# A Sparsity-promoting Dictionary Model for Variational Autoencoders

arXiv: https://arxiv.org/abs/2203.15758 · HTML: https://mlsanity.com/paper/2203.15758/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [A variance modeling framework based on variational autoencoders for speech enhancement](https://mlsanity.com/paper/1902.01605/) (2019)
- [Learning Latent Representations for Speech Generation and Transformation](https://mlsanity.com/paper/1704.04222/) (2017)
- [On Incorporating Inductive Biases into VAEs](https://mlsanity.com/paper/2106.13746/) (2021)
- [Sparsity in Variational Autoencoders](https://mlsanity.com/paper/1812.07238/) (2018)
- [A Benchmark of Dynamical Variational Autoencoders applied to Speech Spectrogram Modeling](https://mlsanity.com/paper/2106.06500/) (2021)
- [A Deep Generative Model of Speech Complex Spectrograms](https://mlsanity.com/paper/1903.03269/) (2019)
- [Deep Variational Generative Models for Audio-visual Speech Separation](https://mlsanity.com/paper/2008.07191/) (2020)

## Built on by (most cited first, 2 of 2)

- [SC-VAE: Sparse Coding-based Variational Autoencoder with Learned ISTA](https://mlsanity.com/paper/2303.16666/) (2023)
- [LASERS: LAtent Space Encoding for Representations with Sparsity for Generative Modeling](https://mlsanity.com/paper/2409.11184/) (2024)

## Abstract (arXiv)

Structuring the latent space in probabilistic deep generative models, e.g., variational autoencoders (VAEs), is important to yield more expressive models and interpretable representations, and to avoid overfitting. One way to achieve this objective is to impose a sparsity constraint on the latent variables, e.g., via a Laplace prior. However, such approaches usually complicate the training phase, and they sacrifice the reconstruction quality to promote sparsity. In this paper, we propose a simple yet effective methodology to structure the latent space via a sparsity-promoting dictionary model, which assumes that each latent code can be written as a sparse linear combination of a dictionary's columns. In particular, we leverage a computationally efficient and tuning-free method, which relies on a zero-mean Gaussian latent prior with learnable variances. We derive a variational inference scheme to train the model. Experiments on speech generative modeling demonstrate the advantage of the proposed approach over competing techniques, since it promotes sparsity while not deteriorating the output speech quality.