CAREER: TenAI: Tensorizing Machine Learning to Leverage Multiway Structure

Machine learning has achieved state-of-the-art performance in image recognition, accelerated large-scale computational simulations, and unleashed the potential of generative modeling. The proliferation of machine learning has brought with it significant demands on computational resources (e.g., storage and energy) and reliance on data-driven models that lack accuracy guarantees. This lack of transparency has made it difficult to trust machine learning tools for high consequence tasks, e.g., drug discovery and cybersecurity. This project aims to bring a new level of scalability and transparency to machine learning using modern high-dimensional data analysis frameworks. These new methodologies, based on multidimensional matrices known as tensors, will uncover interpretable relationships in big data efficiently and will add new levels of flexibility to machine learning tools. By reframing machine learning using mathematically sound techniques, this project will provide a more reliable foundation from which big data, machine learning, and AI can accelerate innovation, drive economic growth, and benefit society broadly. Activities conducted under this project will foster growth in the next generation of computational mathematicians and data scientists, and prepare them to become leaders of an AI-enhanced workforce. This project will “tensorize” AI (TenAI) from two perspectives: (1) employ multilinear operations to exploit existing high-dimensional correlations in the data and models and (2) reveal or impose hidden multiway structures to bring new insights and flexibility to machine learning pipelines. Broadly, the tensorization strategies will take advantage of multiway correlations (e.g., spatio-temporal) to build more effective featurizers as well as efficiently approximate high-dimensional spaces through low-rank, interpretable representations. The new mathematical framework will bring theoretical and statistical insights across three major categories of machine learning: linearized (i.e., kernel methods), probabilistic (i.e., generative modeling), and fundamental (i.e., classification and regression). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.