[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85893-en":3,"doc-seo-85893-105":30,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85893,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","A Control Theory of Predictability in Latent World Models","Latent world models predict future states in a learned representation and are used inside a planner by simulating forward and choosing actions with lowest predicted cost. Existing training objectives minimize prediction error and rollout losses under the belief that smaller errors imply better control, which is shown to fail structurally. A new objective links the discrepancy between predicted and true plan-cost on the planner’s committed plan, yielding provable bounds. Experiments show single-step validation error may not correlate with control success, while a planner-reachable fidelity score does.","arXiv :2607 . 10362v 1 [ cs .LG] 11 Jul 2026  \nA CONTROL THEORY OF PREDICTABILITY IN LATENT WORLD MODELS  \nA PREPRINT  \nHanzhe You1 , Yonggang Zhang2 , Maohao Ran3 , Zhiqin Yang2 , Zhenyuan Zhang2 , Wei Xue2 Jun Song3,* , Xinmei Tian1,* , Yike Guo2,*  \n1University of Science and Technology of China  \n2The Hong Kong University of Science and Technology, HKGAI  \n3Hong Kong Baptist University  \nJuly 14, 2026  \nABSTRACT  \nLatent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single-or multi-step rollout loss on held-out data, as the training and modelselection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner’s suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.  \nKeywords World Models, Joint-Embedding Prediction, Koopman Operators, Pseudospectra, Model-Predictive Control  \n1 Introduction  \nA latent world model supports planning by predicting the future of a compact latent state, which allows an agent to act without modeling every detail of its observations. This places two competing requirements on the representation: it must retain enough of the signal to be useful, and it must remain predictable from its own past by a simple predictor acting in the latent space. Joint-Embedding Predictive Architectures [Assran et al., 2023, LeCun et al., 2022] make this trade-off the explicit training objective, mapping observations to a latent space with a shared encoder and operating a predictor inside that space rather than reconstructing the input. Once trained, the latent model is deployed inside a planner, such as model-predictive control or trajectory optimization in latent space [Hafner et al., 2020, Garcia and Ross, 2013, Assran et al., 2025], that rolls candidate action sequences forward and executes the one of lowest predicted cost.  \n* Corresponding authors.  \nA world model is evaluated not by its prediction error but by the quality of the actions it induces, and here common practice rests on an assumption that we argue is unsound: that lowering the prediction error, the single-or multi-step rollout loss on held-out data, is the correct objective for control. A planner does not query the model on the training distribution. It queries it on the states that candidate actions reach, and those states generally leave the data manifold, where the model extrapolates. The prediction loss is an average over the data distribution, whereas control success is a functional of the states the planner visits; the two need not move together, and we show that they need not.  \nThis paper develops a cont","cbCaith0X3hMb6PQ","https://ap.wps.com/l/cbCaith0X3hMb6PQ","pdf",586545,3,1,33,"English","en",105,"# Abstract\n# 1 Introduction\n## Control objective vs prediction error\n## Contributions and control theory framework\n# Keywords","[{\"question\":\"How are on-manifold residual and off-manifold divergence related to control?\",\"answer\":\"Under a linear-control premise, the discrepancy splits into a small on-manifold residual and an off-manifold divergence. The off-manifold divergence is the binding term: it is seeded when actions move the state off the manifold and it is not bounded by data-averaged prediction error.\"}]",1784207001,83,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"a-control-theory-of-predictability-in-latent-world-models","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/a-control-theory-of-predictability-in-latent-world-models/85893/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"How are on-manifold residual and off-manifold divergence related to control?","Question",{"text":75,"@type":76},"Under a linear-control premise, the discrepancy splits into a small on-manifold residual and an off-manifold divergence. The off-manifold divergence is the binding term: it is seeded when actions move the state off the manifold and it is not bounded by data-averaged prediction error.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]