Hadamard product-based in-memory computing design for floating point neural network training

Deep neural networks (DNNs) are one of the key fields of machine learning. It requires considerable computational resources for cognitive tasks. As a novel technology to perform computing inside/near memory units, in-memory computing (IMC) significantly improves computing efficiency by reducing the need for repetitive data transfer between the processing and memory units. However, prior IMC designs mainly focus on the acceleration for DNN inference. DNN training with the IMC hardware has rarely been proposed. The challenges lie in the requirement of DNN training for high precision (e.g. floating point (FP)) and various operations of tensors (e.g. inner and outer products). These challenges call for the IMC design with new features. This paper proposes a novel Hadamard product-based IMC design for FP DNN training. Our design consists of multiple compartments, which are the basic units for the matrix element-wise processing. We also develop BFloat16 post-processing circuits and fused adder trees, laying the foundation for IMC FP processing. Based on the proposed circuit scheme, we reformulate the back-propagation training algorithm for the convenience and efficiency of the IMC execution. The proposed design is implemented with commercial 28 nm technology process design kits and benchmarked with widely used neural networks. We model the influence of the circuit structural design parameters and provide an analysis framework for design space exploration. Our simulation validates that MobileNet training with the proposed IMC scheme saves 91.2% in energy and 13.9% in time versus the same task with NVIDIA GTX 3060 GPU. The proposed IMC design has a data density of 769.2 Kb mm-2 with the FP processing circuits included, showing a 3.5 x improvement than the prior FP IMC designs.