[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82474-en":3,"doc-seo-82474-105":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},82474,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Scaling Up Thermodynamic AI Models","Thermodynamic computing devices based on the Ising model offer promise for low-power AI inference and edge computing, yet scalable training methods for large models on such hardware are limited. The work converts a high-temperature Gibbs-sampled Ising correspondence into a scalable, purely backpropagation-based training algorithm for deep convolutional networks. Image classification reaches 94.9% on CIFAR-10 and 76.0% on CIFAR-100 under binary Gibbs sampling, with theory and experiments linking inference cost, accuracy, and autocorrelation time control.","arXiv :2607 .00170v1 [ cs .LG] 30 Jun 2026  \nScaling Up Thermodynamic AI Models  \nAndrew G. Moore et alia  \nJune 22, 2026  \nAbstract  \nThermodynamic computing devices based on the Ising model show great promise for low-power AI inference and edge computing, but scalable methods for training large models for such hardware remain limited. Prior theory shows that the time-averaged behavior of high-temperature Gibbs-sampled Ising systems can implement feed-forward neural inference. We turn this theoretical correspondence into a scalable and purely backpropagation-based algorithm for training deep convolutional networks for thermodynamic inference on Ising machine hardware. Our image classification models achieve accuracies of 94 .9% on CIFAR-10 and 76 .0% on CIFAR-100 under binary Gibbs sampling. We then develop and experimentally validate a mathematical theory relating inference cost to accuracy and controlling autocorrelation times. Subsequently, we calculate asymptotic results showing that inference cost is bounded by a well-controlled tradeoff with performance and exhibit algorithms for computing optimal inference schedules. Finally, we discuss implications for hardware development and the future of high-temperature thermodynamic AI models.  \n1 Introduction  \nAI models aggregate many small computations into statistical inferences. However, running an AI model on a GPU, even a quantized one, entails exact error-free computation of every activation. This exactitude at a microscopic level, however, is not necessary for macroscopic performance: small errors in activations generally do not cause catastrophic performance loss. This is the basic principle behind weight quantization methods and dropout layers. On the other hand, keeping those computations error-free comes with an energy cost at the hardware level. In other words, keeping each computation exact during inference is wasteful. Thermodynamic computing hardware, including both stochastic silicon and other probabilistic substrates, promises to perform approximate local computations at a tiny fraction of the energy expenditure. At the macro level, therefore, running a model on such hardware could perform computations far more efficiently without significant accuracy loss. Given the massive and ever-growing energy demands of AI inference, the need to find a more efficient solution is likely to become more pressing over time.  \nThermodynamic computing systems exploit thermal fluctuations, stochastic dynamics, Boltzmann distributions, or non-equilibrium processes rather than suppressing noise as an error source [2] . A canonical example is the Ising computer: any type of hardware which implements a system of binary spins whose probability distribution is governed by the Ising model. Ising computation has a long history with AI, going back to the 80s. The Hopfield network, a canonical example of the connection between statistical mechanics and machine learning, was explicitly based on the low-temperature Ising model. The Boltzmann machine, a positive-temperature cousin, is still relevant today. However, the crown jewels of modern AI inference, such as image classification and natural language processing, have largely remained outside their reach.  \nIsing-based systems have always struggled with a lack of truly scalable and efficient training algorithms for general workloads. This has mostly confined Ising computation in practice to those situations in which a good training method does exist. In applications where a Boltzmann machine is suitable, contrastive divergence or equilibrium propagation provides a solution, but these methods do not scale efficiently to large benchmark problems [16] . Ising computers have also found wide application in combinatorial optimization, where weights can easily be derived analytically from the structure of the problem [14] . However, the lack of a purely backpropagation-based approach has hampered the ability of the technology to tackle largescal","cbCaiuX7GiLLiKJY","https://ap.wps.com/l/cbCaiuX7GiLLiKJY","pdf",3733168,1,37,"English","en",105,"# Introduction\n## Main Contributions","[{\"question\":\"What problem does this paper address for thermodynamic AI hardware?\",\"answer\":\"Scalable and efficient training algorithms for large, general-purpose AI workloads on Ising-based thermodynamic hardware are currently limited.\"},{\"question\":\"How is the theoretical correspondence between Ising systems and neural inference used?\",\"answer\":\"The paper turns time-averaged behavior of high-temperature Gibbs-sampled Ising systems into a practical, scalable training method for deep convolutional networks.\"},{\"question\":\"What results and theory are provided regarding accuracy and inference cost?\",\"answer\":\"The models achieve strong CIFAR-10/CIFAR-100 accuracies under binary Gibbs sampling, and the paper develops and validates theory relating inference cost to accuracy while controlling autocorrelation times and enabling optimized inference schedules.\"}]",1784180748,93,{"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},"scaling-up-thermodynamic-ai-models","",{"@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/scaling-up-thermodynamic-ai-models/82474/",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 problem does this paper address for thermodynamic AI hardware?","Question",{"text":75,"@type":76},"Scalable and efficient training algorithms for large, general-purpose AI workloads on Ising-based thermodynamic hardware are currently limited.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the theoretical correspondence between Ising systems and neural inference used?",{"text":80,"@type":76},"The paper turns time-averaged behavior of high-temperature Gibbs-sampled Ising systems into a practical, scalable training method for deep convolutional networks.",{"name":82,"@type":73,"acceptedAnswer":83},"What results and theory are provided regarding accuracy and inference cost?",{"text":84,"@type":76},"The models achieve strong CIFAR-10/CIFAR-100 accuracies under binary Gibbs sampling, and the paper develops and validates theory relating inference cost to accuracy while controlling autocorrelation times and enabling optimized inference 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