# Why Regularized Auto-Encoders learn Sparse Representation?

arXiv: https://arxiv.org/abs/1505.05561 · HTML: https://mlsanity.com/paper/1505.05561/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2015.

## Built on by (most cited first, 11 of 11)

- [Measuring Progress in Dictionary Learning for Language Model Interpretability with Board Game Models](https://mlsanity.com/paper/2408.00113/) (2024)
- [Analysis of feature learning in weight-tied autoencoders via the mean field lens](https://mlsanity.com/paper/2102.08373/) (2021)
- [SAUCE: Selective Concept Unlearning in Vision-Language Models with Sparse Autoencoders](https://mlsanity.com/paper/2503.14530/) (2025)
- [Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias?](https://mlsanity.com/paper/2504.12883/) (2025)
- [Enhancing Unsupervised Anomaly Detection with Score-Guided Network](https://mlsanity.com/paper/2109.04684/) (2021)
- [Rank Reduction Autoencoders](https://mlsanity.com/paper/2405.13980/) (2024)
- [Universal Solutions of Feedforward ReLU Networks for Interpolations](https://mlsanity.com/paper/2208.07498/) (2022)
- [Advances in Electron Microscopy with Deep Learning](https://mlsanity.com/paper/2101.01178/) (2021)
- [Semantic Autoencoder and Its Potential Usage for Adversarial Attack](https://mlsanity.com/paper/2205.15592/) (2022)
- [Learning Sparsity of Representations with Discrete Latent Variables](https://mlsanity.com/paper/2304.00935/) (2023)
- [Shape Modeling of Longitudinal Medical Images: From Diffeomorphic Metric Mapping to Deep Learning](https://mlsanity.com/paper/2503.21489/) (2025)

## Abstract (arXiv)

While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- textitInternal Covariate Shift-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of mean and standard deviation of input (distribution) to hidden layers inaccurate due to shifting parameter values (especially during initial training epochs). Another fundamental problem with BN is that it cannot be used with batch-size  1  during training. We address these drawbacks of BN by proposing a non-adaptive normalization technique for removing covariate shift, that we call textitNormalization Propagation. Our approach does not depend on batch statistics, but rather uses a data-independent parametric estimate of mean and standard-deviation in every layer thus being computationally faster compared with BN. We exploit the observation that the pre-activation before Rectified Linear Units follow Gaussian distribution in deep networks, and that once the first and second order statistics of any given dataset are normalized, we can forward propagate this normalization without the need for recalculating the approximate statistics for hidden layers.