# ReD-CaNe: A Systematic Methodology for Resilience Analysis and Design of Capsule Networks under Approximations

arXiv: https://arxiv.org/abs/1912.00700 · HTML: https://mlsanity.com/paper/1912.00700/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Towards Energy-Efficient and Secure Edge AI: A Cross-Layer Framework](https://mlsanity.com/paper/2109.09829/) (2021)
- [Exploring Fault-Energy Trade-offs in Approximate DNN Hardware Accelerators](https://mlsanity.com/paper/2101.02860/) (2021)
- [Is Approximation Universally Defensive Against Adversarial Attacks in Deep Neural Networks?](https://mlsanity.com/paper/2112.01555/) (2021)
- [Enabling Capsule Networks at the Edge through Approximate Softmax and Squash Operations](https://mlsanity.com/paper/2206.10200/) (2022)
- [Combining Gradients and Probabilities for Heterogeneous Approximation of Neural Networks](https://mlsanity.com/paper/2208.07265/) (2022)
- [RobCaps: Evaluating the Robustness of Capsule Networks against Affine Transformations and Adversarial Attacks](https://mlsanity.com/paper/2304.03973/) (2023)
- [Explainable AI-Guided Efficient Approximate DNN Generation for Multi-Pod Systolic Arrays](https://mlsanity.com/paper/2503.16583/) (2025)

## Abstract (arXiv)

Recent advances in Capsule Networks (CapsNets) have shown their superior learning capability, compared to the traditional Convolutional Neural Networks (CNNs). However, the extremely high complexity of CapsNets limits their fast deployment in real-world applications. Moreover, while the resilience of CNNs have been extensively investigated to enable their energy-efficient implementations, the analysis of CapsNets' resilience is a largely unexplored area, that can provide a strong foundation to investigate techniques to overcome the CapsNets' complexity challenge. Following the trend of Approximate Computing to enable energy-efficient designs, we perform an extensive resilience analysis of the CapsNets inference subjected to the approximation errors. Our methodology models the errors arising from the approximate components (like multipliers), and analyze their impact on the classification accuracy of CapsNets. This enables the selection of approximate components based on the resilience of each operation of the CapsNet inference. We modify the TensorFlow framework to simulate the injection of approximation noise (based on the models of the approximate components) at different computational operations of the CapsNet inference. Our results show that the CapsNets are more resilient to the errors injected in the computations that occur during the dynamic routing (the softmax and the update of the coefficients), rather than other stages like convolutions and activation functions. Our analysis is extremely useful towards designing efficient CapsNet hardware accelerators with approximate components. To the best of our knowledge, this is the first proof-of-concept for employing approximations on the specialized CapsNet hardware.