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We propose construction rules such that an attractor network may implement an arbitrary finite state machine (FSM), where states and stimuli are represented by high-dimensional random vectors and all state transitions are enacted by the attractor network\u2019s dynamics. Numerical simulations show the capacity of the model, in terms of the maximum size of implementable FSM, to be linear in the size of the attractor network for dense bipolar state vectors and approximately quadratic for sparse binary state vectors. We show that the model is robust to imprecise and noisy weights, and so a prime candidate for implementation with high-density but unreliable devices. By endowing attractor networks with the ability to emulate arbitrary FSMs, we propose a plausible path by which FSMs could exist as a distributed computational primitive in biological neural networks.<\/jats:p>","DOI":"10.1162\/neco_a_01638","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T20:55:50Z","timestamp":1709931350000},"page":"549-595","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":11,"title":["Vector Symbolic Finite State Machines in Attractor Neural Networks"],"prefix":"10.1162","volume":"36","author":[{"given":"Madison","family":"Cotteret","sequence":"first","affiliation":[{"name":"Micro- and Nanoelectronic Systems, Institute of Micro- and Nanotechnologies (IMN) MacroNano, Technische Universit\u00e4t Ilmenau, 98693 Ilmenau, Germany"},{"name":"Bio-Inspired Circuits and Systems Lab, Zernike Institute for Advanced Materials, and Groningen Cognitive Systems and Materials Center, University of Groningen, 9747 AG\u00a0Groningen, Netherlands m.cotteret@rug.nl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hugh","family":"Greatorex","sequence":"additional","affiliation":[{"name":"Bio-Inspired Circuits and Systems Lab, Zernike Institute for Advanced Materials, and Groningen Cognitive Systems and Materials Center, University of Groningen, 9747 AG\u00a0Groningen, Netherlands h.r.greatorex@rug.nl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Ziegler","sequence":"additional","affiliation":[{"name":"Micro- and Nanoelectronic Systems, Institute of Micro- and Nanotechnologies (IMN) MacroNano, Technische Universit\u00e4t Ilmenau, 98693 Ilmenau, Germany martin.ziegler@tu-ilmenau.de"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elisabetta","family":"Chicca","sequence":"additional","affiliation":[{"name":"Bio-Inspired Circuits and Systems Lab, Zernike Institute for Advanced Materials, and Groningen Cognitive Systems and Materials Center, University of Groningen, 9747 AG\u00a0Groningen, Netherlands e.chicca@rug.nl"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"issue":"1","key":"2024032521541729800_bib1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms3072","article-title":"Pattern classification by memristive crossbar circuits using ex situ and in situ training","volume":"4","author":"Alibart","year":"2013","journal-title":"Nature Communications"},{"key":"2024032521541729800_bib2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.5.931","article-title":"An algebraic framework to represent finite state machines in single-layer recurrent neural networks","volume":"7","author":"Alqu\u00e9zar","year":"1995","journal-title":"Neural Computation"},{"issue":"6","key":"2024032521541729800_bib3","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/0893-6080(89)90043-9","article-title":"Characteristics of sparsely encoded associative memory","volume":"2","author":"Amari","year":"1989","journal-title":"Neural Networks"},{"issue":"7","key":"2024032521541729800_bib4","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1073\/pnas.85.7.2141","article-title":"Neural networks counting chimes","volume":"85","author":"Amit","year":"1988","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"2024032521541729800_bib5","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511623257","volume-title":"Modeling brain function: The world of attractor neural network.","author":"Amit","year":"1989"},{"issue":"5","key":"2024032521541729800_bib6","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1162\/neco.1994.6.5.957","article-title":"Learning in neural networks with material synapses","volume":"6","author":"Amit","year":"1994","journal-title":"Neural Computation"},{"issue":"6","key":"2024032521541729800_bib7","doi-asserted-by":"publisher","first-page":"4693","DOI":"10.1007\/s11063-021-10562-2","article-title":"A survey of encoding techniques for signal processing in spiking neural networks","volume":"53","author":"Auge","year":"2021","journal-title":"Neural Processing Letters"},{"issue":"8","key":"2024032521541729800_bib8","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1145\/359576.359579","article-title":"Can programming be liberated from the von Neumann style? 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