ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameters

The self-attention mechanism distinguishes transformer-based large language models (LLMs) apart from convolutional and recurrent neural networks. Despite the performance improvement, achieving real-time LLM inference on silicon remains challenging due to the extensive use of Softmax in self-attention. In addition to the non-linearity, the low arithmetic intensity significantly limits processing parallelism, especially when working with longer contexts. To address this challenge, we propose Constant Softmax (ConSmax), a software-hardware co-design that serves as an efficient alternative to Softmax. ConSmax utilizes differentiable normalization parameters to eliminate the need for maximum searching and denominator summation in Softmax. This approach enables extensive parallelization while still executing the essential functions of Softmax. Moreover, a scalable ConSmax hardware design with a bitwidth-split look-up table (LUT) can achieve lossless non-linear operations and support mixed-precision computing. Experimental results show that ConSmax achieves a minuscule power consumption of 0.2mW and an area of 0.0008mm^2 at 1250MHz working frequency in 16nm FinFET technology. For open-source contribution, we further implement our design with the OpenROAD toolchain under SkyWater's 130nm CMOS technology. The corresponding power is 2.69mW and the area is 0.007mm^2. ConSmax achieves 3.35x power savings and 2.75x area savings in 16nm technology, and 3.15x power savings and 4.14x area savings with the open-source EDA toolchain. In the meantime, it also maintains comparable accuracy on the GPT-2 model and the WikiText103 dataset. The project is available at https://github.com/ReaLLMASIC/ConSmax