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ZipML: Training Linear Models with End-to-End Low Precision, and a Little Bit of Deep Learning
Hantian Zhang · Jerry Li · Kaan Kara · Dan Alistarh · Ji Liu · Ce Zhang

Tue Aug 08 11:06 PM -- 11:24 PM (PDT) @ C4.4

Recently there has been significant interest in training machine-learning models at low precision: by reducing precision, one can reduce computation and communication by one order of magnitude. We examine training at reduced precision, both from a theoretical and practical perspective, and ask: is it possible to train models at end-to-end low precision with provable guarantees? Can this lead to consistent order-of-magnitude speedups? We mainly focus on linear models, and the answer is yes for linear models. We develop a simple framework called ZipML based on one simple but novel strategy called double sampling. Our ZipML framework is able to execute training at low precision with no bias, guaranteeing convergence, whereas naive quantization would introduce significant bias. We validate our framework across a range of applications, and show that it enables an FPGA prototype that is up to 6.5× faster than an implementation using full 32-bit precision. We further develop a variance-optimal stochastic quantization strategy and show that it can make a significant difference in a variety of settings. When applied to linear models together with double sampling, we save up to another 1.7× in data movement compared with uniform quantization. When training deep networks with quantized models, we achieve higher accuracy than the state-of-the-art XNOR-Net.

Author Information

Hantian Zhang (ETH Zurich)
Jerry Li (MIT)
Kaan Kara (ETH Zurich)
Dan Alistarh (IST Austria & ETH Zurich)
Ji Liu (University of Rochester)

Ji Liu is an Assistant Professor in Computer Science, Electrical and Computer Engineering, and Goergen Institute for Data Science at University of Rochester (UR). He received his Ph.D. in Computer Science from University of Wisconsin-Madison. His research interests focus on distributed optimization and machine learning. He also has rich experiences in various data analytics applications in healthcare, bioinformatics, social network, computer vision, etc. His recent research focus is on asynchronous parallel optimization, sparse learning (compressed sensing) theory and algorithm, structural model estimation, online learning, abnormal event detection, feature / pattern extraction, etc. He published more than 40 papers in top CS journals and conferences including JMLR, SIOPT, TPAMI, TIP, TKDD, NIPS, ICML, UAI, SIGKDD, ICCV, CVPR, ECCV, AAAI, IJCAI, ACM MM, etc. He won the award of Best Paper honorable mention at SIGKDD 2010 and the award of Best Student Paper award at UAI 2015.

Ce Zhang (ETH Zurich)

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