# Autoencoders with Intrinsic Dimension Constraints for Learning Low Dimensional Image Representations

arXiv: https://arxiv.org/abs/2304.07686 · HTML: https://mlsanity.com/paper/2304.07686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 16 Apr 2023.

## Builds on (most cited first, 26 of 26)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionality](https://mlsanity.com/paper/1801.02613/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks](https://mlsanity.com/paper/2111.13171/) (2021)
- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [Geometry-Aware Maximum Likelihood Estimation of Intrinsic Dimension](https://mlsanity.com/paper/1904.06151/) (2019)
- [Wider and Deeper, Cheaper and Faster: Tensorized LSTMs for Sequence Learning](https://mlsanity.com/paper/1711.01577/) (2017)
- [Relationship between manifold smoothness and adversarial vulnerability in deep learning with local errors](https://mlsanity.com/paper/2007.02047/) (2020)
- [Weakly-correlated synapses promote dimension reduction in deep neural networks](https://mlsanity.com/paper/2006.11569/) (2020)

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

- [LCIP: Loss-Controlled Inverse Projection of High-Dimensional Image Data](https://mlsanity.com/paper/2602.11141/) (2026)

## Abstract (arXiv)

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly focus on the minimizing the reconstruction error on pixel level of image, while ignoring the preservation of Intrinsic Dimension (ID), which is a fundamental geometric property of data representations in Deep Neural Networks (DNNs). Motivated by the important role of ID, in this paper, we propose a novel deep representation learning approach with autoencoder, which incorporates regularization of the global and local ID constraints into the reconstruction of data representations. This approach not only preserves the global manifold structure of the whole dataset, but also maintains the local manifold structure of the feature maps of each point, which makes the learned low-dimensional features more discriminant and improves the performance of the downstream algorithms. To our best knowledge, existing works are rare and limited on exploiting both global and local ID invariant properties on the regularization of autoencoders. Numerical experimental results on benchmark datasets (Extended Yale B, Caltech101 and ImageNet) show that the resulting regularized learning models achieve better discriminative representations for downstream tasks including image classification and clustering.