# F8Net: Fixed-Point 8-bit Only Multiplication for Network Quantization

arXiv: https://arxiv.org/abs/2202.05239 · HTML: https://mlsanity.com/paper/2202.05239/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 86 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 30 of 59)

- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [A White Paper on Neural Network Quantization](https://mlsanity.com/paper/2106.08295/) (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)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Pruning and Quantization for Deep Neural Network Acceleration: A Survey](https://mlsanity.com/paper/2101.09671/) (2021)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [Differentiable Soft Quantization: Bridging Full-Precision and Low-Bit Neural Networks](https://mlsanity.com/paper/1908.05033/) (2019)
- [Incremental Network Quantization: Towards Lossless CNNs with Low-Precision Weights](https://mlsanity.com/paper/1702.03044/) (2017)
- [Trained Ternary Quantization](https://mlsanity.com/paper/1612.01064/) (2016)
- [Low-bit Quantization of Neural Networks for Efficient Inference](https://mlsanity.com/paper/1902.06822/) (2019)
- [LSQ+: Improving low-bit quantization through learnable offsets and better initialization](https://mlsanity.com/paper/2004.09576/) (2020)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)
- [Fixed Point Quantization of Deep Convolutional Networks](https://mlsanity.com/paper/1511.06393/) (2015)
- [Deep Learning with Low Precision by Half-wave Gaussian Quantization](https://mlsanity.com/paper/1702.00953/) (2017)
- [Degree-Quant: Quantization-Aware Training for Graph Neural Networks](https://mlsanity.com/paper/2008.05000/) (2020)
- [Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming](https://mlsanity.com/paper/2006.10518/) (2020)

## Built on by (most cited first, 28 of 28)

- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [Rethinking Vision Transformers for MobileNet Size and Speed](https://mlsanity.com/paper/2212.08059/) (2022)
- [Outlier Suppression+: Accurate quantization of large language models by equivalent and optimal shifting and scaling](https://mlsanity.com/paper/2304.09145/) (2023)
- [BitsFusion: 1.99 bits Weight Quantization of Diffusion Model](https://mlsanity.com/paper/2406.04333/) (2024)
- [A Survey on Deep Learning Hardware Accelerators for Heterogeneous HPC Platforms](https://mlsanity.com/paper/2306.15552/) (2023)
- [Enhancing Computation Efficiency in Large Language Models through Weight and Activation Quantization](https://mlsanity.com/paper/2311.05161/) (2023)
- [Oaken: Fast and Efficient LLM Serving with Online-Offline Hybrid KV Cache Quantization](https://mlsanity.com/paper/2503.18599/) (2025)
- [To update or not to update? Neurons at equilibrium in deep models](https://mlsanity.com/paper/2207.09455/) (2022)
- [Is Integer Arithmetic Enough for Deep Learning Training?](https://mlsanity.com/paper/2207.08822/) (2022)
- [Low-bit Model Quantization for Deep Neural Networks: A Survey](https://mlsanity.com/paper/2505.05530/) (2025)
- [Designing Large Foundation Models for Efficient Training and Inference: A Survey](https://mlsanity.com/paper/2409.01990/) (2024)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [Efficient Deployment of Spiking Neural Networks on SpiNNaker2 for DVS Gesture Recognition Using Neuromorphic Intermediate Representation](https://mlsanity.com/paper/2504.06748/) (2025)
- [M4BRAM: Mixed-Precision Matrix-Matrix Multiplication in FPGA Block RAMs](https://mlsanity.com/paper/2311.02758/) (2023)
- [Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approach](https://mlsanity.com/paper/2411.05873/) (2024)
- [SoD2: Statically Optimizing Dynamic Deep Neural Network](https://mlsanity.com/paper/2403.00176/) (2024)
- [On Expressive Power of Quantized Neural Networks under Fixed-Point Arithmetic](https://mlsanity.com/paper/2409.00297/) (2024)
- [BOLD: Boolean Logic Deep Learning](https://mlsanity.com/paper/2405.16339/) (2024)
- [Boolean Variation and Boolean Logic BackPropagation](https://mlsanity.com/paper/2311.07427/) (2023)
- [MCU-MixQ: A HW/SW Co-optimized Mixed-precision Neural Network Design Framework for MCUs](https://mlsanity.com/paper/2407.18267/) (2024)
- [Ultra-low Precision Multiplication-free Training for Deep Neural Networks](https://mlsanity.com/paper/2302.14458/) (2023)
- [Quantized Distillation: Optimizing Driver Activity Recognition Models for Resource-Constrained Environments](https://mlsanity.com/paper/2311.05970/) (2023)
- [FPGA-based Acceleration for Convolutional Neural Networks: A Comprehensive Review](https://mlsanity.com/paper/2505.13461/) (2025)
- [Optimizing Neural Networks with Learnable Non-Linear Activation Functions via Lookup-Based FPGA Acceleration](https://mlsanity.com/paper/2508.17069/) (2025)
- [RepQ: Generalizing Quantization-Aware Training for Re-Parametrized Architectures](https://mlsanity.com/paper/2311.05317/) (2023)
- [ISQuant: apply squant to the real deployment](https://mlsanity.com/paper/2407.11037/) (2024)
- [Memory-Efficient Integer-Only Training of Deep Neural Networks](https://mlsanity.com/paper/2610.16298/) (2026)

## Abstract (arXiv)

Neural network quantization is a promising compression technique to reduce memory footprint and save energy consumption, potentially leading to real-time inference. However, there is a performance gap between quantized and full-precision models. To reduce it, existing quantization approaches require high-precision INT32 or full-precision multiplication during inference for scaling or dequantization. This introduces a noticeable cost in terms of memory, speed, and required energy. To tackle these issues, we present F8Net, a novel quantization framework consisting of only fixed-point 8-bit multiplication. To derive our method, we first discuss the advantages of fixed-point multiplication with different formats of fixed-point numbers and study the statistical behavior of the associated fixed-point numbers. Second, based on the statistical and algorithmic analysis, we apply different fixed-point formats for weights and activations of different layers. We introduce a novel algorithm to automatically determine the right format for each layer during training. Third, we analyze a previous quantization algorithm -- parameterized clipping activation (PACT) -- and reformulate it using fixed-point arithmetic. Finally, we unify the recently proposed method for quantization fine-tuning and our fixed-point approach to show the potential of our method. We verify F8Net on ImageNet for MobileNet V1/V2 and ResNet18/50. Our approach achieves comparable and better performance, when compared not only to existing quantization techniques with INT32 multiplication or floating-point arithmetic, but also to the full-precision counterparts, achieving state-of-the-art performance.