure is what ultimately determines when and why signal processing systems transfer across domains. Geometric and data-driven approaches capture a great deal about these systems, but the transfer question, I argue, is answered at the algebraic level. Algebraic Signal Processing (ASP) is the framework I use to pursue this thesis, and it sits at the core of every problem I study.
Before joining CU Denver, I spent five years as a postdoctoral researcher and research scientist at the University of Pennsylvania, where I began using and extending Algebraic Signal Processing (ASP) — working alongside Alejandro Ribeiro — as a rigorous mathematical foundation for deep learning. That work includes foundational results establishing the stability of algebraic neural networks to deformations — showing that the invariance and stability properties long observed empirically in convolutional architectures are consequences of underlying algebraic structure, not incidental to it. I received my Ph.D. in Electrical Engineering from the University of Delaware, where I worked on the general theory of sampling in Compressed Sensing and Graph Signal Processing.
I study a fundamental question in modern information science: when and why do signal processing systems transfer across domains — and what algebraic structure guarantees it? A filter designed for a power grid, a neural network trained on social data, a sampling strategy derived for a manifold — under what conditions do these generalize, and what guarantees can we give? This is not a question about fine-tuning models or adapting datasets. It is a structural question, and I have built my research on the answer being algebraic: transferability is not an empirical accident but a property determined by the algebraic relationships between domains. Making this precise is the founding purpose of ASP — a theory that is predictive, not just descriptive, and that leads to systems more reliable, explainable, and efficient by design.
The central observation driving my work is this: despite radical geometric and topological differences between domains — graphs, graphons, manifolds, quivers, or discrete structures — many share deep algebraic structure. That shared structure is precisely what makes transfer possible. Using tools from operator algebras, representation theory, graphon theory, and category theory, I develop rigorous algebraic frameworks for sampling, filtering, pooling, and stability analysis that are transferable across domains by construction — not by hope.
This algebraic approach has direct consequences for hard problems. In large networked systems, I use graphon representations to characterize the optimality conditions of sampling sets on graphs at massive scale — a framework I have also applied to dimensionality reduction, where the same algebraic structure that guarantees transferable sampling also identifies which degrees of freedom in a large network genuinely carry information. In machine learning, my algebraic theory of convolutional architectures provides guarantees for stability and generalization that purely empirical methods cannot. In signal processing, my algebraic sampling theory produces optimal sampling strategies for complex network data, extending classical sampling theorems to arbitrary domains through a theory of uniqueness sets grounded in operator algebras.
At the ASP Lab, we pursue these questions at the intersection of algebra, geometry, and learning theory — building the mathematical foundations, through Algebraic Signal Processing, that make transferable intelligence principled and provable.
ALEJANDRO PARADA-MAYORGA 