# Low-Precision Mixed-Computation Models for Inference on Edge

arXiv: https://arxiv.org/abs/2312.02210 · HTML: https://mlsanity.com/paper/2312.02210/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [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)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [HAWQ: Hessian AWare Quantization of Neural Networks with Mixed-Precision](https://mlsanity.com/paper/1905.03696/) (2019)
- [LQ-Nets: Learned Quantization for Highly Accurate and Compact Deep Neural Networks](https://mlsanity.com/paper/1807.10029/) (2018)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Training Deep Neural Networks with 8-bit Floating Point Numbers](https://mlsanity.com/paper/1812.08011/) (2018)
- [Scalable Methods for 8-bit Training of Neural Networks](https://mlsanity.com/paper/1805.11046/) (2018)
- [Training Binary Neural Networks with Real-to-Binary Convolutions](https://mlsanity.com/paper/2003.11535/) (2020)
- [Nonuniform-to-Uniform Quantization: Towards Accurate Quantization via Generalized Straight-Through Estimation](https://mlsanity.com/paper/2111.14826/) (2021)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [Any-Precision Deep Neural Networks](https://mlsanity.com/paper/1911.07346/) (2019)
- [Discovering Low-Precision Networks Close to Full-Precision Networks for Efficient Embedded Inference](https://mlsanity.com/paper/1809.04191/) (2018)
- [FracBNN: Accurate and FPGA-Efficient Binary Neural Networks with Fractional Activations](https://mlsanity.com/paper/2012.12206/) (2020)
- [8-bit Numerical Formats for Deep Neural Networks](https://mlsanity.com/paper/2206.02915/) (2022)
- [NICE: Noise Injection and Clamping Estimation for Neural Network Quantization](https://mlsanity.com/paper/1810.00162/) (2018)
- [Deep Positron: A Deep Neural Network Using the Posit Number System](https://mlsanity.com/paper/1812.01762/) (2018)
- [Cheetah: Mixed Low-Precision Hardware & Software Co-Design Framework for DNNs on the Edge](https://mlsanity.com/paper/1908.02386/) (2019)
- [Performance-Efficiency Trade-off of Low-Precision Numerical Formats in Deep Neural Networks](https://mlsanity.com/paper/1903.10584/) (2019)
- [Training Deep Neural Networks Using Posit Number System](https://mlsanity.com/paper/1909.03831/) (2019)
- [ExPAN(N)D: Exploring Posits for Efficient Artificial Neural Network Design in FPGA-based Systems](https://mlsanity.com/paper/2010.12869/) (2020)
- [PLAM: a Posit Logarithm-Approximate Multiplier](https://mlsanity.com/paper/2102.09262/) (2021)
- [Sensitivity-Aware Mixed-Precision Quantization and Width Optimization of Deep Neural Networks Through Cluster-Based Tree-Structured Parzen Estimation](https://mlsanity.com/paper/2308.06422/) (2023)

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

- [Flex-PE: Flexible and SIMD Multi-Precision Processing Element for AI Workloads](https://mlsanity.com/paper/2412.11702/) (2024)
- [POLARON: Precision-aware On-device Learning and Adaptive Runtime-cONfigurable AI acceleration](https://mlsanity.com/paper/2506.08785/) (2025)
- [Fever Detection with Infrared Thermography: Enhancing Accuracy through Machine Learning Techniques](https://mlsanity.com/paper/2407.15302/) (2024)
- [XR-NPE: High-Throughput Mixed-precision SIMD Neural Processing Engine for Extended Reality Perception Workloads](https://mlsanity.com/paper/2508.13049/) (2025)

## Abstract (arXiv)

This paper presents a mixed-computation neural network processing approach for edge applications that incorporates low-precision (low-width) Posit and low-precision fixed point (FixP) number systems. This mixed-computation approach employs 4-bit Posit (Posit4), which has higher precision around zero, for representing weights with high sensitivity, while it uses 4-bit FixP (FixP4) for representing other weights. A heuristic for analyzing the importance and the quantization error of the weights is presented to assign the proper number system to different weights. Additionally, a gradient approximation for Posit representation is introduced to improve the quality of weight updates in the backpropagation process. Due to the high energy consumption of the fully Posit-based computations, neural network operations are carried out in FixP or Posit/FixP. An efficient hardware implementation of a MAC operation with a first Posit operand and FixP for a second operand and accumulator is presented. The efficacy of the proposed low-precision mixed-computation approach is extensively assessed on vision and language models. The results show that, on average, the accuracy of the mixed-computation is about 1.5% higher than that of FixP with a cost of 0.19% energy overhead.