Learning Low-Rank Latent Spaces With Simple Deterministic Autoencoder: Theoretical and Empirical Insights

Alokendu Mazumder, Tirthajit Baruah, Bhartendu Kumar, Rishab Sharma, Vishwajeet Pattanaik, Punit Rathore; Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 2024, pp. 2851-2860

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional latent space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively learn a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional latent space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.