# Finding the Task-Optimal Low-Bit Sub-Distribution in Deep Neural Networks

arXiv: https://arxiv.org/abs/2112.15139 · HTML: https://mlsanity.com/paper/2112.15139/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 111 references that are in the map.
- First posted on arXiv 30 Dec 2021.

## Builds on (most cited first, 30 of 63)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)

## Built on by (most cited first, 9 of 9)

- [DreamLLM: Synergistic Multimodal Comprehension and Creation](https://mlsanity.com/paper/2309.11499/) (2023)
- [DreamVLA: A Vision-Language-Action Model Dreamed with Comprehensive World Knowledge](https://mlsanity.com/paper/2507.04447/) (2025)
- [ShapeLLM: Universal 3D Object Understanding for Embodied Interaction](https://mlsanity.com/paper/2402.17766/) (2024)
- [Compressing LLMs: The Truth is Rarely Pure and Never Simple](https://mlsanity.com/paper/2310.01382/) (2023)
- [PointDistiller: Structured Knowledge Distillation Towards Efficient and Compact 3D Detection](https://mlsanity.com/paper/2205.11098/) (2022)
- [VPP: Efficient Conditional 3D Generation via Voxel-Point Progressive Representation](https://mlsanity.com/paper/2307.16605/) (2023)
- [Stochastic Weight Sharing for Bayesian Neural Networks](https://mlsanity.com/paper/2505.17856/) (2025)
- [Online Resource Allocation for Edge Intelligence with Colocated Model Retraining and Inference](https://mlsanity.com/paper/2405.16029/) (2024)
- [SQS: Bayesian DNN Compression through Sparse Quantized Sub-distributions](https://mlsanity.com/paper/2510.08999/) (2025)

## Abstract (arXiv)

Quantized neural networks typically require smaller memory footprints and lower computation complexity, which is crucial for efficient deployment. However, quantization inevitably leads to a distribution divergence from the original network, which generally degrades the performance. To tackle this issue, massive efforts have been made, but most existing approaches lack statistical considerations and depend on several manual configurations. In this paper, we present an adaptive-mapping quantization method to learn an optimal latent sub-distribution that is inherent within models and smoothly approximated with a concrete Gaussian Mixture (GM). In particular, the network weights are projected in compliance with the GM-approximated sub-distribution. This sub-distribution evolves along with the weight update in a co-tuning schema guided by the direct task-objective optimization. Sufficient experiments on image classification and object detection over various modern architectures demonstrate the effectiveness, generalization property, and transferability of the proposed method. Besides, an efficient deployment flow for the mobile CPU is developed, achieving up to 7.46× inference acceleration on an octa-core ARM CPU. Our codes have been publicly released at urlhttps://github.com/RunpeiDong/DGMS.