Brains build compact models of the world from just a few noisy and conflicting observations. They predict events via memory-based analogies even when resources are limited. The ability of biological intelligence to generalize and complete a wide range of unknown heterogeneous tasks calls for a comprehensive understanding of how networks of interactions among neurons, glia, and vascular systems enable human cognition. This will serve as a basis for advancing the design of artificial general intelligence (AGI). In this talk, we introduce a series of novel mathematical tools which can help us reconstruct networks among neurons, infer their objectives, and identify their learning rules.

To decode the network structure from very scarce and noisy data, we develop the first mathematical framework which identifies the emerging causal fractal memory phenomenon in the spike trains and the neural network topologies. We show that the fractional order operators governing the neuronal spiking dynamics provide insight into the topological properties of the underlying neuronal networks and improve the prediction of animal behavior during cognitive tasks. In addition to this, we propose a variational expectation-maximization approach to mine the optical imaging of brain activity and reconstruct the neuronal network generator, namely the weighted multifractal graph generator. Our proposed network generator inference framework can reproduce network properties, differentiate varying structures in brain networks and chromosomal interactions, and detect topologically associating domain regions in conformation maps of the human genome. Moreover, we develop a multiwavelet-based neural operator in order to infer the objectives and learning rules of complex biological systems. We thus learn the operator kernel of an unknown partial differential equation (PDE) from noisy scarce data. For time-varying PDEs, this model exhibits 2-10X higher accuracy than state-of-the-art machine learning tools.

Bio: Paul Bogdan is the Jack Munushian Early Career Chair and Associate Professor in the Ming Hsieh Department of Electrical and Computer Engineering at University of Southern California. He received his Ph.D. degree in Electrical & Computer Engineering at Carnegie Mellon University. His work has been recognized with a number of honors and distinctions, including the 2021 DoD Trusted Artificial Intelligence (TAI) Challenge award, the USC Stevens Center 2021 Technology Advancement Award for the first AI framework for SARS-CoV-2 vaccine design, the 2019 Defense Advanced Research Projects Agency (DARPA) Director’s Fellowship award, the 2018 IEEE CEDA Ernest S. Kuh Early Career Award, the 2017 DARPA Young Faculty Award, the 2017 Okawa Foundation Award, the 2015 National Science Foundation (NSF) CAREER award, the 2012 A.G. Jordan Award from Carnegie Mellon University for an outstanding Ph.D. thesis and service, and several best paper awards. His research interests include cyber-physical systems, new computational cognitive neuroscience tools for deciphering biological intelligence, the quantification of the degree of trustworthiness and self-optimization of AI systems, new machine learning techniques for complex multi-modal data, the control of complex time-varying networks, the modeling and analysis of biological systems and swarms, new control techniques for dynamical systems exhibiting multi-fractal characteristics, performance analysis and design methodologies for heterogeneous manycore systems.