{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,12]],"date-time":"2025-07-12T22:48:03Z","timestamp":1752360483773},"reference-count":44,"publisher":"MIT Press","issue":"9","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,8,19]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay).<\/jats:p>","DOI":"10.1162\/neco_a_01693","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T20:28:47Z","timestamp":1722976127000},"page":"1886-1911","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":3,"title":["Efficient Hyperdimensional Computing With Spiking Phasors"],"prefix":"10.1162","volume":"36","author":[{"given":"Jeff","family":"Orchard","sequence":"first","affiliation":[{"name":"Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada jorchard@uwaterloo.ca"}]},{"given":"P. Michael","family":"Furlong","sequence":"additional","affiliation":[{"name":"Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada michael.furlong@uwaterloo.ca"}]},{"given":"Kathryn","family":"Simone","sequence":"additional","affiliation":[{"name":"Cheriton School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada kathryn.simone@uwaterloo.ca"}]}],"member":"281","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"issue":"1","key":"2024082018250882200_bib1","doi-asserted-by":"publisher","first-page":"5267","DOI":"10.1038\/s41467-018-07565-4","article-title":"Challenges hindering memristive neuromorphic hardware from going mainstream","volume":"9","author":"Adam","year":"2018","journal-title":"Nature Communications"},{"article-title":"Biologically-based neural representations enable fast online shallow reinforcement learning","year":"2022","author":"Bartlett","key":"2024082018250882200_bib2"},{"key":"2024082018250882200_bib3","doi-asserted-by":"publisher","DOI":"10.3389\/fninf.2013.00048","article-title":"Nengo: A Python tool for building large-scale functional brain models","volume":"7","author":"Bekolay","year":"2014","journal-title":"Frontiers in Neuroinformatics"},{"key":"2024082018250882200_bib4","first-page":"1","article-title":"Hyperdimensional computing using time-to-spike neuromorphic circuits","volume-title":"Proceedings of the International Joint Conference on Neural Networks","author":"Bent","year":"2022"},{"key":"2024082018250882200_bib5","first-page":"1898","article-title":"Parallelizing Legendre memory unit training","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Chilkuri","year":"2021"},{"journal-title":"Language modeling using LMUs: 10x better data efficiency or improved scaling compared to transformers","year":"2021","author":"Chilkuri","key":"2024082018250882200_bib6"},{"key":"2024082018250882200_bib7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.23919\/VLSICircuits52068.2021.9492385","article-title":"Lessons from Loihi: Progress in neuromorphic computing","volume-title":"Proceedings of the 2021 Symposium on VLSI Circuits","author":"Davies","year":"2021"},{"issue":"5","key":"2024082018250882200_bib8","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1109\/JPROC.2021.3067593","article-title":"Advancing neuromorphic computing with Loihi: A survey of results and outlook","volume":"109","author":"Davies","year":"2021","journal-title":"Proceedings of the IEEE"},{"article-title":"Accurate representation for spatial cognition using grid cells","year":"2019","author":"Dumont","key":"2024082018250882200_bib9"},{"article-title":"A model of path integration that connects neural and symbolic representation","year":"2022","author":"Dumont","key":"2024082018250882200_bib10"},{"year":"2003","author":"Eliasmith","key":"2024082018250882200_bib11"},{"key":"2024082018250882200_bib12","first-page":"1","article-title":"A framework for linking computations and rhythm-based timing patterns in neural firing, such as phase precession in hippocampal place cells","author":"Frady","year":"2018"},{"journal-title":"Computing on functions using randomized vector representations","year":"2021","author":"Frady","key":"2024082018250882200_bib13"},{"key":"2024082018250882200_bib14","first-page":"115","article-title":"Computing on functions using randomized vector representations (in brief)","volume-title":"ACM International Conference Proceeding Series","author":"Frady","year":"2022"},{"key":"2024082018250882200_bib15","doi-asserted-by":"publisher","first-page":"18050","DOI":"10.1073\/pnas.1902653116","article-title":"Robust computation with rhythmic spike patterns","volume":"116","author":"Frady","year":"2019","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"article-title":"Fractional binding in vector symbolic architectures as quasi-probability statements","year":"2022","author":"Furlong","key":"2024082018250882200_bib16"},{"key":"2024082018250882200_bib17","first-page":"133","article-title":"Vector symbolic architectures answer Jackendoff\u2019s challenges for cognitive neuroscience","volume-title":"Proceedings of the Joint International Conference on Cognitive Science","author":"Gayler","year":"2003"},{"journal-title":"Mamba: Linear-time sequence modeling with selective state spaces.","year":"2023","author":"Gu","key":"2024082018250882200_bib18"},{"year":"2021","author":"Gu","key":"2024082018250882200_bib19"},{"year":"2022","author":"Gu","key":"2024082018250882200_bib20"},{"key":"2024082018250882200_bib21","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s12559-009-9009-8","article-title":"Hyperdimensional computing: An introduction to computing in distributed representation with high-dimensional random vectors","volume":"1","author":"Kanerva","year":"2009","journal-title":"Cognitive Computation"},{"year":"2021","author":"Kleyko","key":"2024082018250882200_bib22"},{"issue":"9","key":"2024082018250882200_bib23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3558000","article-title":"A survey on hyperdimensional computing aka vector symbolic architectures, Part II Applications, cognitive models, and challenges","volume":"55","author":"Kleyko","year":"2023","journal-title":"ACM Computing Surveys"},{"article-title":"A neural representation of continuous space using fractional binding","year":"2019","author":"Komer","key":"2024082018250882200_bib24"},{"key":"2024082018250882200_bib25","first-page":"1","article-title":"Large associative memory problem in neurobiology and machine learning","volume-title":"Proceedings of the International Conference on Learning Representations","author":"Krotov","year":"2021"},{"key":"2024082018250882200_bib26","doi-asserted-by":"crossref","DOI":"10.1109\/BioCAS.2015.7348414","article-title":"High-dimensional computing with sparse vectors","author":"Laiho","year":"2015"},{"issue":"5985","key":"2024082018250882200_bib27","doi-asserted-by":"publisher","first-page":"1576","DOI":"10.1126\/science.1188210","article-title":"Development of the spatial representation system in the rat","volume":"328","author":"Langston","year":"2010","journal-title":"Science"},{"article-title":"Representing spatial relations with fractional binding","year":"2019","author":"Lu","key":"2024082018250882200_bib28"},{"key":"2024082018250882200_bib29","first-page":"584","article-title":"Phasor neural networks","volume-title":"Neural information processing systems","author":"Noest","year":"1988"},{"key":"2024082018250882200_bib30","doi-asserted-by":"crossref","DOI":"10.1145\/3589737.3605982","article-title":"Hyperdimensional computing with spiking-phasor neurons","author":"Orchard","year":"2023"},{"key":"2024082018250882200_bib31","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2013.00179","article-title":"Does the entorhinal cortex use the Fourier transform?","author":"Orchard","year":"2013"},{"key":"2024082018250882200_bib32","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1109\/72.377968","article-title":"Holographic reduced representations","volume":"6","author":"Plate","year":"1995","journal-title":"IEEE Transactions on Neural Networks"},{"year":"2003","author":"Plate","key":"2024082018250882200_bib33"},{"issue":"2","key":"2024082018250882200_bib34","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1109\/JETCAS.2016.2533298","article-title":"Neuromorphic computing based on emerging memory technologies","volume":"6","author":"Rajendran","year":"2016","journal-title":"IEEE Journal on Emerging and Selected Topics in Circuits and Systems"},{"year":"2022","author":"Renner","key":"2024082018250882200_bib35"},{"year":"2022","author":"Renner","key":"2024082018250882200_bib36"},{"issue":"5774","key":"2024082018250882200_bib37","doi-asserted-by":"publisher","first-page":"758","DOI":"10.1126\/science.1125572","article-title":"Conjunctive representation of position, direction, and velocity in entorhinal cortex","volume":"312","author":"Sargolini","year":"2006","journal-title":"Science"},{"key":"2024082018250882200_bib38","doi-asserted-by":"publisher","first-page":"4523","DOI":"10.1007\/s10462-021-10110-3","article-title":"A comparison of vector symbolic architectures","volume":"55","author":"Schlegel","year":"2022","journal-title":"Artificial Intelligence Review"},{"key":"2024082018250882200_bib39","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1007\/3-540-44581-1_27","article-title":"A generalized representer theorem","volume-title":"Proceedings of the Conference on Computational Learning Theory","author":"Sch\u00f6lkopf","year":"2001"},{"year":"2022","author":"Smith","key":"2024082018250882200_bib40"},{"key":"2024082018250882200_bib41","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.cogsys.2010.06.006","article-title":"A biologically realistic cleanup memory: Autoassociation in spiking neurons","volume":"12","author":"Stewart","year":"2011","journal-title":"Cognitive Systems Research"},{"key":"2024082018250882200_bib42","doi-asserted-by":"publisher","first-page":"e47314","DOI":"10.7554\/eLife.47314","article-title":"Brian 2, an intuitive and efficient neural simulator","volume":"8","author":"Stimberg","year":"2019","journal-title":"eLife"},{"year":"2019","author":"Voelker","key":"2024082018250882200_bib43"},{"key":"2024082018250882200_bib44","doi-asserted-by":"publisher","first-page":"16157","DOI":"10.1523\/JNEUROSCI.0712-11.2011","article-title":"Cosine directional tuning of theta cell burst frequencies: Evidence for spatial coding by oscillatory interference","volume":"31","author":"Welday","year":"2011","journal-title":"Journal of Neuroscience"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/36\/9\/1886\/2465954\/neco_a_01693.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/direct.mit.edu\/neco\/article-pdf\/36\/9\/1886\/2465954\/neco_a_01693.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T18:26:30Z","timestamp":1724178390000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/36\/9\/1886\/123688\/Efficient-Hyperdimensional-Computing-With-Spiking"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,19]]},"references-count":44,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,8,19]]},"published-print":{"date-parts":[[2024,8,19]]}},"URL":"https:\/\/doi.org\/10.1162\/neco_a_01693","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"type":"print","value":"0899-7667"},{"type":"electronic","value":"1530-888X"}],"subject":[],"published-other":{"date-parts":[[2024,9]]},"published":{"date-parts":[[2024,8,19]]}}}