# Fragility, Robustness and Antifragility in Deep Learning

arXiv: https://arxiv.org/abs/2312.09821 · HTML: https://mlsanity.com/paper/2312.09821/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 48 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 30 of 36)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Adversarial Examples: Attacks and Defenses for Deep Learning](https://mlsanity.com/paper/1712.07107/) (2017)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [Adversarial Attacks and Defenses in Images, Graphs and Text: A Review](https://mlsanity.com/paper/1909.08072/) (2019)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Adversarial Robustness vs Model Compression, or Both?](https://mlsanity.com/paper/1903.12561/) (2019)
- [The Impact of Neural Network Overparameterization on Gradient Confusion and Stochastic Gradient Descent](https://mlsanity.com/paper/1904.06963/) (2019)
- [The Intriguing Relation Between Counterfactual Explanations and Adversarial Examples](https://mlsanity.com/paper/2009.05487/) (2020)

## Built on by (most cited first, 2 of 2)

- [Antifragile perimeter control: Thriving on disruptions through reinforcement learning](https://mlsanity.com/paper/2402.12665/) (2024)
- [Parameter Stress Analysis in Reinforcement Learning: Applying Synaptic Filtering to Policy Networks](https://mlsanity.com/paper/2506.23036/) (2025)

## Abstract (arXiv)

We propose a systematic analysis of deep neural networks (DNNs) based on a signal processing technique for network parameter removal, in the form of synaptic filters that identifies the fragility, robustness and antifragility characteristics of DNN parameters. Our proposed analysis investigates if the DNN performance is impacted negatively, invariantly, or positively on both clean and adversarially perturbed test datasets when the DNN undergoes synaptic filtering. We define three textitfiltering scores for quantifying the fragility, robustness and antifragility characteristics of DNN parameters based on the performances for (i) clean dataset, (ii) adversarial dataset, and (iii) the difference in performances of clean and adversarial datasets. We validate the proposed systematic analysis on ResNet-18, ResNet-50, SqueezeNet-v1.1 and ShuffleNet V2 x1.0 network architectures for MNIST, CIFAR10 and Tiny ImageNet datasets. The filtering scores, for a given network architecture, identify network parameters that are invariant in characteristics across different datasets over learning epochs. Vice-versa, for a given dataset, the filtering scores identify the parameters that are invariant in characteristics across different network architectures. We show that our synaptic filtering method improves the test accuracy of ResNet and ShuffleNet models on adversarial datasets when only the robust and antifragile parameters are selectively retrained at any given epoch, thus demonstrating applications of the proposed strategy in improving model robustness.