Depth and breadth are widely contrasted strategies of search for generating new technologies through recombination. Breadth of technological search is often associated with the exploration of new possibilities and is juxtaposed with depth of search, which references the exploitation of existing ones. We argue that the two qualities should be understood and measured independently, with breadth reflecting broad technical recombination and depth technical specificity. We operationalize deep and broad recombination using machine learning to project the network of prior technological combinations onto a Poincaré disk in negatively curved hyperbolic space, which natively represents the hierarchy of technology, with depth captured by components’ difference in radius from center and breadth difference in angle. We validate this model with established metrics, a range of examples, and its conceptual treatment of depth and breadth as independent quantities, holding virtually no empirical correlation. Then we demonstrate how depth drives short-term advancement, increasing the number and quality of early adopters, while breadth forecasts long-term advance, enlarging the scope of relevant audiences to the inventive design. We explore distinct mechanisms through which this occurs, and show that local search garners more local recognition in the short term, but greater “lock-in” in the longer term. Finally, we analyze follow-up invention to reveal the unfolding interplay of exploitation and exploration, highlighting their synergistic relationship, especially within companies that can strategically allocate engineering resources to build on prior advances. We conclude with theoretical and strategic implications of these insights and the novel embedding representations that yielded them.