{"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/learning-dynamics-in-linear-vae-posterior","title":"Learning Dynamics in Linear VAE: Posterior Collapse Threshold, Superfluous Latent Space Pitfalls, and Speedup with KL Annealing","arxiv_id":"2310.15440","date":"2023-10-24","proceeding":null,"authors":["Yuma Ichikawa","Koji Hukushima"],"abstract":"Variational autoencoders (VAEs) face a notorious problem wherein the variational posterior often aligns closely with the prior, a phenomenon known as posterior collapse, which hinders the quality of representation learning. To mitigate this problem, an adjustable hyperparameter $\\beta$ and a strategy for annealing this parameter, called KL annealing, are proposed. This study presents a theoretical analysis of the learning dynamics in a minimal VAE. It is rigorously proved that the dynamics converge to a deterministic process within the limit of large input dimensions, thereby enabling a detailed dynamical analysis of the generalization error. Furthermore, the analysis shows that the VAE initially learns entangled representations and gradually acquires disentangled representations. A fixed-point analysis of the deterministic process reveals that when $\\beta$ exceeds a certain threshold, posterior collapse becomes inevitable regardless of the learning period. Additionally, the superfluous latent variables for the data-generative factors lead to overfitting of the background noise; this adversely affects both generalization and learning convergence. The analysis further unveiled that appropriately tuned KL annealing can accelerate convergence.","url_abs":"https://arxiv.org/abs/2310.15440v1","url_pdf":"https://arxiv.org/pdf/2310.15440v1.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":"learning-dynamics-in-linear-vae-posterior","repo_url":"https://github.com/Yuma-Ichikawa/LearningDynamicsVAE","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2310.15440","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2310.15440"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Yuma-Ichikawa/LearningDynamicsVAE","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"ad03c46f9887b15e","entry":"criterion","repo":"Yuma-Ichikawa/LearningDynamicsVAE","repo_kind":"official","path":"src/vae.py","file_url":"https://github.com/Yuma-Ichikawa/LearningDynamicsVAE/blob/HEAD/src/vae.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ad03c46f9887b15e"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}