# Deep Transform and Metric Learning Network: Wedding Deep Dictionary Learning and Neural Networks

arXiv: https://arxiv.org/abs/2002.07898 · HTML: https://mlsanity.com/paper/2002.07898/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [Understanding approximate and unrolled dictionary learning for pattern recovery](https://mlsanity.com/paper/2106.06338/) (2021)
- [AbsTopK: Rethinking Sparse Autoencoders For Bidirectional Features](https://mlsanity.com/paper/2510.00404/) (2025)
- [Deep Transform and Metric Learning Networks](https://mlsanity.com/paper/2104.10329/) (2021)
- [Refining Self-Supervised Learning in Imaging: Beyond Linear Metric](https://mlsanity.com/paper/2202.12921/) (2022)
- [Stability Bounds for the Unfolded Forward-Backward Algorithm](https://mlsanity.com/paper/2412.17888/) (2024)
- [Proximal Vision Transformer: Enhancing Feature Representation through Two-Stage Manifold Geometry](https://mlsanity.com/paper/2508.17081/) (2025)

## Abstract (arXiv)

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the improved recently proposed Deep DL (DDL) methods have also fallen short on a number of issues. We propose herein, a novel DDL approach where each DL layer can be formulated as a combination of one linear layer and a Recurrent Neural Network (RNN). The RNN is shown to flexibly account for the layer-associated and learned metric. Our proposed work unveils new insights into Neural Networks and DDL and provides a new, efficient and competitive approach to jointly learn a deep transform and a metric for inference applications. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing DDL but also state-of-the-art generic CNNs.