Segment-Wise Accumulation: Low-Error Logarithmic Domain Computing for Efficient Large Language Model Inference

Logarithmic domain computing (LDC) has great potential for reducing quantization errors and computational complexity in Large Language Models (LLMs). While logarithmic multiplication can be efficiently implemented using fixed-point addition, the primary challenge in multiply-accumulate (MAC) operations is balancing the precision of logarithmic adders with their hardware overhead. Through a detailed analysis of the errors inherent in LDC-based LLMs, we propose segment-wise accumulation (SWA) to mitigate these errors. In addition, a processing element (PE) is introduced to enable SWA in the systolic array architecture. Compared with the accumulation scheme devised for enhancing floating-point computing, the proposed SWA facilitates the integration into existing accelerator architectures, resulting in lower hardware overhead. The experimental results show that SWA allows LDC under low-precision configurations to achieve remarkable accuracy in LLMs, demonstrating higher hardware efficiency than merely increasing the precision of individual computations. Our method, while maintaining a lower hardware overhead than traditional LDC, achieves more than 13.9% improvement in average accuracy across multiple zero-shot benchmarks in LLAMA-2-7B. Furthermore, compared to integer domain computing, a logarithmic processing element array based on the proposed SWA yields reductions of 24.6% in area and 42.3% in power, while achieving higher accuracy.