[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85598-en":3,"doc-seo-85598-105":29,"detail-sidebar-cat-0-en-105":91},{"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},85598,3848291630094,"Emma Wilson","https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Causal Foundation Models with Continuous Treatments","Causal inference for observational data is built to estimate causal effects, but continuous treatment variables—where interventions span a real-valued range—remain much less developed than binary settings. This work introduces a first causal foundation model tailored to continuous treatments, meta-learning causal-effect prediction across many unseen tasks without training or fine-tuning. A new continuous-treatment prior generates rich causal corpora, while a transformer reconstructs treatment-response curves from observational context using in-context learning to amortize Bayesian posterior inference and achieve state-of-the-art reconstruction performance.","Causal Foundation Models with Continuous Treatments  \nChristopher Stith∗  \nLayer 6 AI  \n[christopher@layer6.ai](christopher@layer6.ai)  \nMedha Barath∗  \nUniversity of Toronto  \n[medha.barath@mail.utoronto.ca](medha.barath@mail.utoronto.ca)  \nVahid Balazadeh  \nUniversity of Toronto Vector Institute  \n[vahid@cs.toronto.edu](vahid@cs.toronto.edu)  \narXiv :2605 . 15 133v2 [ cs .LG] 13 Jul 2026  \nJesse C. Cresswell  \nLayer 6 AI [jesse@layer6.ai](jesse@layer6.ai)  \nRahul G. Krishnan  \nUniversity of Toronto Vector Institute  \n[rahulgk@cs.toronto.edu](rahulgk@cs.toronto.edu)  \nAbstract  \nCausal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has a continuous range. This setting is far less explored and represents a substantial shift from the binary treatment setting, with models needing to represent effects across a continuum of treatment values. In this paper, we present the first causal foundation model for the continuous treatment setting. Our model meta-learns the ability to predict causal effects across a wide variety of unseen tasks without additional training or fine-tuning. First, we design a novel prior over data-generating processes with continuous treatment variables in order to generate a rich causal training corpus. We then train a transformer to reconstruct individual treatment-response curves given only observational data, leveraging in-context learning to amortize expensive Bayesian posterior inference. Our model achieves state-of-the-art performance on individual treatment-response curve reconstruction tasks compared to causal models which are trained specifically for those tasks. Inference code (including trained model weights) can be found at [github.com/layer6ai-labs/CCPFN-inference](github.com/layer6ai-labs/CCPFN-inference).  \nFigure 1: Estimating causal effects for continuous treatments (right) is much more challenging than for binary treatments (left), as multiple treatment-response curves fit the observed data equally well.  \n1 Introduction  \nCausal inference is a central task for decision-making across many domains, including precision medicine [1, 43], econometric policy-making [2, 9], and algorithmic marketing [6, 14] . Estimating the  \n∗Equal Contribution  \nPreprint.  \neffect of an intervention from observational data alone is complicated, as the presence of confounders can bias naive estimators of potential outcomes. The causal inference community has built a rich library of estimators under the framework of ignorability, which assumes no unobserved confounding exists [34] . However, the end-to-end implementation of these estimators involves considerable time and effort: for any given task, a domain expert must inspect the data, propose an underlying mechanism to model it, choose an estimator that fits this mechanism, and only then train their model. In addition to this approach, there has been recent work at the intersection of causal inference and meta-learning [8] . The goal here is to train a model to perform a wide variety of causal inference tasks. A particularly promising framework has been Bayesian inference and in-context learning (ICL) [40, 3, 32] . Here, a model is trained over a diverse set of causal data-generating processes (DGPs) drawn from a prior π on possible DGPs, learning how to approximate the posterior-predictive distribution (PPD) for any new dataset. At inference, observational data for a given unseen task is passed to the model as context, from which the model learns the PPD for the causal estimand of interest, amortizing the cost of posterior inference. This pipeline turns the typically expensive and manual approach to causal inference into a completely data-driven process.  \nMost previous work in Bayesian causal inference focuses on the binary treatment setting, where units can be split into control a","cbCaifOHClhh1bVm","https://ap.wps.com/l/cbCaifOHClhh1bVm","pdf",2829186,1,21,"English","en",105,"# Abstract\n# Introduction\n## Motivation and background\n## Challenges in continuous treatments\n## Proposed approach: CCPFN","[{\"question\":\"What problem does the paper address?\",\"answer\":\"It addresses causal inference in the continuous treatment setting, where interventions take continuous values and require estimating full treatment-response curves rather than a single effect.\"},{\"question\":\"How does CCPFN generate causal training data?\",\"answer\":\"It designs a novel prior over data-generating processes with continuous treatment variables to produce a diverse causal training corpus.\"},{\"question\":\"How does the model perform inference on new tasks?\",\"answer\":\"It uses in-context learning: observational data are provided as context so the transformer reconstructs individual treatment-response curves, amortizing expensive Bayesian posterior inference without additional training or fine-tuning.\"}]",1784204833,53,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"causal-foundation-models-with-continuous-treatments","",{"@graph":35,"@context":85},[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/causal-foundation-models-with-continuous-treatments/85598/",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",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What 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