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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 deep neural networks with Rectified Linear Unit (ReLU) activation function using gradient descent and stochastic gradient descent. In particular, we study the binary classification problem and show that for…

Machine Learning · Computer Science 2018-12-31 Difan Zou , Yuan Cao , Dongruo Zhou , Quanquan Gu

Stochastic neurons 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 stochastic neurons, i.e.,…

Machine Learning · Computer Science 2013-05-15 Yoshua Bengio

In neural networks with binary activations and or binary weights the training by gradient descent is complicated as the model has piecewise constant response. We consider stochastic binary networks, obtained by adding noises in front of…

Machine Learning · Statistics 2020-11-05 Alexander Shekhovtsov , Viktor Yanush , Boris Flach

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

Training neural networks with binary weights and activations is a challenging problem due to the lack of gradients and difficulty of optimization over discrete weights. Many successful experimental results have been achieved with empirical…

Machine Learning · Statistics 2021-10-20 Alexander Shekhovtsov , Viktor Yanush

Quantization reduces computation costs of neural networks but suffers from performance degeneration. Is this accuracy drop due to the reduced capacity, or inefficient training during the quantization procedure? After looking into the…

Computer Vision and Pattern Recognition · Computer Science 2019-12-24 Qing Jin , Linjie Yang , Zhenyu Liao

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

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

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be…

Artificial Intelligence · Computer Science 2023-07-11 Zhun Yang , Joohyung Lee , Chiyoun Park

To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the…

Machine Learning · Computer Science 2019-03-06 Yu Bai , Yu-Xiang Wang , Edo Liberty

Despite significant work on low-bit quantization-aware training (QAT), there is still an accuracy gap between such techniques and native training. To address this, we introduce CAGE (Curvature-Aware Gradient Estimation), a new QAT method…

Machine Learning · Computer Science 2025-11-11 Soroush Tabesh , Mher Safaryan , Andrei Panferov , Alexandra Volkova , Dan Alistarh

Neural network training relies on gradient computation through backpropagation, yet memory requirements for storing layer activations present significant scalability challenges. We present the first adaptation of control-theoretic matrix…

Machine Learning · Computer Science 2025-10-02 Harbir Antil , Deepanshu Verma

Straight-through estimator (STE), which enables the gradient flow over the non-differentiable function via approximation, has been favored in studies related to quantization-aware training (QAT). However, STE incurs unstable convergence…

Machine Learning · Computer Science 2023-07-04 Juncheol Shin , Junhyuk So , Sein Park , Seungyeop Kang , Sungjoo Yoo , Eunhyeok Park

Gradient-based neural network training traditionally enforces symmetry between forward and backward propagation, requiring activation functions to be differentiable (or sub-differentiable) and strictly monotonic in certain regions to…

Neural and Evolutionary Computing · Computer Science 2025-09-10 Luigi Troiano , Francesco Gissi , Vincenzo Benedetto , Genny Tortora

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

Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for…

Machine Learning · Statistics 2020-01-16 Dominic Kafka , Daniel N. Wilke

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common…

Machine Learning · Statistics 2024-04-16 Jiaxin Shi , Yuhao Zhou , Jessica Hwang , Michalis K. Titsias , Lester Mackey

Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few…

Machine Learning · Computer Science 2022-02-04 Georgii Novikov , Daniel Bershatsky , Julia Gusak , Alex Shonenkov , Denis Dimitrov , Ivan Oseledets

One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies…

Machine Learning · Computer Science 2019-02-06 Simon S. Du , Xiyu Zhai , Barnabas Poczos , Aarti Singh