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Photonic computing shows promise for transformative advancements in machinelearning (ML) acceleration, offering ultra-fast speed, massive parallelism, andhigh energy efficiency. However, current photonic tensor core (PTC) designsbased on standard optical components hinder scalability and compute density dueto their large spatial footprint. To address this, we propose an ultra-compactPTC using customized programmable multi-operand multimode interference (MOMMI)devices, named M3ICRO. The programmable MOMMI leverages the intrinsic lightpropagation principle, providing a single-device programmable matrix unitbeyond the conventional computing paradigm of one multiply-accumulate (MAC)operation per device. To overcome the optimization difficulty of customizeddevices that often requires time-consuming simulation, we apply ML for opticsto predict the device behavior and enable a differentiable optimization flow.We thoroughly investigate the reconfigurability and matrix expressivity of ourcustomized PTC, and introduce a novel block unfolding method to fully exploitthe computing capabilities of a complex-valued PTC for near-universalreal-valued linear transformations. Extensive evaluations demonstrate thatM3ICRO achieves a 3.4-9.6x smaller footprint, 1.6-4.4x higher speed, 10.6-42xhigher compute density, 3.7-12x higher system throughput, and superior noiserobustness compared to state-of-the-art coherent PTC designs, while maintainingclose-to-digital task accuracy across various ML benchmarks. Our code isopen-sourced at https://github.com/JeremieMelo/M3ICRO-MOMMI.

M3ICRO: Machine Learning-Enabled Compact Photonic Tensor Core based on PRogrammable Multi-Operand Multimode Interference