Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full-precision counterparts. To maintain the same performance level especially at low bit-widths, QDNNs must be retrained. Their training involves piece-wise constant activation functions and discrete weights; hence, mathematical challenges arise. We introduce the notion of coarse gradient and propose the blended coarse gradient descent (BCGD) algorithm, for training fully quantized neural networks. Coarse gradient is generally not a gradient of any function but an artificial ascent direction. The weight update of BCGD goes by coarse gradient correction of a weighted average of the full-precision weights and their quantization (the so-called blending), which yields sufficient descent in the objective value and thus accelerates the training. Our experiments demonstrate that this simple blending technique is very effective for quantization at extremely low bit-width such as binarization. In full quantization of ResNet-18 for ImageNet classification task, BCGD gives 64.36% top-1 accuracy with binary weights across all layers and 4-bit adaptive activation. If the weights in the first and last layers are kept in full precision, this number increases to 65.46%. As theoretical justification, we show convergence analysis of coarse gradient descent for a two-linear-layer neural network model with Gaussian input data and prove that the expected coarse gradient correlates positively with the underlying true gradient.
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Quantization and Training of Low Bit-Width Convolutional Neural Networks for Object Detection
We present LBW-Net, an efficient optimization based method for quantization and
training of the low bit-width convolutional neural networks (CNNs). Specifically, we quantize
the weights to zero or powers of 2 by minimizing the Euclidean distance between
full-precision weights and quantized weights during back-propagation (weight learning).
We characterize the combinatorial nature of the low bit-width quantization problem. For
2-bit (ternary) CNNs, the quantization of N weights can be done by an exact formula
in O(N log N) complexity. When the bit-width is 3 and above, we further propose a
semi-analytical thresholding scheme with a single free parameter for quantization that is
computationally inexpensive. The free parameter is further determined by network retraining
and object detection tests. The LBW-Net has several desirable advantages over
full-precision CNNs, including considerable memory savings, energy efficiency, and faster
deployment. Our experiments on PASCAL VOC dataset show that compared with its
32-bit floating-point counterpart, the performance of the 6-bit LBW-Net is nearly lossless
in the object detection tasks, and can even do better in real world visual scenes, while
empirically enjoying more than 4× faster deployment.
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- Award ID(s):
- 1632935
- NSF-PAR ID:
- 10112553
- Date Published:
- Journal Name:
- Journal of Computational Mathematics
- Volume:
- 37
- Issue:
- 3
- ISSN:
- 0254-9409
- Page Range / eLocation ID:
- 349-359
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.4208/jcm.1803-m2017-0301.
