LNS-Madam: Low-Precision Training in Logarithmic Number System Using Multiplicative Weight Update

Representing deep neural networks (DNNs) in low-precision is a promising approach to enable efficient acceleration and memory reduction. Previous methods that train DNNs in low-precision typically keep a copy of weights in high-precision during the weight updates. Directly training with low-precisio...

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Bibliographic Details
Published in:IEEE transactions on computers 2022-12, Vol.71 (12), p.3179-3190
Main Authors: Zhao, Jiawei, Dai, Steve, Venkatesan, Rangharajan, Zimmer, Brian, Ali, Mustafa, Liu, Ming-Yu, Khailany, Brucek, Dally, William J., Anandkumar, Anima
Format: Article
Language:English
Subjects:
Algorithms
Arithmetic
Artificial neural networks
Computer vision
Costs
Energy consumption
Hardware
hardware acceleration
Logarithms
Machine learning
Natural language (computers)
Neural networks
Number systems
optimization
Quantization (signal)
Table lookup
Training
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Summary:Representing deep neural networks (DNNs) in low-precision is a promising approach to enable efficient acceleration and memory reduction. Previous methods that train DNNs in low-precision typically keep a copy of weights in high-precision during the weight updates. Directly training with low-precision weights leads to accuracy degradation due to complex interactions between the low-precision number systems and the learning algorithms. To address this issue, we develop a co-designed low-precision training framework, termed LNS-Madam, in which we jointly design a logarithmic number system (LNS) and a multiplicative weight update algorithm (Madam). We prove that LNS-Madam results in low quantization error during weight updates, leading to stable performance even if the precision is limited. We further propose a hardware design of LNS-Madam that resolves practical challenges in implementing an efficient datapath for LNS computations. Our implementation effectively reduces energy overhead incurred by LNS-to-integer conversion and partial sum accumulation. Experimental results show that LNS-Madam achieves comparable accuracy to full-precision counterparts with only 8 bits on popular computer vision and natural language tasks. Compared to FP32 and FP8, LNS-Madam reduces the energy consumption by over 90% and 55%, respectively.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2022.3202747