# Mixed Precision Low-bit Quantization of Neural Network Language Models for Speech Recognition

arXiv: https://arxiv.org/abs/2112.11438 · HTML: https://mlsanity.com/paper/2112.11438/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 97 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 30 of 54)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [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)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Listen, Attend and Spell](https://mlsanity.com/paper/1508.01211/) (2015)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [HAQ: Hardware-Aware Automated Quantization with Mixed Precision](https://mlsanity.com/paper/1811.08886/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [A Structured Self-attentive Sentence Embedding](https://mlsanity.com/paper/1703.03130/) (2017)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)

## Built on by (most cited first, 5 of 5)

- [Effective and Efficient Mixed Precision Quantization of Speech Foundation Models](https://mlsanity.com/paper/2501.03643/) (2025)
- [On Accelerating Edge AI: Optimizing Resource-Constrained Environments](https://mlsanity.com/paper/2501.15014/) (2025)
- [Verifiable and Energy Efficient Medical Image Analysis with Quantised Self-attentive Deep Neural Networks](https://mlsanity.com/paper/2209.15287/) (2022)
- [QuantuneV2: Compiler-Based Local Metric-Driven Mixed Precision Quantization for Practical Embedded AI Applications](https://mlsanity.com/paper/2501.07161/) (2025)
- [NanoQuant: Efficient Sub-1-Bit Quantization of Large Language Models](https://mlsanity.com/paper/2602.06694/) (2026)

## Abstract (arXiv)

State-of-the-art language models (LMs) represented by long-short term memory recurrent neural networks (LSTM-RNNs) and Transformers are becoming increasingly complex and expensive for practical applications. Low-bit neural network quantization provides a powerful solution to dramatically reduce their model size. Current quantization methods are based on uniform precision and fail to account for the varying performance sensitivity at different parts of LMs to quantization errors. To this end, novel mixed precision neural network LM quantization methods are proposed in this paper. The optimal local precision choices for LSTM-RNN and Transformer based neural LMs are automatically learned using three techniques. The first two approaches are based on quantization sensitivity metrics in the form of either the KL-divergence measured between full precision and quantized LMs, or Hessian trace weighted quantization perturbation that can be approximated efficiently using matrix free techniques. The third approach is based on mixed precision neural architecture search. In order to overcome the difficulty in using gradient descent methods to directly estimate discrete quantized weights, alternating direction methods of multipliers (ADMM) are used to efficiently train quantized LMs. Experiments were conducted on state-of-the-art LF-MMI CNN-TDNN systems featuring speed perturbation, i-Vector and learning hidden unit contribution (LHUC) based speaker adaptation on two tasks: Switchboard telephone speech and AMI meeting transcription. The proposed mixed precision quantization techniques achieved "lossless" quantization on both tasks, by producing model size compression ratios of up to approximately 16 times over the full precision LSTM and Transformer baseline LMs, while incurring no statistically significant word error rate increase.