Reducing bit-widths of activations and weights of deep networks makes it efficient to compute and store them in memory, which is crucial in their deployments to resourcelimited devices, such as mobile phones. However, decreasing bit-widths with quantization generally yields drastically degraded accuracy. To tackle this problem, we propose to learn to quantize activations and weights via a trainable quantizer that transforms and discretizes them. Specifically, we parameterize the quantization intervals and obtain their optimal values by directly minimizing the task loss of the network. This quantization-interval-learning (QIL) allows the quantized networks to maintain the accuracy of the fullprecision (32-bit) networks with bit-width as low as 4-bit and minimize the accuracy degeneration with further bitwidth reduction (i.e., 3 and 2-bit). Moreover, our quantizer can be trained on a heterogeneous dataset, and thus can be used to quantize pretrained networks without access to their training data. We demonstrate the effectiveness of our trainable quantizer on ImageNet dataset with various network architectures such as ResNet-18, -34 and AlexNet, on which it outperforms existing methods to achieve the stateof-the-art accuracy.

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[1] It has been suggested that drift loss to the magnetopause can be one of the major loss mechanisms contributing to relativistic electron flux dropouts. In this study, we examine details of relativistic electrons' drift physics to determine the extent to which the drift loss through the magnetopause is important to the total loss of the outer radiation belt. We have numerically computed drift paths of relativistic electrons' guiding center for various pitch angles, various measurement positions, and different solar wind conditions using the Tsyganenko T02 model. We specifically demonstrate how the drift loss effect depends on these various parameters. Most importantly, we present various estimates of relative changes of the omnidirectional flux of 1 MeV electrons between two different solar wind conditions based on a simple form of the directional flux function. For a change of the dynamic pressure from 4 nPa to 10 nPa with a fixed IMF B Z = 0 nT, our estimate indicates that after this increase in pressure, the equatorial omnidirectional flux at midnight near geosynchronous altitude decreases by $56 to $97%, depending on the specific pitch angle dependence of the directional flux. The effect rapidly decreases at regions earthward of geosynchronous orbit and shows a general trend of decrease away from midnight. For a change of the IMF B Z from 0 nT to À15 nT with a fixed dynamic pressure of 4 nPa, the relative decrease of the omnidirectional flux at geosynchronous altitude on the nightside is much smaller than that for the pressure increase, but its effect becomes substantial only beyond geosynchronous orbit. Possibilities exist that our results may change to some extent for a different magnetospheric model than the one used here.