<p>Propelled by advancements in artificial intelligence, the demand for field-programmable devices has grown rapidly in the last decade. Among various state-of-the-art platforms, programmable integrated photonics emerges as a promising candidate, offering a new strategy to drastically enhance computational power for data-intensive tasks. However, intrinsic weak nonlinear responses of dielectric materials have limited traditional photonic programmability to the linear domain, leaving out the most common and complex activation functions used in artificial intelligence. Here we push the capabilities of photonic field-programmability into the nonlinear realm by meticulous spatial control of distributed carrier excitations and their dynamics within an active semiconductor. Leveraging the architecture of photonic nonlinear computing through polynomial building blocks, our field-programmable photonic nonlinear microprocessor demonstrates in situ training of photonic polynomial networks with dynamically reconfigured nonlinear connections. Our results offer a new paradigm to revolutionize photonic reconfigurable computing, enabling the handling of intricate tasks using a polynomial network with unparalleled simplicity and efficiency.</p>