Innovation is a major contributor to national security, productivity, competitiveness, and economic growth. Recent legislation and policies, most notably the CHIPS + Science Act of 2022, provide significant support to transform the science and research enterprise, with a focus on strengthening commercialization ecosystems and providing opportunities for historically underserved students and communities to be engaged in science, technology, engineering, and mathematics. On June 13-14, 2023, the Government-University-Research Roundtable of the National Academies of Sciences, Engineering, and Medicine held a workshop to consider the axioms of innovation - the underpinning norms, conditions, and culture of innovation environments in the United States and globally. Participants discussed new trends in the theory and practice of innovation, as well as innovation-fostering partnerships and collaboration across sectors and disciplines. This publication summarizes the presentations and discussion of the workshop.