# Closed-Loop Transcription via Convolutional Sparse Coding

arXiv: https://arxiv.org/abs/2302.09347 · HTML: https://mlsanity.com/paper/2302.09347/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 68 references that are in the map.
- First posted on arXiv 18 Feb 2023.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction](https://mlsanity.com/paper/2105.10446/) (2021)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [Dual Contradistinctive Generative Autoencoder](https://mlsanity.com/paper/2011.10063/) (2020)
- [On the Principles of Parsimony and Self-Consistency for the Emergence of Intelligence](https://mlsanity.com/paper/2207.04630/) (2022)
- [Sparse Modeling for Image and Vision Processing](https://mlsanity.com/paper/1411.3230/) (2014)
- [Learned Convolutional Sparse Coding](https://mlsanity.com/paper/1711.00328/) (2017)
- [Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method](https://mlsanity.com/paper/1407.1543/) (2014)
- [Polynomial-time Tensor Decompositions with Sum-of-Squares](https://mlsanity.com/paper/1610.01980/) (2016)
- [Complete Dictionary Recovery over the Sphere](https://mlsanity.com/paper/1504.06785/) (2015)
- [Subgradient Descent Learns Orthogonal Dictionaries](https://mlsanity.com/paper/1810.10702/) (2018)
- [Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction](https://mlsanity.com/paper/2111.06636/) (2021)
- [Incremental Learning of Structured Memory via Closed-Loop Transcription](https://mlsanity.com/paper/2202.05411/) (2022)
- [Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training](https://mlsanity.com/paper/2103.00673/) (2021)
- [Fast and robust tensor decomposition with applications to dictionary learning](https://mlsanity.com/paper/1706.08672/) (2017)
- [Revisiting Sparse Convolutional Model for Visual Recognition](https://mlsanity.com/paper/2210.12945/) (2022)

## Built on by (most cited first, 4 of 4)

- [Image Clustering via the Principle of Rate Reduction in the Age of Pretrained Models](https://mlsanity.com/paper/2306.05272/) (2023)
- [EMWaveNet: Physically Explainable Neural Network Based on Electromagnetic Propagation for SAR Target Recognition](https://mlsanity.com/paper/2410.09749/) (2024)
- [Bayesian Neural Networks: A Min-Max Game Framework](https://mlsanity.com/paper/2311.11126/) (2023)
- [Training-Adaptive Convolutional Sparse Coding via Information Bottleneck for Robust Visual Representation](https://mlsanity.com/paper/2609.19122/) (2026)

## Abstract (arXiv)

Autoencoding has achieved great empirical success as a framework for learning generative models for natural images. Autoencoders often use generic deep networks as the encoder or decoder, which are difficult to interpret, and the learned representations lack clear structure. In this work, we make the explicit assumption that the image distribution is generated from a multi-stage sparse deconvolution. The corresponding inverse map, which we use as an encoder, is a multi-stage convolution sparse coding (CSC), with each stage obtained from unrolling an optimization algorithm for solving the corresponding (convexified) sparse coding program. To avoid computational difficulties in minimizing distributional distance between the real and generated images, we utilize the recent closed-loop transcription (CTRL) framework that optimizes the rate reduction of the learned sparse representations. Conceptually, our method has high-level connections to score-matching methods such as diffusion models. Empirically, our framework demonstrates competitive performance on large-scale datasets, such as ImageNet-1K, compared to existing autoencoding and generative methods under fair conditions. Even with simpler networks and fewer computational resources, our method demonstrates high visual quality in regenerated images. More surprisingly, the learned autoencoder performs well on unseen datasets. Our method enjoys several side benefits, including more structured and interpretable representations, more stable convergence, and scalability to large datasets. Our method is arguably the first to demonstrate that a concatenation of multiple convolution sparse coding/decoding layers leads to an interpretable and effective autoencoder for modeling the distribution of large-scale natural image datasets.