[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123929-en":3,"doc-seo-123929-105":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":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},123929,5909877438554,"Maeve","https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272",8,"Research & Report","Probabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and Neuromorphic Computing","As traditional CPU speeds struggle to match rising big-data demands, new computing paradigms are needed for NP-hard optimization and learning workloads. This dissertation develops parallelized algorithms and probabilistic hardware architectures based on Ising-model formulations, using Boltzmann Machines. The work explores machine-learning techniques, structured algorithm-to-hardware mapping, and hybrid approaches. It demonstrates promising solutions for 16-bit integer factorization, 3-SAT, and LDPC codes, and accelerates MAX-CUT on FPGA, GPU, and TPU. Finally, it presents PASS, a clock-free neuromorphic Ising-based sampler implemented in fully CMOS.","UC Berkeley  \nUC Berkeley Electronic Theses and Dissertations  \nTitle  \nProbabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and Neuromorphic Computing  \nPermalink  \n[https://escholarship.org/uc/item/15f6p94m](https://escholarship.org/uc/item/15f6p94m)  \nAuthor  \nPatel, Saavan Kanu  \nPublication Date  \n2023  \nPeer reviewed|Thesis/dissertation  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nProbabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and  \nNeuromorphic Computing  \nBy  \nSaavan K Patel  \nA dissertation submitted in partial satisfaction of the requirements for the degree of  \nDoctor of Philosophy  \nin  \nEngineering-Electrical Engineering and Computer Sciences  \nin the  \nGraduate Division  \nof the  \nUniversity of California, Berkeley  \nCommittee in charge:  \nProfessor Sayeef Salahuddin, Chair  \nProfessor Jan Rabaey  \nProfessor Bruno Olshausen  \nSummer 2023  \nProbabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and  \nNeuromorphic Computing  \nCopyright 2023  \nby  \nSaavan K Patel  \n1  \nAbstract  \nProbabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and  \nNeuromorphic Computing  \nby  \nSaavan K Patel  \nDoctor of Philosophy in Engineering-Electrical Engineering and Computer Sciences  \nUniversity of California, Berkeley  \nProfessor Sayeef Salahuddin, Chair  \nAs the demand for big data increases and the speed of traditional CPUs cannot keep pace, new computing paradigms and architectures are needed to meet the demands for our data hungry world. To keep pace with this, Ising Computing and probabilistic computing have emerged as a method to solve NP-Hard optimization problems (such as logistics, place and route in circuits), perform Machine Learning training and inference, model decision making in animal brains, and much more.  \nThis work centers around parallelized computing algorithms and hardware based on probabilistic formulations of the Ising Model, known as Boltzmann Machines. The algorithms demonstrated use techniques from machine learning, structured algorithmic mapping, and mixed approaches. Using these algorithms we demonstrate potential solutions to 16 bit Integer Factorization, 3-SAT, LDPC Codes and scalable techniques for solutions to a variety of problems.  \nWe map these algorithms to a variety of hardware, from small and medium scale (≈ 1000sof nodes) FPGA approaches to large and ultra large (> 100 , 000 nodes) scale on GPU and TPU instances. These accelerated instances demonstrate state of the art performance on the MAX-CUT benchmark problem.  \nWe finally demonstrate the Parallel Asynchronous Stochastic Sampler (PASS), a neuromorphic, clock-free accelerator that mimics brain-like asynchronous computation using the Ising Model. This has the potential for orders of magnitude speed increase over traditional methods for solving these problems while being the first on-chip, fully CMOS, demonstration of such an architecture.  \ni  \nTo my family  \nFor their unwavering support, compassion, and understanding  \nand to Divya  \nfor helping me through the hard times, and celebrating every small achievement  \nii  \nContents  \nContents ii  \nList of Figures iv  \nList of Tables xiv  \n1 Introduction, Ising Model Computation 1  \n1.1 Introduction .................................... 1  \n1.2 The Ising Model .................................. 1  \n1.3 Hardware Accelerators for Ising Model Problems ................ 4  \n2 Stochastic Sampling Methods 7  \n2.1 Introduction .................................... 7  \n2.2 Monte Carlo Methods for sampling ....................... 8  \n2.3 Markov Chains .................................. 9  \n2.4 Markov Chain Monte Carlo Sampling ...................... 10  \n2.5 The Restricted Boltzmann Machine (RBM) for Parallelized Sampling .... 16  \n3 Inverse Logic Algorithms 18  \n3.1 Introduction .................................... 18  \n3.2","cbCaiczwddS92X1Y","https://ap.wps.com/l/cbCaiczwddS92X1Y","pdf",5499485,1,132,"English","en",105,"# 1 Introduction, Ising Model Computation\n## 1.1 Introduction\n## 1.2 The Ising Model\n## 1.3 Hardware Accelerators for Ising Model Problems\n# 2 Stochastic Sampling Methods\n## 2.1 Introduction\n## 2.2 Monte Carlo Methods for sampling\n## 2.3 Markov Chains\n## 2.4 Markov Chain Monte Carlo Sampling\n## 2.5 The Restricted Boltzmann Machine (RBM) for Parallelized Sampling\n# 3 Inverse Logic Algorithms\n## 3.1 Introduction\n## 3.2 The Restricted Boltzmann Machine\n## 3.3 Contrastive Divergence Learning\n## 3.4 Merging RBMs\n## 3.5 Mathematical details of Merging RBMs\n## 3.6 Convergence Theorems of Merged RBMs\n## 3.7 Low Density Parity Check Codes and Communications Algorithms\n# 4 Direct Mapping Algorithms\n## 4.1 Introduction\n## 4.2 MaxCUT problems\n## 4.3 Effect of Sampler Parameters on Algorithm Performance\n## 4.4 Scaling and Connectivity\n## 4.5 Effect of C and graph embedding on algorithm performance\n# 5 FPGA based RBM accelerators\n## 5.1 Introduction\n## 5.2 RBM Inference Accelerator for Inverse Logic\n## 5.3 Performance Analysis\n## 5.4 RBM Accelerator for MaxCut and General Problems\n## 5.5 Scaled RBM on FPGA Accelerator\n## 5.6 Conclusion\n# 6 TPU and GPU based RBM Accelerators\n## 6.1 Introduction and Motivation\n## 6.2 Parallelized MCMC\n## 6.3 Programming Paradigms\n## 6.4 Results and Discussion\n## 6.5 Conclusion\n# 7 PASS: The Parallel Asynchronous Stochastic Sampler\n## 7.1 Introduction and Problem Statement\n## 7.2 Relation to State of the Art\n## 7.3 Design of the PASS Accelerator\n## 7.4 Results and Applications\n## 7.5 Conclusion\n# 8 Conclusion and Future Work\n## 8.1 Chapter Summaries and Takeaways","[{\"question\":\"What computing approach does the dissertation focus on to address NP-hard optimization and learning demands?\",\"answer\":\"It focuses on probabilistic computing based on the Ising model, implemented through Boltzmann Machines, with parallelized algorithms and hardware architectures that accelerate optimization and learning workloads.\"},{\"question\":\"Which algorithms and problem domains are demonstrated in the work?\",\"answer\":\"The work demonstrates solutions for 16-bit integer factorization, 3-SAT, and LDPC codes, using techniques from machine learning, structured mapping, and hybrid algorithmic approaches.\"},{\"question\":\"How are the probabilistic Ising/Boltzmann methods mapped to hardware, and what benchmarks are emphasized?\",\"answer\":\"The dissertation maps the algorithms to FPGA, GPU, and TPU implementations, including large-scale instances. It highlights state-of-the-art performance on the MAX-CUT benchmark and analyzes how sampler parameters and scaling affect performance.\"}]","Probabilistic Ising Architectures for Combinatorial Optimization, Machine Learning and Neuromorphic Computing | PDF",1785819287,333,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"probabilistic-ising-architectures-for-combinatorial-optimization-machine-learning-and-neuromorphic-computing","",{"@graph":36,"@context":86},[37,54,69],{"@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/probabilistic-ising-architectures-for-combinatorial-optimization-machine-learning-and-neuromorphic-computing/123929/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"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","2026-08-05","2026-08-04",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 computing approach does the dissertation focus on to address NP-hard optimization and learning demands?","Question",{"text":76,"@type":77},"It focuses on probabilistic computing based on the Ising model, implemented through Boltzmann Machines, with parallelized algorithms and hardware architectures that accelerate optimization and learning workloads.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which algorithms and problem domains are demonstrated in the work?",{"text":81,"@type":77},"The work demonstrates solutions for 16-bit integer factorization, 3-SAT, and LDPC codes, using techniques from machine learning, structured mapping, and hybrid algorithmic approaches.",{"name":83,"@type":74,"acceptedAnswer":84},"How are the probabilistic Ising/Boltzmann methods mapped to hardware, and what benchmarks are emphasized?",{"text":85,"@type":77},"The dissertation maps the algorithms to FPGA, GPU, and TPU implementations, including large-scale instances. It highlights state-of-the-art performance on the MAX-CUT benchmark and analyzes how sampler parameters and scaling affect performance.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]