COVID-19 and deep learning have each marked pivotal milestones in the evolution of modern science. Since the onset of the pandemic, researchers from diverse disciplines have converged to address urgent, real-world challenges, while deep learning has catalyzed methodological innovation across fields. These two phenomena exemplify distinct scientific paradigms: spread-out science, which propagates novel ideas and methods, and merge-in science, which synthesizes existing knowledge to solve complex problems. We introduce the concept of sci-entropy, defined as the difference between the semantic entropy of a paper’s citations and references. Positive sci-entropy reflects the diffusion of new ideas (spread-out), whereas negative values indicate knowledge consolidation (merge-in). Our analysis, spanning deep learning, COVID-19, and 19 additional disciplines, reveals that scientific progress is governed by the dynamic interplay between these two forces. Excessively high sci-entropy may fragment research, while overly low values can stifle innovation. Our findings suggest that the balance between innovation and synthesis is fundamental to the trajectory of scientific development, offering a new framework for understanding interdisciplinary research and knowledge integration.

COVID-19 and deep learning have each marked pivotal milestones in the evolution of modern science. Since the onset of the pandemic, researchers from diverse disciplines have converged to address urgent, real-world challenges, while deep learning has catalyzed methodological innovation across fields. These two phenomena exemplify distinct scientific paradigms: spread-out science, which propagates novel ideas and methods, and merge-in science, which synthesizes existing knowledge to solve complex problems. We introduce the concept of sci-entropy, defined as the difference between the semantic entropy of a paper’s citations and references. Positive sci-entropy reflects the diffusion of new ideas (spread-out), whereas negative values indicate knowledge consolidation (merge-in). Our analysis, spanning deep learning, COVID-19, and 19 additional disciplines, reveals that scientific progress is governed by the dynamic interplay between these two forces. Excessively high sci-entropy may fragment research, while overly low values can stifle innovation. Our findings suggest that the balance between innovation and synthesis is fundamental to the trajectory of scientific development, offering a new framework for understanding interdisciplinary research and knowledge integration.