Efficient Precision-Adjustable Architecture for Softmax Function in Deep Learning
Abstract
The softmax function has been widely used in deep neural networks (DNNs), and studies on efficient hardware accelerators for DNN have also attracted tremendous attention. However, it is very challenging to design efficient hardware architectures for softmax because of the expensive exponentiation and division calculations in it. In this brief, the softmax function is firstly simplified by exploring algorithmic strength reductions. Afterwards, a hardware-friendly and precision-adjustable calculation method for softmax is proposed, which can meet different precision requirements in various deep learning (DL) tasks. Based on the above innovations, an efficient architecture for softmax is presented. By tuning the parameter P , the system accuracy and complexity can be adjusted dynamically to achieve a good tradeoff between them. The proposed design is coded using hardware description language (HDL) and evaluated on two platforms, Xilinx Zynq-7000 ZC706 development board and TSMC 28-nm CMOS technology, respectively. Hardware implementation results show that our architecture significantly outperforms other works in speed and area, and that by adjusting P , the accuracy can be further increased with little hardware overhead.
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Various approximation methods that hold floating-point arithmetic lower certain computational costs but cannot meet the demands of integer arithmetic.
“In addition, various approximation methods that hold floating-point arithmetic are presented [36, 50]; while they lower certain computational costs, they cannot meet the demands of integer arithmetic.”
From I-ViT: Integer-only Quantization for Efficient Vision Transformer Inference (2023) · cites this paper as [50]
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Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers
Stevens, J. R., Venkatesan, R., Dai, S., Khailany, B., & Raghunathan, A. (2021) · 2021 58th ACM/IEEE Design Automation Conference (DAC) · doi:10.1109/dac18074.2021.9586134 · Cited by 148 · see citing works
I-ViT: Integer-only Quantization for Efficient Vision Transformer Inference
Li, Z., & Gu, Q. (2023) · 2023 IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv51070.2023.01565 · Cited by 141 · see citing works
“In addition, various approximation methods that hold floating-point arithmetic are presented [20, 26]; while they lower certain computational costs, they cannot meet the demands of integer arithmetic.”
Method
- Authors
- Zhu, D., Lu, S., Wang, M., Lin, J., & Wang, Z.
- Affiliations
- Nanjing University (CN)
- Venue
- IEEE Transactions on Circuits and Systems II: Express Briefs
- Published
- 2020-12
- Volume
- 67
- Issue
- 12
- Pages
- 3382-3386
- ISSN
- 1549-7747 (ISSN-L)
- 1558-3791
- OpenAlex
- W3036061420
- Cited by
- 115
- References
- 0
- Citations by year
- 2026: 12 · 2025: 33 · 2024: 26 · 2023: 25 · 2022: 12 · 2021: 5 · 2020: 2
- FWCI
- 5.45
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Circuits & Systems II Express Briefs (publishedVersion)
- Funders
- National Natural Science Foundation of China (61774082, 61604068)
- Fundamental Research Funds for the Central Universities (021014380065)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Low-power high-performance VLSI design
- Keywords
- softmax, hardware accelerators, accuracy-complexity trade-off, deep neural network hardware, FPGA implementation, CMOS implementation
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