Photonic computing shows promise for transformative advancements in machine learning (ML) acceleration, offering ultrafast speed, massive parallelism, and high energy efficiency. However, current photonic tensor core (PTC) designs based on standard optical components hinder scalability and compute density due to their large spatial footprint. To address this, we propose an ultracompact PTC using customized programmable multi-operand multimode interference (MOMMI) devices, named M3ICRO. The programmable MOMMI leverages the intrinsic light propagation principle, providing a single-device programmable matrix unit beyond the conventional computing paradigm of one multiply-accumulate operation per device. To overcome the optimization difficulty of customized devices that often requires time-consuming simulation, we apply ML for optics to predict the device behavior and enable differentiable optimization flow. We thoroughly investigate the reconfigurability and matrix expressivity of our customized PTC and introduce a novel block unfolding method to fully exploit the computing capabilities of a complex-valued PTC for near-universal real-valued linear transformations. Extensive evaluation
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