# Custom Gradient Estimators are Straight-Through Estimators in Disguise

arXiv: https://arxiv.org/abs/2405.05171 · HTML: https://mlsanity.com/paper/2405.05171/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 63 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Bi-Real Net: Enhancing the Performance of 1-bit CNNs With Improved Representational Capability and Advanced Training Algorithm](https://mlsanity.com/paper/1808.00278/) (2018)
- [Forward and Backward Information Retention for Accurate Binary Neural Networks](https://mlsanity.com/paper/1909.10788/) (2019)
- [Learning to Quantize Deep Networks by Optimizing Quantization Intervals with Task Loss](https://mlsanity.com/paper/1808.05779/) (2018)
- [Quantization Networks](https://mlsanity.com/paper/1911.09464/) (2019)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [Overcoming Oscillations in Quantization-Aware Training](https://mlsanity.com/paper/2203.11086/) (2022)
- [Network Quantization with Element-wise Gradient Scaling](https://mlsanity.com/paper/2104.00903/) (2021)
- [Nonuniform-to-Uniform Quantization: Towards Accurate Quantization via Generalized Straight-Through Estimation](https://mlsanity.com/paper/2111.14826/) (2021)
- [Rotated Binary Neural Network](https://mlsanity.com/paper/2009.13055/) (2020)
- [Regularizing Activation Distribution for Training Binarized Deep Networks](https://mlsanity.com/paper/1904.02823/) (2019)
- [Latent Weights Do Not Exist: Rethinking Binarized Neural Network Optimization](https://mlsanity.com/paper/1906.02107/) (2019)
- [PokeBNN: A Binary Pursuit of Lightweight Accuracy](https://mlsanity.com/paper/2112.00133/) (2021)
- [How Do Adam and Training Strategies Help BNNs Optimization?](https://mlsanity.com/paper/2106.11309/) (2021)
- [A comprehensive review of Binary Neural Network](https://mlsanity.com/paper/2110.06804/) (2021)

## Built on by (most cited first, 6 of 6)

- [LittleBit: Ultra Low-Bit Quantization via Latent Factorization](https://mlsanity.com/paper/2506.13771/) (2025)
- [Improving the Straight-Through Estimator with Zeroth-Order Information](https://mlsanity.com/paper/2510.23926/) (2025)
- [Continuous Approximations for Improving Quantization Aware Training of LLMs](https://mlsanity.com/paper/2410.10849/) (2024)
- [Compact Rule-Based Classifier Learning via Gradient Descent](https://mlsanity.com/paper/2502.01375/) (2025)
- [Learning Binary Sampling Patterns for Single-Pixel Imaging using Bilevel Optimisation](https://mlsanity.com/paper/2508.19068/) (2025)
- [TinyNeRV: Compact Neural Video Representations via Capacity Scaling, Distillation, and Low-Precision Inference](https://mlsanity.com/paper/2604.09220/) (2026)

## Abstract (arXiv)

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 have been proposed to address this issue. In this paper, we prove that when the learning rate is sufficiently small, a large class of weight gradient estimators is equivalent with the straight through estimator (STE). Specifically, after swapping in the STE and adjusting both the weight initialization and the learning rate in SGD, the model will train in almost exactly the same way as it did with the original gradient estimator. Moreover, we show that for adaptive learning rate algorithms like Adam, the same result can be seen without any modifications to the weight initialization and learning rate. We experimentally show that these results hold for both a small convolutional model trained on the MNIST dataset and for a ResNet50 model trained on ImageNet.