# Approximate Multiplier Induced Error Propagation in Deep Neural Networks

arXiv: https://arxiv.org/abs/2512.06537 · HTML: https://mlsanity.com/paper/2512.06537/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 6 Dec 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Gemmini: Enabling Systematic Deep-Learning Architecture Evaluation via Full-Stack Integration](https://mlsanity.com/paper/1911.09925/) (2019)
- [Hardware Approximate Techniques for Deep Neural Network Accelerators: A Survey](https://mlsanity.com/paper/2203.08737/) (2022)
- [Insights into DeepSeek-V3: Scaling Challenges and Reflections on Hardware for AI Architectures](https://mlsanity.com/paper/2505.09343/) (2025)
- [TFApprox: Towards a Fast Emulation of DNN Approximate Hardware Accelerators on GPU](https://mlsanity.com/paper/2002.09481/) (2020)
- [ApproxTrain: Fast Simulation of Approximate Multipliers for DNN Training and Inference](https://mlsanity.com/paper/2209.04161/) (2022)
- [Approximate Computing Survey, Part II: Application-Specific & Architectural Approximation Techniques and Applications](https://mlsanity.com/paper/2307.11128/) (2023)

## Abstract (arXiv)

Deep Neural Networks (DNNs) rely heavily on dense arithmetic operations, motivating the use of Approximate Multipliers (AxMs) to reduce energy consumption in hardware accelerators. However, a rigorous mathematical characterization of how AxMs error distributions influence DNN accuracy remains underdeveloped. This work presents an analytical framework that connects the statistical error moments of an AxM to the induced distortion in General Matrix Multiplication (GEMM). Using the Frobenius norm of the resulting error matrix, we derive a closed form expression for practical DNN dimensions that demonstrates the distortion is predominantly governed by the multiplier mean error (bias). To evaluate this model in realistic settings, we incorporate controlled error injection into GEMM and convolution layers and examine its effect on ImageNet scale networks. The predicted distortion correlates strongly with the observed accuracy degradation, and an error configurable AxM case study implemented on an FPGA further confirms the analytical trends. By providing a lightweight alternative to behavioral or hardware level simulations, this framework enables rapid estimation of AxM impact on DNN inference quality.