However, I'm unsure which type of PhD lab would provide better preparation: either a problem-first lab (e.g., like Yet-Ming Chiang at MIT) or a technology-first lab (e.g., your typical academic lab that focuses on novel science without a predetermined application, and where commercialization happens largely by chance — when a technology happens to have a valuable market application).

I've looked at advice online from successful hard-tech entrepreneurs, but the answers are conflicting. Some say to work backwards from a problem, but others argue that problem-first approaches often don't work since deep tech is inherently different: you often can't force a scientific breakthrough for a predetermined problem. Instead, they argue that most hard-tech companies are only founded because somebody made a scientific breakthrough and realized afterwards that there might be a commercial application. Indeed, the VC firm Pillar VC says that most deep-tech companies they know were "technology-first."

With that in mind, does anybody have any advice on which type of PhD lab to join?