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Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this…

Machine Learning · Computer Science 2019-09-26 Penghang Yin , Jiancheng Lyu , Shuai Zhang , Stanley Osher , Yingyong Qi , Jack Xin

Despite the achievements of recent binarization methods on reducing the performance degradation of Binary Neural Networks (BNNs), gradient mismatching caused by the Straight-Through-Estimator (STE) still dominates quantized networks. This…

Computer Vision and Pattern Recognition · Computer Science 2020-09-11 Junjie Liu , Dongchao Wen , Deyu Wang , Wei Tao , Tse-Wei Chen , Kinya Osa , Masami Kato

Network quantization aims at reducing bit-widths of weights and/or activations, particularly important for implementing deep neural networks with limited hardware resources. Most methods use the straight-through estimator (STE) to train…

Computer Vision and Pattern Recognition · Computer Science 2021-04-05 Junghyup Lee , Dohyung Kim , Bumsub Ham

Quantization has become a predominant approach for model compression, enabling deployment of large models trained on GPUs onto smaller form-factor devices for inference. Quantization-aware training (QAT) optimizes model parameters with…

Machine Learning · Computer Science 2022-12-13 Zheng Wang , Juncheng B Li , Shuhui Qu , Florian Metze , Emma Strubell

Quantized neural network training optimizes a discrete, non-differentiable objective. The straight-through estimator (STE) enables backpropagation through surrogate gradients and is widely used. While previous studies have primarily focused…

Machine Learning · Statistics 2025-10-14 Yuma Ichikawa , Shuhei Kashiwamura , Ayaka Sakata

Training quantized neural networks requires addressing the non-differentiable and discrete nature of the underlying optimization problem. To tackle this challenge, the straight-through estimator (STE) has become the most widely adopted…

Machine Learning · Computer Science 2025-05-26 Halyun Jeong , Jack Xin , Penghang Yin

Training quantised neural networks (QNNs) is a non-differentiable optimisation problem since weights and features are output by piecewise constant functions. The standard solution is to apply the straight-through estimator (STE), using…

Machine Learning · Computer Science 2022-03-23 Matteo Spallanzani , Gian Paolo Leonardi , Luca Benini

The discontinuous operations inherent in quantization and sparsification introduce a long-standing obstacle to backpropagation, particularly in ultra-low precision and sparse regimes. While the community has long viewed quantization as…

Machine Learning · Computer Science 2026-03-11 Chengxi Ye , Grace Chu , Yanfeng Liu , Yichi Zhang , Lukasz Lew , Li Zhang , Mark Sandler , Andrew Howard

Deep neural networks (DNNs) are quantized for efficient inference on resource-constrained platforms. However, training deep learning models with low-precision weights and activations involves a demanding optimization task, which calls for…

Machine Learning · Computer Science 2021-05-25 Ziang Long , Penghang Yin , Jack Xin

Neural network quantization aims to reduce the bit-widths of weights and activations, making it a critical technique for deploying deep neural networks on resource-constrained hardware. Most Quantization-Aware Training (QAT) methods rely on…

Machine Learning · Computer Science 2025-09-03 Kaiqi Zhao

The quantized neural networks (QNNs) can be useful for neural network acceleration and compression, but during the training process they pose a challenge: how to propagate the gradient of loss function through the graph flow with a…

Machine Learning · Computer Science 2020-03-26 Jun Chen , Yong Liu , Hao Zhang , Shengnan Hou , Jian Yang

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,…

Machine Learning · Computer Science 2019-01-08 Penghang Yin , Shuai Zhang , Jiancheng Lyu , Stanley Osher , Yingyong Qi , Jack Xin

Quantized neural networks can be viewed as a chain of noisy channels, where rounding in each layer reduces capacity as bit-width shrinks; the floating-point (FP) checkpoint sets the maximum input rate. We track capacity dynamics as the…

Machine Learning · Computer Science 2025-11-12 Sergey Salishev , Ian Akhremchik

Spiking and Quantized Neural Networks (NNs) are becoming exceedingly important for hyper-efficient implementations of Deep Learning (DL) algorithms. However, these networks face challenges when trained using error backpropagation, due to…

Machine Learning · Computer Science 2022-02-16 Jason K. Eshraghian , Corey Lammie , Mostafa Rahimi Azghadi , Wei D. Lu

Quantization-aware training comes with a fundamental challenge: the derivative of quantization functions such as rounding are zero almost everywhere and nonexistent elsewhere. Various differentiable approximations of quantization functions…

Machine Learning · Computer Science 2024-05-24 Matt Schoenbauer , Daniele Moro , Lukasz Lew , Andrew Howard

The Straight-Through Estimator (STE) is widely used for back-propagating gradients through the quantization function, but the STE technique lacks a complete theoretical understanding. We propose an alternative methodology called…

Machine Learning · Computer Science 2019-05-22 Zhi-Gang Liu , Matthew Mattina

We introduce a method to train Quantized Neural Networks (QNNs) --- neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At train-time the quantized weights and activations are used for computing…

Neural and Evolutionary Computing · Computer Science 2016-09-23 Itay Hubara , Matthieu Courbariaux , Daniel Soudry , Ran El-Yaniv , Yoshua Bengio

Stochastic neurons and hard non-linearities can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such…

Machine Learning · Computer Science 2013-08-16 Yoshua Bengio , Nicholas Léonard , Aaron Courville

We study the problem of training neural networks with quantized parameters. Learning low-precision quantized parameters by enabling computation of gradients via the Straight-Through Estimator (STE) can be challenging. While the STE enables…

Machine Learning · Computer Science 2025-10-29 Ningfeng Yang , Tor M. Aamodt

Training neural networks requires significant computational resources and energy. Methods like mixed-precision and quantization-aware training reduce bit usage, yet they still depend heavily on computationally expensive gradient-based…

Machine Learning · Computer Science 2025-09-30 Noa Cohen , Omkar Joglekar , Dotan Di Castro , Vladimir Tchuiev , Shir Kozlovsky , Michal Moshkovitz
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