Question: The straight through estimator is clearly defined in literature (see Bengio et al. 2013) as back propagation through a function as it would have been the identity function (thus gradient of 1 in the backwards path). However, in the manuscript any approximate gradient is defined as a STE gradient. Perhaps this misuse of terminology makes it extra difficult and confusing to understand the work? Especially since it is of theoretical nature. (“In this paper, we refer to the proxy of the gradient as the STE gradient.”)
Evidence: Quantization of the weights and the activations is a promising technique to save the memory and accelerate the inference speed in deep neural networks (DNNs) which have been getting wider and deeper in recent years. There are two main approaches of the quantization for DNNs (Krishnamoorthi ()): Post-training quantization (PTQ) and quantization-aware training (QAT). In the PTQ, the pre-trained networks are simply quantized without re-training the model. This approach allows us to achieve the nearly floating point accuracy at 8-bits, while below 8-bits, this results in significant accuracy degradation. Although there have been recent attempts to alleviate the accuracy degradation in PTQ;;;), the QAT, where the quantized weights and activations are trained (e.g.,;;), usually leads to better accuracy.
The difficulty in QAT is that the weights and the activations are discretized, and intrinsically nondifferentiable. If we take the derivatives forcibly, they either vanish or diverge. To avoid this problem, we replace them with the derivatives of some differentiable function in the backward pass only, called the Straight-Through Estimator (STE);). Since the replacement leads to bias, it is not always possible to learn the network successfully. However this approach can be applied to the low bits below 8-bits with tolerable accuracy degradation;;;).
Originally, STE was introduced as the replacement with the derivative of the identity function by. Later, the term "STE" has been extensively used as the replacement with various functions. In the binary network, studied the replacement with the derivative of sigmoid function as well as the original STE, and used the derivative of the identity function clipped in the region of |x| ≤ 1. In low-bits network, used the quantized gradient after the replacement with the identity function, and, and used the the derivative of the clipped Relu (cRelu) for leaning the step size.
Originally, STE was introduced as the replacement with the derivative of the identity function by Hinton et al. (2012). Later, the term ”STE” has been extensively used as the replacement with various functions. In the binary network, Bengio et al. (2013) studied the replacement with the derivative of sigmoid function as well as the original STE, and Hubara et al. (2017) used the derivative of the identity function clipped in the region of |x| ≤ 1. In low-bits network, Zhou et al. (2016) used the quantized gradient after the replacement with the identity function, and Choi et al. (2018), Esser et al. (2019), and Bhalgat et al. (2020) used the the derivative of the clipped Relu (cRelu) for leaning the step size.
Answer: Thank you very much for the comments.  To our knowledge, after the STE is defined as you mentioned in Bengio et al. 2013, in the low-bit network community the term STE is extensively used as the replacement with some differentiable function (see Hubara et al. 2017, Zhou et al. 2016, Esser et al. 2019, Yin et al. 2019) Actually, also in Bengio’s paper, they have studied the replacement with the derivative of the sigmoid. (They refer it  as "a variant".)  To make it clear for readers we have added the explanation about the term “STE” to the introduction as follows: ….Originally, STE was introduced as the replacement with the derivative of the identity function by Hinton et. al, 2012. Later, the term "STE" has been extensively used as the replacement with various functions. …