Neural networks have achieved remarkable results across numerous scientific domains because of their ability to uncover complex patterns. However, despite their effectiveness, these networks rely on heuristic training of highly non-convex objective functions, limiting theoretical understanding and practical reliability. Recent work has shown that shallow neural networks with scalar outputs can be formulated as convex optimization problems, bridging empirical success with theory. In this work, we build upon this framework for vector-valued outputs, introducing a convex formulation for two-layer ReLU networks based on an atomic norm and expressible as a semidefinite program (SDP). This yields a principled convex relaxation of multi-output networks that is both expressive and tractable. We validate the approach using standard SDP solvers, demonstrating its feasibility. These results extend convex neural network training beyond scalar outputs and provide a foundation for scalable, robust alternatives to current heuristic deep learning methods. Our method achieved a 7.3% increase in classification accuracy compared to a baseline convex multi-output network.

Scientific visualization of a computer model of global carbon dioxide.

The Advanced Visualization Lab (AVL) is part of the the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana-Champaign. The AVL is led by Professor Donna Cox, who coined the term "Renaissance Team", with the belief that bringing together specialists of diverse backgrounds creates a team that is greater than the sum of its parts, and members of the AVL team reflect that in our interdisciplinarity. We specialize in creating high-quality cinematic scientific visualizations of supercomputer simulations for public outreach.

course Public Access Share on Communicating science through visualization in an age of alternative facts Authors: Kalina Borkiewicz University of Illinois at Urbana-Champaign University of Illinois at Urbana-ChampaignView Profile , A J Christensen University of Illinois at Urbana-Champaign University of Illinois at Urbana-ChampaignView Profile , John E. Stone University of Illinois at Urbana-Champaign University of Illinois at Urbana-ChampaignView Profile Authors Info & Claims SA '17: SIGGRAPH Asia 2017 CoursesNovember 2017 Article No.: 3Pages 1–122https://doi.org/10.1145/3134472.3134488Published:27 November 2017Publication History 0citation291DownloadsMetricsTotal Citations0Total Downloads291Last 12 Months23Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF