# Scalable Convolutional Dictionary Learning with Constrained Recurrent Sparse Auto-encoders

arXiv: https://arxiv.org/abs/1807.04734 · HTML: https://mlsanity.com/paper/1807.04734/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

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

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Stable and Interpretable Unrolled Dictionary Learning](https://mlsanity.com/paper/2106.00058/) (2021)
- [On the convergence of group-sparse autoencoders](https://mlsanity.com/paper/2102.07003/) (2021)
- [Unrolled Compressed Blind-Deconvolution](https://mlsanity.com/paper/2209.14165/) (2022)
- [Mixture Model Auto-Encoders: Deep Clustering through Dictionary Learning](https://mlsanity.com/paper/2110.04683/) (2021)
- [RoseCDL: Robust and Scalable Convolutional Dictionary Learning for Rare event and Anomaly Detection](https://mlsanity.com/paper/2509.07523/) (2025)

## Abstract (arXiv)

Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.