# Reintroducing Straight-Through Estimators as Principled Methods for Stochastic Binary Networks

arXiv: https://arxiv.org/abs/2006.06880 · HTML: https://mlsanity.com/paper/2006.06880/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 15 of 15)

- [PV-Tuning: Beyond Straight-Through Estimation for Extreme LLM Compression](https://mlsanity.com/paper/2405.14852/) (2024)
- [Binarizing Split Learning for Data Privacy Enhancement and Computation Reduction](https://mlsanity.com/paper/2206.04864/) (2022)
- [Stochastic Approximation Beyond Gradient for Signal Processing and Machine Learning](https://mlsanity.com/paper/2302.11147/) (2023)
- [Improving Discrete Optimisation Via Decoupled Straight-Through Estimator](https://mlsanity.com/paper/2410.13331/) (2024)
- [Bias-Variance Tradeoffs in Single-Sample Binary Gradient Estimators](https://mlsanity.com/paper/2110.03549/) (2021)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)
- [AskewSGD : An Annealed interval-constrained Optimisation method to train Quantized Neural Networks](https://mlsanity.com/paper/2211.03741/) (2022)
- [Effective Neural Network L0 Regularization With BinMask](https://mlsanity.com/paper/2304.11237/) (2023)
- [SQUAT: Stateful Quantization-Aware Training in Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2404.19668/) (2024)
- [S3NN: Time Step Reduction of Spiking Surrogate Gradients for Training Energy Efficient Single-Step Spiking Neural Networks](https://mlsanity.com/paper/2201.10879/) (2022)
- [Bit-wise Training of Neural Network Weights](https://mlsanity.com/paper/2202.09571/) (2022)
- [Understanding weight-magnitude hyperparameters in training binary networks](https://mlsanity.com/paper/2303.02452/) (2023)
- [A Principled Bayesian Framework for Training Binary and Spiking Neural Networks](https://mlsanity.com/paper/2505.17962/) (2025)
- [Energy-Efficient Supervised Learning with a Binary Stochastic Forward-Forward Algorithm](https://mlsanity.com/paper/2507.06461/) (2025)
- [Stability and Generalization of Straight-Through Estimators for Training Two-Layer Quantized Neural Networks](https://mlsanity.com/paper/2609.06430/) (2026)

## Abstract (arXiv)

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 straight-through (ST) approaches, proposing a variety of ad-hoc rules for propagating gradients through non-differentiable activations and updating discrete weights. At the same time, ST methods can be truly derived as estimators in the stochastic binary network (SBN) model with Bernoulli weights. We advance these derivations to a more complete and systematic study. We analyze properties, estimation accuracy, obtain different forms of correct ST estimators for activations and weights, explain existing empirical approaches and their shortcomings, explain how latent weights arise from the mirror descent method when optimizing over probabilities. This allows to reintroduce ST methods, long known empirically, as sound approximations, apply them with clarity and develop further improvements.