# Deep Transform and Metric Learning Networks

arXiv: https://arxiv.org/abs/2104.10329 · HTML: https://mlsanity.com/paper/2104.10329/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 21 Apr 2021.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Deep Neural Network Structures Solving Variational Inequalities](https://mlsanity.com/paper/1808.07526/) (2018)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Deep Dictionary Learning: A PARametric NETwork Approach](https://mlsanity.com/paper/1803.04022/) (2018)
- [Deep Transform and Metric Learning Network: Wedding Deep Dictionary Learning and Neural Networks](https://mlsanity.com/paper/2002.07898/) (2020)
- [Structured Analysis Dictionary Learning for Image Classification](https://mlsanity.com/paper/1805.00597/) (2018)
- [Analysis Dictionary Learning based Classification: Structure for Robustness](https://mlsanity.com/paper/1807.04899/) (2018)
- [Analysis Dictionary Learning: An Efficient and Discriminative Solution](https://mlsanity.com/paper/1903.03058/) (2019)
- [DeConFuse : A Deep Convolutional Transform based Unsupervised Fusion Framework](https://mlsanity.com/paper/2011.04337/) (2020)

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

- [Refining Self-Supervised Learning in Imaging: Beyond Linear Metric](https://mlsanity.com/paper/2202.12921/) (2022)
- [Proximal Vision Transformer: Enhancing Feature Representation through Two-Stage Manifold Geometry](https://mlsanity.com/paper/2508.17081/) (2025)

## Abstract (arXiv)

Based on its great successes in inference and denosing tasks, Dictionary Learning (DL) and its related sparse optimization formulations have garnered a lot of research interest. While most solutions have focused on single layer dictionaries, the recently improved Deep DL methods have also fallen short on a number of issues. We hence propose a novel Deep DL approach where each DL layer can be formulated and solved as a combination of one linear layer and a Recurrent Neural Network, where the RNN is flexibly regraded as a layer-associated learned metric. Our proposed work unveils new insights between the Neural Networks and Deep DL, and provides a novel, efficient and competitive approach to jointly learn the deep transforms and metrics. Extensive experiments are carried out to demonstrate that the proposed method can not only outperform existing Deep DL, but also state-of-the-art generic Convolutional Neural Networks.