We propose a new variant of the Adam optimizer [Kingma and Ba, 2014] called MICROADAM that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed into the optimizer state, thereby reducing its memory footprint significantly. We control the resulting compression error via a novel instance of the classical error feedback mechanism from distributed optimization [Seide et al., 2014, Alistarh et al., 2018, Karimireddy et al., 2019] in which the error correction information is itself compressed to allow for practical memory gains. We prove that the resulting approach maintains theoretical convergence guarantees competitive to those of AMSGrad, while providing good practical performance. Specifically, we show that MICROADAM can be implemented efficiently on GPUs: on both million-scale (BERT) and billion-scale (LLaMA) models, MicroAdam provides practical convergence competitive to that of the uncompressed Adam baseline, with lower memory usage and similar running time. Our code is available at https://github.com/IST-DASLab/MicroAdam.

Photonic computing shows promise for transformative advancements in machine learning (ML) acceleration, offering ultra-fast 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 ultra-compact 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 (MAC) 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 a 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 evaluations demonstrate that M3ICRO achieves a 3.4-9.6x smaller footprint, 1.6-4.4x higher speed, 10.6-42x higher compute density, 3.7-12x higher system throughput, and superior noise robustness compared to state-of-the-art coherent PTC designs, while maintaining close-to-digital task accuracy across various ML benchmarks. Our code is open-sourced at https://github.com/JeremieMelo/M3ICRO-MOMMI.