[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117630-en":3,"doc-seo-117630-105":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":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":27,"seo_description":14,"update_tm":28,"read_time":29},117630,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Approximate Bayesian Inference via Bitstring Representations - read online free","The paper addresses scalable probabilistic inference under quantized, discrete parameter representations, enabling learning of continuous distributions using finite bitstrings. It develops a tractable learning framework based on probabilistic circuits and studies performance on both 2D density estimation and quantized neural networks. Results demonstrate that bitstring-based approximate inference can achieve efficient inference for complex distributions while maintaining accuracy. Experiments validate the approach across multiple model settings and provide insight into model behavior.","This is an electronic reprint of the original article.  \nThis reprint may differ from the original in pagination and typographic detail.  \nSladek, Aleksanteri; Trapp, Martin; Solin, Arno  \nApproximate Bayesian Inference via Bitstring Representations  \nPublished in:  \nProceedings of Machine Learning Research  \nPublished: 01/01/2025  \nDocument Version  \nPublisher's PDF, also known as Version of record  \nPublished under the following license:  \nCC BY  \nPlease cite the original version:  \nSladek, A. , Trapp, M. , & Solin, A. (2025) . Approximate Bayesian Inference via Bitstring Representations. Proceedings of Machine Learning Research, 286, 3939-3948.  \n[https://proceedings.mlr.press/v286/sladek25a.html](https://proceedings.mlr.press/v286/sladek25a.html)  \nThis material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you foryour research use or educational purposes in electronic or print form. You must obtain permission for anyother use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user.  \nApproximate Bayesian Inference via Bitstring Representations  \nAleksanteri Sladek 1 Martin Trapp 1 Arno Solin 1  \n1Department of Computer Science, Aalto University, Espoo, Finland  \nAbstract  \nThe machine learning community has recently put effort into quantized or low-precision arithmeticsto scale large models. This paper proposes performing probabilistic inference in the quantized, discrete parameter space created by these representations, effectively enabling us to learn a continuous distribution using discrete parameters. We consider both 2D densities and quantized neural networks, where we introduce a tractable learning approach using probabilistic circuits. This method offers a scalable solution to manage complex distributions and provides clear insights into model behavior. We validate our approach with various models, demonstrating inference efficiency without sacrificing accuracy. This work advances scalable, interpretable machine learning by utilizing discrete approximations for probabilistic computations.  \n1 INTRODUCTION  \nProbabilistic inference is central to modern machine learning, providing a principled framework for reasoning under uncertainty. In Bayesian inference, uncertainty is captured through probability distributions over parameters, with Bayes’ theorem offering a systematic way to update beliefs with data. However, exact Bayesian inference is often intractable due to the complexity of the integrals involved. Variational inference (VI) [Blei et al., 2017, Jordan et al., 1999, Wainwright and Jordan, 2008] is typically employed as a scalable alternative to Markov chain Monte Carlo (MCMC) methods, enabling inference in high-dimensional models. Despite its success, VI relies on continuous parameterizations and often restrictive Gaussian assumptions, which can introduce representational and computational inefficiencies, particularly in large-scale settings.  \nTo address computational constraints, the machine learning  \nFigure 1: Capturing a 1D Gaussian mixture with BitVI with different numbers of bits in the bitstring. Even the 4-bit result serves a practical purpose, while the model saturates around 8 bits when compared to its 16 bit version.  \ncommunity has increasingly embraced quantization techniques. These methods reduce numerical precision to improve efficiency, leveraging low-bit representations for storage and computation. Many of those can be related to reducing the numerical precision, such as developing tailored low-precision number systems [Gustafson and Yonemoto, 2017, Agrawal et al., 2019] or methods for parameter quantization. Recent works leveraging large-scale mixed-precision FP8 [e.g., Liu et al., 2024], FP4 [Wang et al., 2025], or even 1-bit neural architectures [Ma et al., 2024] have shown ","cbCaibDd7CjJ6DqY","https://ap.wps.com/l/cbCaibDd7CjJ6DqY","pdf",1835094,1,20,"English","en",105,"# Introduction\n## Probabilistic inference and variational inference\n## Quantization and low-precision representations\n## Bitstring formulation motivation\n# Proposed method: BitVI\n## Probabilistic circuits for tractable learning\n## Learning and inference in bitstring space\n# Validation and experiments\n## Benchmark densities\n## Bayesian deep learning in neural networks","[{\"question\":\"What kinds of experiments are used to validate the approach?\",\"answer\":\"The paper validates BitVI on benchmark density modeling and on Bayesian deep learning with quantized neural network models, showing efficient inference while preserving accuracy.\"}]","Approximate Bayesian Inference via Bitstring Representations - read online free | PDF",1785677446,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"approximate-bayesian-inference-via-bitstring-representations-read-online-free","",{"@graph":36,"@context":77},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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/approximate-bayesian-inference-via-bitstring-representations-read-online-free/117630/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What kinds of experiments are used to validate the approach?","Question",{"text":75,"@type":76},"The paper validates BitVI on benchmark density modeling and on Bayesian deep learning with quantized neural network models, showing efficient inference while preserving accuracy.","Answer","https://schema.org",{"og:url":52,"og:type":79,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":81,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,106,111,114,118,121,125],{"id":20,"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":53,"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":29,"slug":105},6,"Technology","technology",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":21,"slug":117},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":21,"slug":120},"World Cup","world-cup",{"id":122,"doc_module":4,"doc_module_name":46,"category_name":123,"show_sort_weight":122,"slug":124},10,"Lifestyle","lifestyle",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":98,"slug":128},19,"General","general"]