[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86247-en":3,"doc-seo-86247-105":30,"detail-sidebar-cat-0-en-105":92},{"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},86247,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","DAG-FM A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms","Causal discovery from observational tabular data remains difficult due to heterogeneous causal mechanisms and the large combinatorial search space of directed acyclic graphs (DAGs). This paper introduces DAG-FM, a foundation model that amortizes causal discovery by decomposing the task into two auto-regressive Transformer stages: a leaf-node predictor and a parent-node predictor. A tabular interaction block models row-column dependencies, while Mixture-of-Leaf-Experts adapts to diverse functional causal model families. Iterative inference extracts causal orderings and builds valid DAGs, achieving state-of-the-art results on synthetic and real datasets with improved accuracy and scalability.","arXiv :2607 . 1 15 10v 1 [ cs .LG] 13 Jul 2026  \nDAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms  \nYikang Chen 1 , Zhengkang Guan 1 , Haoyuan Qian 1 , Peng Cui2 , Yi Yang 1 , Kun Kuang 1 ∗  \n1Zhejiang University  \n2Tsinghua University  \nAbstract  \nCausal discovery from observational tabular data remains fundamentally challenging, primarily due to the heterogeneity of underlying causal mechanisms and the high-dimensional combinatorial search space of Directed Acyclic Graphs (DAGs) .  \nIn this paper, we propose DAG-FM, a novel foundation model architecture that amortizes causal discovery. Unlike direct matrix prediction, DAG-FM decomposes the causal discovery process into two auto-regressive stages using two specialized Transformer-based sub-modules: a leaf-node predictor and a parent-node predictor. To effectively model complex row-column interactions, we adopt a robust tabular interaction block to output feature-wise representations. Crucially, to handle diverse and unknown Functional Causal Model (FCM) assumptions in real-world scenarios, we introduce Mixture-of-Leaf-Experts (MoLE), allowing the model to dynamically route and adapt to identifiable mechanism families.  \nThrough an iterative inference algorithm, DAG-FM seamlessly extracts causal orderings and constructs valid DAGs. Extensive experiments demonstrate that DAG-FM achieves state-of-the-art performance on both synthetic benchmarks and complex real-world datasets, significantly outperforming traditional classical algorithms and recent foundation models in both accuracy and scalability.  \n1 Introduction  \nCausal discovery aims to recover causal structures from data (Pearl, 2009), playing a pivotal role in diverse fields such as bioinformatics (Zhang et al., 2013), epidemiology (Vandenbroucke et al., 2016), sociology (Huber, 2024), and manufacturing (Vukovi & Thalmann, 2022) . A primary objective of this task is to identify the underlying Directed Acyclic Graphs (DAGs) from observational data. Existing approaches, spanning constraint-based (Spirtes & Glymour, 1991; Spirtes, 1995), score-based (Cooper & Herskovits, 1992; Chickering, 2002), and optimization-based (Zheng et al., 2018; Bello et al., 2022) methods, have been extensively developed. However, without additional assumptions, these methods can only identify causal structures up to Markov equivalence classes. Functional Causal Models (FCMs) introduce supplementary structural assumptions into Structural Causal Models (SCMs), ensuring theoretical identifiability of the underlying DAGs from observational distributions when specific conditions are met. Notable examples include Linear NonGaussian Acyclic Models (LiNGAMs, Shimizu et al. (2006)), Additive Noise Models (ANMs, Hoyer et al. (2008)), Heteroscedastic Noise Models (HNMs, Tagasovska et al. (2020)), and PostNonlinear models (PNLs, Zhang & Hyvrinen (2009)) .  \nBuilding upon the theoretical guarantees of DAG identifiability, FCM-based causal discovery methods have been developed for empirical DAG recovery. However, these methods typically assume homogeneous causal mechanisms, fundamentally limiting their generalizability. To render statistical hypothesis testing tractable, most existing approaches are narrowly tailored to specific theoretical frameworks, such as LiNGAM or ANM (Shimizu et al., 2006; 2011; Peters et al., 2014; Rolland et al., 2022) . Alternatively, some methods derive causal orderings by extracting specific statistical features, yet they remain effective only under highly restrictive conditions (Reisach et al., 2021; 2023) . Consequently, the robustness and validity of these traditional methods under model misspecification or within highly complex real-world scenarios remain largely questionable.  \n∗ Corresponding author: [kunkuang@zju.edu.cn](kunkuang@zju.edu.cn)  \nIn parallel, amortized algorithms have emerged for causal discovery, empirically demonstrating consistent superiority over traditional methods in c","cbCailOGrWhf3mcN","https://ap.wps.com/l/cbCailOGrWhf3mcN","pdf",570720,6,1,17,"English","en",105,"# Abstract\n# Introduction\n## Problem and background\n## Limitations of existing methods\n## Proposed approach and contributions","[{\"question\":\"What key challenge does DAG-FM address in causal discovery from observational data?\",\"answer\":\"It targets the difficulty caused by heterogeneous causal mechanisms and the large combinatorial space of possible DAGs when learning causal structure from observational tabular data.\"},{\"question\":\"How does DAG-FM reformulate causal discovery compared with direct matrix prediction?\",\"answer\":\"DAG-FM decomposes the process into two auto-regressive stages, using a leaf-node predictor and a parent-node predictor based on Transformer modules.\"},{\"question\":\"How does DAG-FM handle unknown or diverse functional causal model (FCM) assumptions?\",\"answer\":\"It introduces Mixture-of-Leaf-Experts (MoLE) to dynamically route and adapt to identifiable mechanism families during inference.\"}]",1784209789,43,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"dag-fm-a-foundation-model-for-causal-discovery-under-heterogeneous-causal-mechanisms","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/dag-fm-a-foundation-model-for-causal-discovery-under-heterogeneous-causal-mechanisms/86247/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What 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