  Photonic computing is a compelling avenue for performing highly efficient
matrix multiplication, a crucial operation in Deep Neural Networks (DNNs).
While this method has shown great success in DNN inference, meeting the high
precision demands of DNN training proves challenging due to the precision
limitations imposed by costly data converters and the analog noise inherent in
photonic hardware. This paper proposes Mirage, a photonic DNN training
accelerator that overcomes the precision challenges in photonic hardware using
the Residue Number System (RNS). RNS is a numeral system based on modular
arithmetic, allowing us to perform high-precision operations via multiple
low-precision modular operations. In this work, we present a novel
micro-architecture and dataflow for an RNS-based photonic tensor core
performing modular arithmetic in the analog domain. By combining RNS and
photonics, Mirage provides high energy efficiency without compromising
precision and can successfully train state-of-the-art DNNs achieving accuracy
comparable to FP32 training. Our study shows that on average across several
DNNs when compared to systolic arrays, Mirage achieves more than $23.8\times$
faster training and $32.1\times$ lower EDP in an iso-energy scenario and
consumes $42.8\times$ lower power with comparable or better EDP in an iso-area
scenario.
