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Dimension-Free Bounds for Low-Precision Training
Zheng Li · Christopher De Sa

Wed Dec 11 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #159
Low-precision training is a promising way of decreasing the time and energy cost of training machine learning models. Previous work has analyzed low-precision training algorithms, such as low-precision stochastic gradient descent, and derived theoretical bounds on their convergence rates. These bounds tend to depend on the dimension of the model $d$ in that the number of bits needed to achieve a particular error bound increases as $d$ increases. In this paper, we derive new bounds for low-precision training algorithms that do not contain the dimension $d$ , which lets us better understand what affects the convergence of these algorithms as parameters scale. Our methods also generalize naturally to let us prove new convergence bounds on low-precision training with other quantization schemes, such as low-precision floating-point computation and logarithmic quantization.

Author Information

Zheng Li (Tsinghua University)
Christopher De Sa (Cornell)

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