# Post-training Quantization with Multiple Points: Mixed Precision without Mixed Precision

arXiv: https://arxiv.org/abs/2002.09049 · HTML: https://mlsanity.com/paper/2002.09049/

## Key facts

- Cited by 21 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 21 of 21)

- [IntraQ: Learning Synthetic Images with Intra-Class Heterogeneity for Zero-Shot Network Quantization](https://mlsanity.com/paper/2111.09136/) (2021)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [Lightweight Deep Learning for Resource-Constrained Environments: A Survey](https://mlsanity.com/paper/2404.07236/) (2024)
- [Data Quality-aware Mixed-precision Quantization via Hybrid Reinforcement Learning](https://mlsanity.com/paper/2302.04453/) (2023)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Confounding Tradeoffs for Neural Network Quantization](https://mlsanity.com/paper/2102.06366/) (2021)
- [Fine-grained Data Distribution Alignment for Post-Training Quantization](https://mlsanity.com/paper/2109.04186/) (2021)
- [A SAM-guided Two-stream Lightweight Model for Anomaly Detection](https://mlsanity.com/paper/2402.19145/) (2024)
- [Towards Accurate Binary Neural Networks via Modeling Contextual Dependencies](https://mlsanity.com/paper/2209.01404/) (2022)
- [Long-Range Zero-Shot Generative Deep Network Quantization](https://mlsanity.com/paper/2211.06816/) (2022)
- [MixQuant: Mixed Precision Quantization with a Bit-width Optimization Search](https://mlsanity.com/paper/2309.17341/) (2023)
- [Compute-Optimal Quantization-Aware Training](https://mlsanity.com/paper/2509.22935/) (2025)
- [Efficient Transformer-based 3D Object Detection with Dynamic Token Halting](https://mlsanity.com/paper/2303.05078/) (2023)
- [GREEN-CODE: Learning to Optimize Energy Efficiency in LLM-based Code Generation](https://mlsanity.com/paper/2501.11006/) (2025)
- [Augmenting Hessians with Inter-Layer Dependencies for Mixed-Precision Post-Training Quantization](https://mlsanity.com/paper/2306.04879/) (2023)
- [Order of Compression: A Systematic and Optimal Sequence to Combinationally Compress CNN](https://mlsanity.com/paper/2403.17447/) (2024)
- [FlexiQ: Adaptive Mixed-Precision Quantization for Latency/Accuracy Trade-Offs in Deep Neural Networks](https://mlsanity.com/paper/2510.02822/) (2025)
- [Energy awareness in low precision neural networks](https://mlsanity.com/paper/2202.02783/) (2022)
- [Assessing the Potential for Catastrophic Failure in Dynamic Post-Training Quantization](https://mlsanity.com/paper/2510.02457/) (2025)
- [Enhancing deep learning performance on burned area delineation from SPOT-6/7 imagery for emergency management](https://mlsanity.com/paper/2512.12056/) (2025)
- [Slithering Through Gaps: Capturing Discrete Isolated Modes via Logistic Bridging](https://mlsanity.com/paper/2604.10821/) (2026)

## Abstract (arXiv)

We consider the post-training quantization problem, which discretizes the weights of pre-trained deep neural networks without re-training the model. We propose multipoint quantization, a quantization method that approximates a full-precision weight vector using a linear combination of multiple vectors of low-bit numbers; this is in contrast to typical quantization methods that approximate each weight using a single low precision number. Computationally, we construct the multipoint quantization with an efficient greedy selection procedure, and adaptively decides the number of low precision points on each quantized weight vector based on the error of its output. This allows us to achieve higher precision levels for important weights that greatly influence the outputs, yielding an 'effect of mixed precision' but without physical mixed precision implementations (which requires specialized hardware accelerators). Empirically, our method can be implemented by common operands, bringing almost no memory and computation overhead. We show that our method outperforms a range of state-of-the-art methods on ImageNet classification and it can be generalized to more challenging tasks like PASCAL VOC object detection.