# FP=xINT:Representing Neural Networks via Low-Bit Series Basis Functions

arXiv: https://arxiv.org/abs/2412.06865 · HTML: https://mlsanity.com/paper/2412.06865/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [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)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [HAWQ-V2: Hessian Aware trace-Weighted Quantization of Neural Networks](https://mlsanity.com/paper/1911.03852/) (2019)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [QDrop: Randomly Dropping Quantization for Extremely Low-bit Post-Training Quantization](https://mlsanity.com/paper/2203.05740/) (2022)
- [Loss Aware Post-training Quantization](https://mlsanity.com/paper/1911.07190/) (2019)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)
- [PD-Quant: Post-Training Quantization based on Prediction Difference Metric](https://mlsanity.com/paper/2212.07048/) (2022)
- [Post-training 4-bit quantization of convolution networks for rapid-deployment](https://mlsanity.com/paper/1810.05723/) (2018)

## Built on by (most cited first, 4 of 4)

- [DVP-MVS: Synergize Depth-Edge and Visibility Prior for Multi-View Stereo](https://mlsanity.com/paper/2412.11578/) (2024)
- [SED-MVS: Segmentation-Driven and Edge-Aligned Deformation Multi-View Stereo with Depth Restoration and Occlusion Constraint](https://mlsanity.com/paper/2503.13721/) (2025)
- [A General Error-Theoretical Analysis Framework for Constructing Compression Strategies](https://mlsanity.com/paper/2502.15802/) (2025)
- [Rethinking Parameter Sharing as Graph Coloring for Structured Compression](https://mlsanity.com/paper/2511.06786/) (2025)

## Abstract (arXiv)

Post-Training Quantization (PTQ) converts pre-trained Full-Precision (FP) models into quantized versions without training. While existing methods reduce size and computational costs, they also significantly degrade performance and quantization efficiency at extremely low settings due to quantization noise. We introduce a deep model series expansion framework to address this issue, enabling rapid and accurate approximation of unquantized models without calibration sets or fine-tuning. This is the first use of series expansion for neural network quantization. Specifically, our method expands the FP model into multiple low-bit basis models. To ensure accurate quantization, we develop low-bit basis model expansions at different granularities (tensor, layer, model), and theoretically confirm their convergence to the dense model, thus restoring FP model accuracy. Additionally, we design AbelianAdd/Mul operations between isomorphic models in the low-bit expansion, forming an Abelian group to ensure operation parallelism and commutativity. The experiments show that our algorithm achieves state-of-the-art performance in low-bit settings; for example, 4-bit quantization of ResNet-50 surpasses the original accuracy, reaching 77.03%. The code will be made public.