# Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction

arXiv: https://arxiv.org/abs/2111.06636 · HTML: https://mlsanity.com/paper/2111.06636/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 74 references that are in the map.
- First posted on arXiv 12 Nov 2021.

## Builds on (most cited first, 30 of 44)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [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)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Conditional Image Synthesis With Auxiliary Classifier GANs](https://mlsanity.com/paper/1610.09585/) (2016)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [A Learned Representation For Artistic Style](https://mlsanity.com/paper/1610.07629/) (2016)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [InfoVAE: Information Maximizing Variational Autoencoders](https://mlsanity.com/paper/1706.02262/) (2017)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Disentangling factors of variation in deep representations using adversarial training](https://mlsanity.com/paper/1611.03383/) (2016)
- [IntroVAE: Introspective Variational Autoencoders for Photographic Image Synthesis](https://mlsanity.com/paper/1807.06358/) (2018)
- [ReduNet: A White-box Deep Network from the Principle of Maximizing Rate Reduction](https://mlsanity.com/paper/2105.10446/) (2021)

## Built on by (most cited first, 17 of 17)

- [On the Principles of Parsimony and Self-Consistency for the Emergence of Intelligence](https://mlsanity.com/paper/2207.04630/) (2022)
- [Image Clustering via the Principle of Rate Reduction in the Age of Pretrained Models](https://mlsanity.com/paper/2306.05272/) (2023)
- [Simplifying DINO via Coding Rate Regularization](https://mlsanity.com/paper/2502.10385/) (2025)
- [Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression](https://mlsanity.com/paper/2306.00788/) (2023)
- [EMP-SSL: Towards Self-Supervised Learning in One Training Epoch](https://mlsanity.com/paper/2304.03977/) (2023)
- [Incremental Learning of Structured Memory via Closed-Loop Transcription](https://mlsanity.com/paper/2202.05411/) (2022)
- [A Global Geometric Analysis of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2406.01909/) (2024)
- [Unsupervised Manifold Linearizing and Clustering](https://mlsanity.com/paper/2301.01805/) (2023)
- [Unsupervised Learning of Structured Representations via Closed-Loop Transcription](https://mlsanity.com/paper/2210.16782/) (2022)
- [Pursuit of a Discriminative Representation for Multiple Subspaces via Sequential Games](https://mlsanity.com/paper/2206.09120/) (2022)
- [Closed-Loop Transcription via Convolutional Sparse Coding](https://mlsanity.com/paper/2302.09347/) (2023)
- [Scanpath Prediction in Panoramic Videos via Expected Code Length Minimization](https://mlsanity.com/paper/2305.02536/) (2023)
- [Structural Adversarial Objectives for Self-Supervised Representation Learning](https://mlsanity.com/paper/2310.00357/) (2023)
- [Text Attribute Control via Closed-Loop Disentanglement](https://mlsanity.com/paper/2312.00277/) (2023)
- [Sample-efficient Quantum Born Machine through Coding Rate Reduction](https://mlsanity.com/paper/2211.10418/) (2022)
- [Bayesian Neural Networks: A Min-Max Game Framework](https://mlsanity.com/paper/2311.11126/) (2023)
- [On the Limits of Maximal Coding Rate Reduction for Out-of-Distribution Generalisation](https://mlsanity.com/paper/2609.21001/) (2026)

## Abstract (arXiv)

This work proposes a new computational framework for learning a structured generative model for real-world datasets. In particular, we propose to learn a closed-loop transcription between a multi-class multi-dimensional data distribution and a linear discriminative representation (LDR) in the feature space that consists of multiple independent multi-dimensional linear subspaces. In particular, we argue that the optimal encoding and decoding mappings sought can be formulated as the equilibrium point of a two-player minimax game between the encoder and decoder. A natural utility function for this game is the so-called rate reduction, a simple information-theoretic measure for distances between mixtures of subspace-like Gaussians in the feature space. Our formulation draws inspiration from closed-loop error feedback from control systems and avoids expensive evaluating and minimizing approximated distances between arbitrary distributions in either the data space or the feature space. To a large extent, this new formulation unifies the concepts and benefits of Auto-Encoding and GAN and naturally extends them to the settings of learning a both discriminative and generative representation for multi-class and multi-dimensional real-world data. Our extensive experiments on many benchmark imagery datasets demonstrate tremendous potential of this new closed-loop formulation: under fair comparison, visual quality of the learned decoder and classification performance of the encoder is competitive and often better than existing methods based on GAN, VAE, or a combination of both. Unlike existing generative models, the so learned features of the multiple classes are structured: different classes are explicitly mapped onto corresponding independent principal subspaces in the feature space. Source code can be found at https://github.com/Delay-Xili/LDR.