{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/closed-loop-data-transcription-to-an-ldr-via-1","title":"Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction","arxiv_id":"2111.06636","date":"2021-11-12","proceeding":null,"authors":["Xili Dai","Shengbang Tong","Mingyang Li","Ziyang Wu","Michael Psenka","Kwan Ho Ryan Chan","Pengyuan Zhai","Yaodong Yu","Xiaojun Yuan","Heung Yeung Shum","Yi Ma"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2111.06636v3","url_pdf":"https://arxiv.org/pdf/2111.06636v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"closed-loop-data-transcription-to-an-ldr-via-1","repo_url":"https://github.com/delay-xili/ldr","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2111.06636","atlas_url":"https://app.syntology.ai/?focus=2111.06636","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2111.06636"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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