[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82497-en":3,"doc-seo-82497-105":29,"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":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},82497,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782109480056885918",8,"Research & Report","DiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning","Large language models perform well on reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT), but many problems require composing multi-step reasoning inside a single forward pass. This work studies two-hop reasoning, where a model must combine multiple pieces of parametric knowledge in one pass. It identifies a representational bottleneck in looped Transformers and shows a simple training-free realignment closes a generalization gap. It then proposes DiscoLoop, combining discrete embeddings and continuous hidden states in a looping architecture. DiscoLoop achieves near-perfect accuracy with fewer training steps and improves performance on real-world pretraining benchmarks.","arXiv :2607 .0034 1v 1 [ cs .CL] 1 Jul 2026  \nDiscoLoop: Looping Discrete Embeddings and Continuous Hidden States for Multi-hop Reasoning  \nHengyu Fu 1 ∗  \nJason D. Lee 1  \nTianyu Guo 1 ∗  \nJiantao Jiao 1  \nZixuan Wang 1 ,2 ∗  \nStuart Russell 1  \nHanlin Zhu 1 ∗  \nSong Mei 1  \nAbstract  \nLarge language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT) . However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass.  \nStandard non-recurrent Transformers suffer from a depth-local storage problem:  \nfacts learned in earlier layers are unavailable where second-hop retrieval happens.  \nWe found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap.  \nBuilding upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hiddenstate channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks.  \nWhen applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.  \n1 Introduction  \nCurrent large language models (LLMs) heavily rely on long traces of Chain-of-Thought (CoT) [Wei et al., 2022] to achieve strong performance in various challenging tasks, including math [Jaechet al., 2024, Guo et al., 2025] and coding [Chen et al., 2021, Cao et al., 2026] . Yet many questions implicitly require several reasoning steps before generating the answer token, which must happen internally through the forward pass [Yang et al., 2024] . Ideally, an intelligent model should reason in a parameter and context-efficient way by storing atomic facts and composing them implicitly on demand, which reduces the need to verbalize every intermediate step in the context. Unfortunately, many recent works show that transformer-based LLMs struggle with such implicit reasoning [Ye et al., 2024, Press et al., 2023, Yang et al., 2025] despite their excellent performance with CoT. Towards understanding the failure on implicit reasoning, a symbolic two-hop reasoning task [Wanget al., 2024, Ye et al., 2025b] was proposed as the most fundamental version of implicit reasoning.  \nAs an example, with atomic facts like “Alice’s son is Bob” and “Bob’s wife is Carol”, the composite ∗Equal Contribution.  \n1 University of California, Berkeley. Email: {hengyuf,tianyu_guo,[hanlinzhu}@berkeley.edu](hanlinzhu}@berkeley.edu)[ ](hanlinzhu}@berkeley.edu)2 Princeton University. Email: [zw2814@princeton.edu](zw2814@princeton.edu)  \nPreprint.  \nquery should be “Who is the wife of Alice’s son?”. Traditional transformer-based LLMs surprisingly struggle to learn this seemingly simple task [Yang et al., 2024, Biran et al., 2024, Balesni et al., 2024, Wang et al., 2024], and models often fail to compose two learned facts when the exact composite query was not observed during training.  \nThe failure was previously attributed to a depth-local storage problem in standard transformers [Biran et al., 2024, Wang et al., 2024] . In this view, a non-recurrent Transformer solves two-hop reasoning through a depth-wise circuit by assigning differen","cbCaivU1P4NRMGp0","https://ap.wps.com/l/cbCaivU1P4NRMGp0","pdf",2536695,1,16,"English","en",105,"# Abstract\n# Introduction\n## Motivation and Key Questions\n## Two-hop Reasoning Setup\n## Depth-local Storage and Looped Transformers","[{\"question\":\"How does DiscoLoop improve over looped-transformer baselines?\",\"answer\":\"DiscoLoop uses a looping architecture carrying both a discrete embedding channel and a continuous hidden-state channel, enabling near-perfect accuracy with substantially fewer training steps and lower training loss with stronger benchmark performance in real-world pretraining.\"}]",1784180929,40,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":27},"discoloop-looping-discrete-embeddings-and-continuous-hidden-states-for-multi-hop-reasoning","",{"@graph":35,"@context":77},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/discoloop-looping-discrete-embeddings-and-continuous-hidden-states-for-multi-hop-reasoning/82497/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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 does DiscoLoop improve over looped-transformer baselines?","Question",{"text":75,"@type":76},"DiscoLoop uses a looping architecture carrying both a discrete embedding channel and a continuous hidden-state channel, enabling near-perfect accuracy with substantially fewer training steps and lower training loss with stronger benchmark performance in real-world pretraining.","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":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,111,114,119,122,126],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":28,"slug":110},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":45,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":98,"slug":129},19,"General","general"]