We consider the post-training quantization problem, which discretizes the weights of pre-trained deep neural networks without re-training the model. We propose multipoint quantization, a quantization method that approximates a full-precision weight vector using a linear combination of multiple vectors of low-bit numbers; this is in contrast to typical quantization methods that approximate each weight using a single low precision number. Computationally, we construct the multipoint quantization with an efficient greedy selection procedure, and adaptively decides the number of low precision points on each quantized weight vector based on the error of its output. This allows us to achieve higher precision levels for important weights that greatly influence the outputs, yielding an 'effect of mixed precision' but without physical mixed precision implementations (which requires specialized hardware accelerators). Empirically, our method can be implemented by common operands, bringing almost no memory and computation overhead. We show that our method outperforms a range of state-of-the-art methods on ImageNet classification and it can be generalized to more challenging tasks like PASCAL VOC object detection.
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BinaryRelax: A Relaxation Approach for Training Deep Neural Networks with Quantized Weights
We propose BinaryRelax, a simple two-phase algorithm, for training deep neural networks with quantized
weights. The set constraint that characterizes the quantization of weights is not imposed until
the late stage of training, and a sequence of pseudo quantized weights is maintained. Specifically, we
relax the hard constraint into a continuous regularizer via Moreau envelope, which turns out to be
the squared Euclidean distance to the set of quantized weights. The pseudo quantized weights are
obtained by linearly interpolating between the float weights and their quantizations. A continuation
strategy is adopted to push the weights towards the quantized state by gradually increasing the
regularization parameter. In the second phase, exact quantization scheme with a small learning rate
is invoked to guarantee fully quantized weights. We test BinaryRelax on the benchmark CIFAR
and ImageNet color image datasets to demonstrate the superiority of the relaxed quantization approach
and the improved accuracy over the state-of-the-art training methods. Finally, we prove the
convergence of BinaryRelax under an approximate orthogonality condition.
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- Award ID(s):
- 1632935
- NSF-PAR ID:
- 10112539
- Date Published:
- Journal Name:
- SIAM journal on imaging sciences
- Volume:
- 11
- Issue:
- 4
- ISSN:
- 1936-4954
- Page Range / eLocation ID:
- 2205-2223
- 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/DOI:10.1137/18M1166134
