# Up or Down? Adaptive Rounding for Post-Training Quantization

arXiv: https://arxiv.org/abs/2004.10568 · HTML: https://mlsanity.com/paper/2004.10568/

## Key facts

- Cited by 621 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2020.

## Built on by (most cited first, 30 of 621)

- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (2021)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [OmniQuant: Omnidirectionally Calibrated Quantization for Large Language Models](https://mlsanity.com/paper/2308.13137/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [A Survey on Model Compression for Large Language Models](https://mlsanity.com/paper/2308.07633/) (2023)
- [Extreme Compression of Large Language Models via Additive Quantization](https://mlsanity.com/paper/2401.06118/) (2024)
- [Implicit Diffusion Models for Continuous Super-Resolution](https://mlsanity.com/paper/2303.16491/) (2023)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [DuQuant: Distributing Outliers via Dual Transformation Makes Stronger Quantized LLMs](https://mlsanity.com/paper/2406.01721/) (2024)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)
- [A Fast Post-Training Pruning Framework for Transformers](https://mlsanity.com/paper/2204.09656/) (2022)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networks](https://mlsanity.com/paper/2103.00476/) (2021)
- [RepQ-ViT: Scale Reparameterization for Post-Training Quantization of Vision Transformers](https://mlsanity.com/paper/2212.08254/) (2022)
- [FlatQuant: Flatness Matters for LLM Quantization](https://mlsanity.com/paper/2410.09426/) (2024)

## Abstract (arXiv)

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.