# Binary Ensemble Neural Network: More Bits per Network or More Networks per Bit?

arXiv: https://arxiv.org/abs/1806.07550 · HTML: https://mlsanity.com/paper/1806.07550/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2018.

## Built on by (most cited first, 30 of 39)

- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy](https://mlsanity.com/paper/2310.01334/) (2023)
- [Nonuniform-to-Uniform Quantization: Towards Accurate Quantization via Generalized Straight-Through Estimation](https://mlsanity.com/paper/2111.14826/) (2021)
- [Why So Pessimistic? Estimating Uncertainties for Offline RL through Ensembles, and Why Their Independence Matters](https://mlsanity.com/paper/2205.13703/) (2022)
- [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)
- [BiViT: Extremely Compressed Binary Vision Transformer](https://mlsanity.com/paper/2211.07091/) (2022)
- [SiMaN: Sign-to-Magnitude Network Binarization](https://mlsanity.com/paper/2102.07981/) (2021)
- [Lightweight Pixel Difference Networks for Efficient Visual Representation Learning](https://mlsanity.com/paper/2402.00422/) (2024)
- [BEBERT: Efficient and Robust Binary Ensemble BERT](https://mlsanity.com/paper/2210.15976/) (2022)
- [Low-Precision Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2206.09909/) (2022)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [REx: Data-Free Residual Quantization Error Expansion](https://mlsanity.com/paper/2203.14645/) (2022)
- [Self-Distribution Binary Neural Networks](https://mlsanity.com/paper/2103.02394/) (2021)
- [BCNN: Binary Complex Neural Network](https://mlsanity.com/paper/2104.10044/) (2021)
- [Improving Binary Neural Networks through Fully Utilizing Latent Weights](https://mlsanity.com/paper/2110.05850/) (2021)
- [BNAS v2: Learning Architectures for Binary Networks with Empirical Improvements](https://mlsanity.com/paper/2110.08562/) (2021)
- [Binarized ResNet: Enabling Robust Automatic Modulation Classification at the resource-constrained Edge](https://mlsanity.com/paper/2110.14357/) (2021)
- [Compacting Binary Neural Networks by Sparse Kernel Selection](https://mlsanity.com/paper/2303.14470/) (2023)
- [Realizing Neural Decoder at the Edge with Ensembled BNN](https://mlsanity.com/paper/2106.09925/) (2021)
- [Soft Threshold Ternary Networks](https://mlsanity.com/paper/2204.01234/) (2022)
- [Binarizing by Classification: Is soft function really necessary?](https://mlsanity.com/paper/2205.07433/) (2022)
- [E2FIF: Push the limit of Binarized Deep Imagery Super-resolution using End-to-end Full-precision Information Flow](https://mlsanity.com/paper/2207.06893/) (2022)
- [RepBNN: towards a precise Binary Neural Network with Enhanced Feature Map via Repeating](https://mlsanity.com/paper/2207.09049/) (2022)
- [Stabilizing Quantization-Aware Training by Implicit-Regularization on Hessian Matrix](https://mlsanity.com/paper/2503.11159/) (2025)
- [Towards Efficient and Accurate Spiking Neural Networks via Adaptive Bit Allocation](https://mlsanity.com/paper/2506.23717/) (2025)
- [PAC-Bayesian Learning of Aggregated Binary Activated Neural Networks with Probabilities over Representations](https://mlsanity.com/paper/2110.15137/) (2021)
- [How to train accurate BNNs for embedded systems?](https://mlsanity.com/paper/2206.12322/) (2022)
- [Transfer learning for ensembles: reducing computation time and keeping the diversity](https://mlsanity.com/paper/2206.13116/) (2022)
- [In-Distribution Consistency Regularization Improves the Generalization of Quantization-Aware Training](https://mlsanity.com/paper/2402.13497/) (2024)

## Abstract (arXiv)

Binary neural networks (BNN) have been studied extensively since they run dramatically faster at lower memory and power consumption than floating-point networks, thanks to the efficiency of bit operations. However, contemporary BNNs whose weights and activations are both single bits suffer from severe accuracy degradation. To understand why, we investigate the representation ability, speed and bias/variance of BNNs through extensive experiments. We conclude that the error of BNNs is predominantly caused by the intrinsic instability (training time) and non-robustness (train & test time). Inspired by this investigation, we propose the Binary Ensemble Neural Network (BENN) which leverages ensemble methods to improve the performance of BNNs with limited efficiency cost. While ensemble techniques have been broadly believed to be only marginally helpful for strong classifiers such as deep neural networks, our analyses and experiments show that they are naturally a perfect fit to boost BNNs. We find that our BENN, which is faster and much more robust than state-of-the-art binary networks, can even surpass the accuracy of the full-precision floating number network with the same architecture.