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.

Competitive influence diffusion occurs in settings ranging from product competition to online information propagation. Classical models often predict winner-takes-all outcomes, whereas persistent coexistence is observed in practice. We revisit this discrepancy by jointly considering incomplete network observation and information overload. An isotropic-Gaussian surrogate for a network embedding enables tractable mean-field estimation of overload timing. We then derive the competing dynamics before and after overload. Without overload, a strictly stronger influence asymptotically approaches dominance. Under overload, users become progressively less sensitive to influence strength, limiting further amplification and driving relative shares toward stable values determined by the initial state, strengths, and overload timing. We derive a first-order approximation to the exponential post-overload dynamics and evaluate its accuracy numerically. Experiments use six real network topologies but simulated competitive diffusion; they test internal predictions and structural sensitivity, not whether real users undergo the posited behavioral transition. Results are robust to alternative overload functions but sensitive to label-dependent priority cues. Recovering missing links can improve overload-time and final-share estimates, although link-prediction accuracy does not necessarily imply better diffusion prediction. Overall, information overload can interrupt cumulative strength amplification and thereby sustain coexistence under the stated assumptions.