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Register a new userCluster-Promoting Quantization with Bit-Drop for Minimizing Network Quantization Loss
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Jung Hyun Lee
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Network quantization, which aims to reduce the bit-lengths of the network weights and activations, has emerged for their deployments to resource-limited devices. Although recent studies have successfully discretized a full-precision network, they still incur large quantization errors after training, thus giving rise to a significant performance gap between a full-precision network and its quantized counterpart. In this work, we propose a novel quantization method for neural networks, Cluster-Promoting Quantization (CPQ) that finds the optimal quantization grids while naturally encouraging the underlying full-precision weights to gather around those quantization grids cohesively during training. This property of CPQ is thanks to our two main ingredients that enable differentiable quantization: i) the use of the categorical distribution designed by a specific probabilistic parametrization in the forward pass and ii) our proposed multi-class straight-through estimator (STE) in the backward pass. Since our second component, multi-class STE, is intrinsically biased, we additionally propose a new bit-drop technique, DropBits, that revises the standard dropout regularization to randomly drop bits instead of neurons. As a natural extension of DropBits, we further introduce the way of learning heterogeneous quantization levels to find proper bit-length for each layer by imposing an additional regularization on DropBits. We experimentally validate our method on various benchmark datasets and network architectures, and also support a new hypothesis for quantization: learning heterogeneous quantization levels outperforms the case using the same but fixed quantization levels from scratch.
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Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. It is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the continuous parameters (unconstrained) as the dual of the quantized ones, we introduce a Mirror Descent (MD) framework for NN quantization. Specifically, we provide conditions on the projections (i.e., mapping from continuous to quantized ones) which would enable us to derive valid mirror maps and in turn the respective MD updates. Furthermore, we present a numerically stable implementation of MD that requires storing an additional set of auxiliary variables (unconstrained), and show that it is strikingly analogous to the Straight Through Estimator (STE) based method which is typically viewed as a trick to avoid vanishing gradients issue. Our experiments on CIFAR-10/100, TinyImageNet, and ImageNet classification datasets with VGG-16, ResNet-18, and MobileNetV2 architectures show that our MD variants obtain quantized networks with state-of-the-art performance. Code is available at https://github.com/kartikgupta-at-anu/md-bnn.
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