[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81800-en":3,"doc-seo-81800-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81800,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Sequentially-Controlled Interactive Multi-Particle Flow-Maps for Online Feedback-Driven Search","Online feedback-driven search often faces strict interaction budgets and lacks a priori preference knowledge, requiring broad exploration to find high-utility regions. The proposed Sequentially-Controlled Interactive Multi-Particle Flow-Maps (IMPFM) enables sample-efficient online adaptation by progressively transporting an ensemble of interacting particles via flow maps. Posterior sample sharing corrects particle drift at each resampling step, maximizing sample utility while mitigating reward over-optimization and preserving structural diversity. A multi-particle interaction-aware Feynman–Kac corrector steers particles toward a KL-tilted target distribution, preventing mode collapse, and extensive experiments confirm performance gains.","arXiv :2607 .0 1 144v 1 [ cs .LG] 1 Jul 2026  \nSequentially-Controlled Interactive Multi-Particle Flow-Maps for Online Feedback-Driven Search  \nBinglin Ji 1∗, Anindya Sarkar 1∗, Hengchang Lu 1 , Jens Sjölund2 , Yevgeniy Vorobeychik 1  \n{binglin.j, anindya, [yvorobeychik}@wustl.edu](yvorobeychik}@wustl.edu) ,  \n1Department of CSE, Washington University in St.Louis, USA  \n2Department of Information Technology, Uppsala University, Sweden  \nAbstract  \nWhile generative models have enabled training-free reward alignment, current methods typically excel in local exploration within narrow regions of the underlying distribution. These approaches struggle when preferences are unknown a priori and only revealed through sequential feedback—a scenario demanding broad exploration to uncover high-utility regions. To address this, we propose Sequentially-Controlled Interactive Multi-Particle Flow-Maps (IMPFM), a framework for sample-efficient online feedback-driven search. IMPFM progressively transports a group of interactive particles toward the target distribution, maintaining the broad coverage essential for heterogeneous preference alignment. IMPFM introduces a principled and efficient posterior sample sharing mechanism across particles powered by flow maps. By correcting individual particle drift with the collective posterior samples of the entire ensemble at each resampling step, the framework maximizes sample utility to enable global exploration while actively mitigating reward over-optimization, typical of standard control frameworks. Paired with a principled exploration-exploitation reweighting mechanism involving multiparticle interaction, this sequentially corrected multi-particle dynamics explicitly preserves structural diversity and overcomes the weight degeneracy inherent to standard SMC samplers. Crucially, we prove that the resulting sampling framework yields a multi-particle interaction-aware Feynman-Kac corrector that progressively steers the multi-particle system toward a KL-tilted target distribution, facilitating global exploration and preventing mode collapse. Extensive empirical evaluations and rigorous ablations across diverse search and alignment tasks confirm the efficacy of IMPFM over existing baselines.  \n1 Introduction  \nAcross diverse scientific and engineering disciplines, the pace of discovery is fundamentally constrained by the high cost of evaluation. This bottleneck gives rise to the ubiquitous challenge of online feedback-driven search, where finding an optimal solution requires iteratively proposing candidates and adapting based on sequential feedback. Whether designing life-saving therapeutics or optimizing interactive visual recommendation systems, these real-world applications often rely on costly physical experiments or human engagement. Consequently, minimizing the number of such interactions is a central requirement. Accelerating breakthroughs in these domains demands a robust sampling framework capable of strategic, global exploration across complex, high-dimensional spaces—such as molecular structures or natural images. Crucially, such a framework must seamlessly integrate sequential feedback to optimize the search trajectory under strict sampling budgets.  \nExisting methods remain fundamentally ill-equipped for this challenge. For instance, online RL fine-tuning of diffusion models [1] relies on a mode-seeking KL-divergence objective that inherently  \n∗ Equal Contribution  \nPreprint.  \nfails to capture diverse, high-utility regions. Furthermore, these approaches depend on online-trained reward models, whose early-stage biases frequently misdirect fine-tuning and degrade sample quality. Conversely, recent Sequential Monte Carlo (SMC) inference-time scaling methods [2, 3] avoid finetuning by leveraging fixed generative priors. Yet, they suffer from severe weight degeneracy, leading to proposal collapse and diminished diversity [4] . Tree-based samplers [5, 6] attempt to mitigate these evaluation bot","cbCaicIdPgNxvByp","https://ap.wps.com/l/cbCaicIdPgNxvByp","pdf",36884390,1,28,"English","en",105,"# Introduction\n## Motivation and challenge of online feedback-driven search\n## Limitations of existing RL, SMC, and tree-based samplers\n## Core concept and overview of IMPFM","[{\"question\":\"What problem does IMPFM address in online feedback-driven search?\",\"answer\":\"IMPFM targets scenarios where preferences are unknown and only revealed through sequential feedback, making it necessary to perform broad exploration under tight interaction budgets.\"},{\"question\":\"How does IMPFM improve exploration and sample efficiency compared with standard SMC methods?\",\"answer\":\"IMPFM uses interactive multi-particle dynamics with a posterior sample sharing mechanism across particles to correct drift at each resampling step, increasing sample utility and mitigating weight degeneracy and proposal collapse.\"},{\"question\":\"What role do multi-particle interaction-aware Feynman-Kac correctors play in IMPFM?\",\"answer\":\"They progressively steer the ensemble toward a KL-tilted target distribution while preserving structural diversity, thereby helping prevent mode collapse during 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problem does IMPFM address in online feedback-driven search?","Question",{"text":74,"@type":75},"IMPFM targets scenarios where preferences are unknown and only revealed through sequential feedback, making it necessary to perform broad exploration under tight interaction budgets.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does IMPFM improve exploration and sample efficiency compared with standard SMC methods?",{"text":79,"@type":75},"IMPFM uses interactive multi-particle dynamics with a posterior sample sharing mechanism across particles to correct drift at each resampling step, increasing sample utility and mitigating weight degeneracy and proposal collapse.",{"name":81,"@type":72,"acceptedAnswer":82},"What role do multi-particle interaction-aware Feynman-Kac correctors play in IMPFM?",{"text":83,"@type":75},"They progressively steer the ensemble toward a KL-tilted target distribution while preserving structural diversity, thereby helping prevent mode collapse during 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