# Hierarchical Invariance for Robust and Interpretable Vision Tasks at Larger Scales

arXiv: https://arxiv.org/abs/2402.15430 · HTML: https://mlsanity.com/paper/2402.15430/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 87 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 30 of 55)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [CNN-generated images are surprisingly easy to spot... for now](https://mlsanity.com/paper/1912.11035/) (2019)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Thinking in Frequency: Face Forgery Detection by Mining Frequency-aware Clues](https://mlsanity.com/paper/2007.09355/) (2020)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Detecting Adversarial Samples from Artifacts](https://mlsanity.com/paper/1703.00410/) (2017)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)

## Built on by (most cited first, 1 of 1)

- [Distilling Latent Manifolds: Resolution Extrapolation by Variational Autoencoders](https://mlsanity.com/paper/2603.14536/) (2026)

## Abstract (arXiv)

Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in the fundamental image representation. However, such invariant representations typically exhibit limited discriminability, limiting their applications in larger-scale trustworthy vision tasks. For this open problem, we conduct a systematic investigation of hierarchical invariance, exploring this topic from theoretical, practical, and application perspectives. At the theoretical level, we show how to construct over-complete invariants with a Convolutional Neural Networks (CNN)-like hierarchical architecture yet in a fully interpretable manner. The general blueprint, specific definitions, invariant properties, and numerical implementations are provided. At the practical level, we discuss how to customize this theoretical framework into a given task. With the over-completeness, discriminative features w.r.t. the task can be adaptively formed in a Neural Architecture Search (NAS)-like manner. We demonstrate the above arguments with accuracy, invariance, and efficiency results on texture, digit, and parasite classification experiments. Furthermore, at the application level, our representations are explored in real-world forensics tasks on adversarial perturbations and Artificial Intelligence Generated Content (AIGC). Such applications reveal that the proposed strategy not only realizes the theoretically promised invariance, but also exhibits competitive discriminability even in the era of deep learning. For robust and interpretable vision tasks at larger scales, hierarchical invariant representation can be considered as an effective alternative to traditional CNN and invariants.