# Sampling From Autoencoders' Latent Space via Quantization And Probability Mass Function Concepts

arXiv: https://arxiv.org/abs/2308.10704 · HTML: https://mlsanity.com/paper/2308.10704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 21 Aug 2023.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [And the Bit Goes Down: Revisiting the Quantization of Neural Networks](https://mlsanity.com/paper/1907.05686/) (2019)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [SDD-FIQA: Unsupervised Face Image Quality Assessment with Similarity Distribution Distance](https://mlsanity.com/paper/2103.05977/) (2021)
- [Hamiltonian Variational Auto-Encoder](https://mlsanity.com/paper/1805.11328/) (2018)
- [Data Augmentation in High Dimensional Low Sample Size Setting Using a Geometry-Based Variational Autoencoder](https://mlsanity.com/paper/2105.00026/) (2021)
- [Pythae: Unifying Generative Autoencoders in Python -- A Benchmarking Use Case](https://mlsanity.com/paper/2206.08309/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Iris-GAN: Learning to Generate Realistic Iris Images Using Convolutional GAN](https://mlsanity.com/paper/1812.04822/) (2018)
- [Haven't I Seen You Before? Assessing Identity Leakage in Synthetic Irises](https://mlsanity.com/paper/2211.05629/) (2022)

## Abstract (arXiv)

In this study, we focus on sampling from the latent space of generative models built upon autoencoders so as the reconstructed samples are lifelike images. To do to, we introduce a novel post-training sampling algorithm rooted in the concept of probability mass functions, coupled with a quantization process. Our proposed algorithm establishes a vicinity around each latent vector from the input data and then proceeds to draw samples from these defined neighborhoods. This strategic approach ensures that the sampled latent vectors predominantly inhabit high-probability regions, which, in turn, can be effectively transformed into authentic real-world images. A noteworthy point of comparison for our sampling algorithm is the sampling technique based on Gaussian mixture models (GMM), owing to its inherent capability to represent clusters. Remarkably, we manage to improve the time complexity from the previous O(n× d × k × i) associated with GMM sampling to a much more streamlined O(n× d), thereby resulting in substantial speedup during runtime. Moreover, our experimental results, gauged through the Fr'echet inception distance (FID) for image generation, underscore the superior performance of our sampling algorithm across a diverse range of models and datasets. On the MNIST benchmark dataset, our approach outperforms GMM sampling by yielding a noteworthy improvement of up to 0.89 in FID value. Furthermore, when it comes to generating images of faces and ocular images, our approach showcases substantial enhancements with FID improvements of 1.69 and 0.87 respectively, as compared to GMM sampling, as evidenced on the CelebA and MOBIUS datasets. Lastly, we substantiate our methodology's efficacy in estimating latent space distributions in contrast to GMM sampling, particularly through the lens of the Wasserstein distance.