# Neural Population Geometry Reveals the Role of Stochasticity in Robust Perception

arXiv: https://arxiv.org/abs/2111.06979 · HTML: https://mlsanity.com/paper/2111.06979/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 60 references that are in the map.
- First posted on arXiv 12 Nov 2021.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Audio Adversarial Examples: Targeted Attacks on Speech-to-Text](https://mlsanity.com/paper/1801.01944/) (2018)
- [Adversarial Robustness Toolbox v1.0.0](https://mlsanity.com/paper/1807.01069/) (2018)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Imperceptible, Robust, and Targeted Adversarial Examples for Automatic Speech Recognition](https://mlsanity.com/paper/1903.10346/) (2019)
- [Adversarial Attacks Against Automatic Speech Recognition Systems via Psychoacoustic Hiding](https://mlsanity.com/paper/1808.05665/) (2018)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Neural population geometry: An approach for understanding biological and artificial neural networks](https://mlsanity.com/paper/2104.07059/) (2021)
- [Emergence of Separable Manifolds in Deep Language Representations](https://mlsanity.com/paper/2006.01095/) (2020)
- [Neural tuning and representational geometry](https://mlsanity.com/paper/2104.09743/) (2021)
- [Probing artificial neural networks: insights from neuroscience](https://mlsanity.com/paper/2104.08197/) (2021)
- [Geodesics of learned representations](https://mlsanity.com/paper/1511.06394/) (2015)
- [Untangling in Invariant Speech Recognition](https://mlsanity.com/paper/2003.01787/) (2020)
- [Linear Readout of Object Manifolds](https://mlsanity.com/paper/1512.01834/) (2015)

## Built on by (most cited first, 12 of 12)

- [Learning Efficient Coding of Natural Images with Maximum Manifold Capacity Representations](https://mlsanity.com/paper/2303.03307/) (2023)
- [Representational dissimilarity metric spaces for stochastic neural networks](https://mlsanity.com/paper/2211.11665/) (2022)
- [A Spectral Theory of Neural Prediction and Alignment](https://mlsanity.com/paper/2309.12821/) (2023)
- [Brain-Model Evaluations Need the NeuroAI Turing Test](https://mlsanity.com/paper/2502.16238/) (2025)
- [Extreme Image Transformations Affect Humans and Machines Differently](https://mlsanity.com/paper/2212.13967/) (2022)
- [Beyond accuracy: generalization properties of bio-plausible temporal credit assignment rules](https://mlsanity.com/paper/2206.00823/) (2022)
- [Learning Robust Kernel Ensembles with Kernel Average Pooling](https://mlsanity.com/paper/2210.00062/) (2022)
- [Probing Human Visual Robustness with Neurally-Guided Deep Neural Networks](https://mlsanity.com/paper/2405.02564/) (2024)
- [Demolition and Reinforcement of Memories in Spin-Glass-like Neural Networks](https://mlsanity.com/paper/2403.02537/) (2024)
- [Sensory robustness through top-down feedback and neural stochasticity in recurrent vision models](https://mlsanity.com/paper/2508.07115/) (2025)
- [Neural Variability Enhances Artificial Network Robustness](https://mlsanity.com/paper/2606.13801/) (2026)
- [Curvature Under Attack in hZACH-ViT: Gauge Symmetry, Boundary Saturation, and Adversarial Failure](https://mlsanity.com/paper/2610.00680/) (2026)

## Abstract (arXiv)

Adversarial examples are often cited by neuroscientists and machine learning researchers as an example of how computational models diverge from biological sensory systems. Recent work has proposed adding biologically-inspired components to visual neural networks as a way to improve their adversarial robustness. One surprisingly effective component for reducing adversarial vulnerability is response stochasticity, like that exhibited by biological neurons. Here, using recently developed geometrical techniques from computational neuroscience, we investigate how adversarial perturbations influence the internal representations of standard, adversarially trained, and biologically-inspired stochastic networks. We find distinct geometric signatures for each type of network, revealing different mechanisms for achieving robust representations. Next, we generalize these results to the auditory domain, showing that neural stochasticity also makes auditory models more robust to adversarial perturbations. Geometric analysis of the stochastic networks reveals overlap between representations of clean and adversarially perturbed stimuli, and quantitatively demonstrates that competing geometric effects of stochasticity mediate a tradeoff between adversarial and clean performance. Our results shed light on the strategies of robust perception utilized by adversarially trained and stochastic networks, and help explain how stochasticity may be beneficial to machine and biological computation.