Exploiting Inherent Properties of Complex Numbers for Accelerating Complex Valued Neural Networks

Since conventional Deep Neural Networks (DNNs) use real numbers as their data, they are unable to capture the imaginary values and the correlations between real and imaginary values in applications that use complex numbers. To address this limitation, Complex Valued Neural Networks (CVNNs) have been introduced, enabling to capture the context of complex numbers for various applications such as Magnetic Resonance Imaging (MRI), radar, and sensing. CVNNs handle their data with complex numbers and adopt complex number arithmetic to their layer operations, so they exhibit distinct design challenges with real-valued DNNs. The first challenge is the data representation of the complex number, which requires two values for a single data, doubling the total data size of the networks. Moreover, due to the unique operations of the complex-valued layers, CVNNs require a specialized scheduling policy to fully utilize the hardware resources and achieve optimal performance. To mitigate the design challenges, we propose software and hardware co-design techniques that effectively resolves the memory and compute overhead of CVNNs. First, we propose Polar Form Aware Quantization (PAQ) that utilizes the characteristics of the complex number and their unique value distribution on CVNNs. Then, we propose our hardware accelerator that supports PAQ and CVNN operations. Lastly, we design a CVNN-aware scheduling scheme that optimizes the performance and resource utilization of an accelerator by aiming at the special layer operations of CVNN. PAQ achieves 62.5% data compression over CVNNs using FP16 while retaining a similar error with INT8 quantization, and our hardware support PAQ with only 2% area overhead over conventional systolic array architecture. In our evaluation, PAQ hardware with the scheduling scheme achieves a 32% lower latency and 30% lower energy consumption than other accelerators.