{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T18:47:42Z","timestamp":1790621262493,"version":"4.1.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T00:00:00Z","timestamp":1740528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Commun Eng"],"DOI":"10.1038\/s44172-025-00360-2","type":"journal-article","created":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T16:25:04Z","timestamp":1740587104000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The logarithmic memristor-based Bayesian machine"],"prefix":"10.1038","volume":"4","author":[{"given":"Cl\u00e9ment","family":"Turck","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kamel-Eddine","family":"Harabi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien","family":"Pontlevy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Th\u00e9o","family":"Ballet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tifenn","family":"Hirtzlin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elisa","family":"Vianello","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2904-1327","authenticated-orcid":false,"given":"Rapha\u00ebl","family":"Laurent","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jacques","family":"Droulez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Bessi\u00e8re","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3777-5793","authenticated-orcid":false,"given":"Marc","family":"Bocquet","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Michel","family":"Portal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0295-1008","authenticated-orcid":false,"given":"Damien","family":"Querlioz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"360_CR1","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s11747-019-00710-5","volume":"48","author":"A Rai","year":"2020","unstructured":"Rai, A. Explainable AI: from black box to glass box. J. Acad. Mark. Sci. 48, 137\u2013141 (2020).","journal-title":"J. Acad. Mark. Sci."},{"key":"360_CR2","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1038\/s41928-018-0092-2","volume":"1","author":"D Ielmini","year":"2018","unstructured":"Ielmini, D. & Wong, H.-S. P. In-memory computing with resistive switching devices. Nat. Electron. 1, 333 (2018).","journal-title":"Nat. Electron."},{"key":"360_CR3","doi-asserted-by":"crossref","unstructured":"Spiga, S., Sebastian, A., Querlioz, D. & Rajendran, B. (eds). In Memristive Devices for Brain-Inspired Computing: From Materials, Devices, and Circuits to Applications\u2014Computational Memory, Deep Learning, and Spiking Neural Networks (Woodhead Publishing, 2020).","DOI":"10.1016\/B978-0-08-102782-0.00001-0"},{"key":"360_CR4","doi-asserted-by":"publisher","first-page":"768","DOI":"10.1038\/s41586-023-06337-5","volume":"620","author":"S Ambrogio","year":"2023","unstructured":"Ambrogio, S. et al. An analog-AI chip for energy-efficient speech recognition and transcription. Nature 620, 768\u2013775 (2023).","journal-title":"Nature"},{"key":"360_CR5","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-45670-9","volume":"15","author":"F Aguirre","year":"2024","unstructured":"Aguirre, F. et al. Hardware implementation of memristor-based artificial neural networks. Nat. Commun. 15, 1974 (2024).","journal-title":"Nat. Commun."},{"key":"360_CR6","doi-asserted-by":"crossref","unstructured":"Huang, Y. et al. Memristor-based hardware accelerators for artificial intelligence. Nat. Rev. Electr. Eng. 1, 286\u2013299 (2024).","DOI":"10.1038\/s44287-024-00037-6"},{"key":"360_CR7","first-page":"52","volume":"6","author":"K-E Harabi","year":"2023","unstructured":"Harabi, K.-E. et al. A memristor-based Bayesian machine. Nat. Electron. 6, 52\u201363 (2023).","journal-title":"Nat. Electron."},{"key":"360_CR8","doi-asserted-by":"crossref","unstructured":"Gong, T. et al. First demonstration of a Bayesian machine based on unified memory and random source achieved by 16-layer stacking 3d Fe-diode with high noise density and high area efficiency. In 2023 International Electron Devices Meeting (IEDM), 1\u20134 (IEEE, 2023).","DOI":"10.1109\/IEDM45741.2023.10413799"},{"key":"360_CR9","doi-asserted-by":"crossref","unstructured":"Jaynes, E. T. Probability Theory: The Logic of Science (Cambridge University Press, 2003).","DOI":"10.1017\/CBO9780511790423"},{"key":"360_CR10","doi-asserted-by":"crossref","unstructured":"Bessi\u00e8re, P., Mazer, E., Ahuactzin, J. M. & Mekhnacha, K. Bayesian Programming (CRC press, 2013).","DOI":"10.1201\/b16111"},{"key":"360_CR11","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1038\/nature14541","volume":"521","author":"Z Ghahramani","year":"2015","unstructured":"Ghahramani, Z. Probabilistic machine learning and artificial intelligence. Nature 521, 452\u2013459 (2015).","journal-title":"Nature"},{"key":"360_CR12","doi-asserted-by":"publisher","first-page":"1350","DOI":"10.1214\/15-AOAS848","volume":"9","author":"B Letham","year":"2015","unstructured":"Letham, B., Rudin, C., McCormick, T. H. & Madigan, D. Interpretable classifiers using rules and Bayesian analysis: building a better stroke prediction model. Ann. Appl. Stat. 9, 1350\u20131371 (2015).","journal-title":"Ann. Appl. Stat."},{"key":"360_CR13","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1109\/MDAT.2016.2573586","volume":"34","author":"A Pedram","year":"2017","unstructured":"Pedram, A., Richardson, S., Horowitz, M., Galal, S. & Kvatinsky, S. Dark memory and accelerator-rich system optimization in the dark silicon era. IEEE Des. Test. 34, 39\u201350 (2017).","journal-title":"IEEE Des. Test."},{"key":"360_CR14","doi-asserted-by":"crossref","unstructured":"Gaines, B. R. Stochastic computing systems. In Advances in Information Systems Science 37\u2013172 (Springer, 1969).","DOI":"10.1007\/978-1-4899-5841-9_2"},{"key":"360_CR15","first-page":"92","volume":"12","author":"A Alaghi","year":"2013","unstructured":"Alaghi, A. & Hayes, J. P. Survey of stochastic computing. ACM TECS 12, 92 (2013).","journal-title":"ACM TECS"},{"key":"360_CR16","first-page":"895","volume":"63","author":"JS Friedman","year":"2016","unstructured":"Friedman, J. S., Calvet, L. E., Bessi\u00e8re, P., Droulez, J. & Querlioz, D. Bayesian inference with Muller c-elements. IEEE Trans. Circuits Syst. I: Regul. Pap. 63, 895\u2013904 (2016).","journal-title":"IEEE Trans. Circuits Syst. I: Regul. Pap."},{"key":"360_CR17","doi-asserted-by":"crossref","unstructured":"Fernandes, H., Aslam, M. A., Lobo, J., Ferreira, J. F. & Dias, J. Bayesian inference implemented on FPGA with stochastic bitstreams for an autonomous robot. In 2016 26th International Conference on Field Programmable Logic and Applications (FPL), 1\u20134 (IEEE, 2016).","DOI":"10.1109\/FPL.2016.7577312"},{"key":"360_CR18","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1109\/TETC.2016.2609926","volume":"7","author":"M Faix","year":"2016","unstructured":"Faix, M., Laurent, R., Bessi\u00e8re, P., Mazer, E. & Droulez, J. Design of stochastic machines dedicated to approximate Bayesian inferences. IEEE Trans. Emerg. Top. Comput. 7, 60\u201366 (2016).","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"key":"360_CR19","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-017-14240-z","volume":"7","author":"Y Shim","year":"2017","unstructured":"Shim, Y., Chen, S., Sengupta, A. & Roy, K. Stochastic spin\u2013orbit torque devices as elements for Bayesian inference. Sci. Rep. 7, 14101 (2017).","journal-title":"Sci. Rep."},{"key":"360_CR20","doi-asserted-by":"publisher","first-page":"045101","DOI":"10.1063\/1.5021332","volume":"8","author":"R Faria","year":"2018","unstructured":"Faria, R., Camsari, K. Y. & Datta, S. Implementing Bayesian networks with embedded stochastic MRAM. AIP Adv. 8, 045101 (2018).","journal-title":"AIP Adv."},{"key":"360_CR21","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1109\/TCAD.2019.2897631","volume":"39","author":"X Jia","year":"2019","unstructured":"Jia, X. et al. Spinbis: spintronics-based Bayesian inference system with stochastic computing. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 39, 789\u2013802 (2019).","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"360_CR22","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.ijar.2019.05.007","volume":"112","author":"DH Hoe","year":"2019","unstructured":"Hoe, D. H. Bayesian inference using stochastic logic: a study of buffering schemes for mitigating autocorrelation. Int. J. Approx. Reason. 112, 4\u201321 (2019).","journal-title":"Int. J. Approx. Reason."},{"key":"360_CR23","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-020-72842-6","volume":"10","author":"P Debashis","year":"2020","unstructured":"Debashis, P. et al. Hardware implementation of Bayesian network building blocks with stochastic spintronic devices. Sci. Rep. 10, 16002 (2020).","journal-title":"Sci. Rep."},{"key":"360_CR24","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-33053-x","volume":"13","author":"Y Zheng","year":"2022","unstructured":"Zheng, Y. et al. Hardware implementation of Bayesian network based on two-dimensional memtransistors. Nat. Commun. 13, 5578 (2022).","journal-title":"Nat. Commun."},{"key":"360_CR25","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1109\/MCAS.2020.3027425","volume":"21","author":"L Sousa","year":"2021","unstructured":"Sousa, L. Nonconventional computer arithmetic circuits, systems and applications. IEEE Circuits Syst. Mag. 21, 6\u201340 (2021).","journal-title":"IEEE Circuits Syst. Mag."},{"key":"360_CR26","doi-asserted-by":"crossref","unstructured":"Turck, C. et al. Energy-efficient Bayesian inference using near-memory computation with memristors. In 2023 Design, Automation & Test in Europe Conference & Exhibition (DATE), 1\u20132 (IEEE, 2023).","DOI":"10.23919\/DATE56975.2023.10137312"},{"key":"360_CR27","doi-asserted-by":"crossref","unstructured":"Turck, C. et al. Bayesian in-memory computing with resistive memories. In 2023 International Electron Devices Meeting (IEDM) 1\u20134 (IEEE, 2023).","DOI":"10.1109\/IEDM45741.2023.10413773"},{"key":"360_CR28","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1109\/TC.2007.70791","volume":"57","author":"JN Coleman","year":"2008","unstructured":"Coleman, J. N. et al. The European logarithmic microprocessor. IEEE Trans. Comput. 57, 532\u2013546 (2008).","journal-title":"IEEE Trans. Comput."},{"key":"360_CR29","doi-asserted-by":"crossref","unstructured":"Popoff, Y. et al. High-efficiency logarithmic number unit design based on an improved cotransformation scheme. In 2016 Design, Automation & Test in Europe Conference & Exhibition (DATE) 1387\u20131392 (IEEE, 2016).","DOI":"10.3850\/9783981537079_0174"},{"key":"360_CR30","doi-asserted-by":"crossref","unstructured":"Chang, Y.-F. et al. eNVM RRAM reliability performance and modeling in 22FFL FinFET technology. In 2020 IEEE International Reliability Physics Symposium (IRPS) 1\u20134 (IEEE, 2020).","DOI":"10.1109\/IRPS45951.2020.9128359"},{"key":"360_CR31","doi-asserted-by":"crossref","unstructured":"Wu, C.-Y. et al. Emerging memory RRAM embedded in 12FFC FinFET technology for industrial applications. In 2023 International Electron Devices Meeting (IEDM) 1\u20134 (IEEE, 2023).","DOI":"10.1109\/IEDM45741.2023.10413775"},{"key":"360_CR32","doi-asserted-by":"crossref","unstructured":"Ly, D. R. B. et al. Role of synaptic variability in resistive memory-based spiking neural networks with unsupervised learning. J. Phys. D: Appl. Phys. 51, 444002 (2018).","DOI":"10.1088\/1361-6463\/aad954"},{"key":"360_CR33","doi-asserted-by":"publisher","first-page":"2200145","DOI":"10.1002\/aisy.202200145","volume":"4","author":"E Esmanhotto","year":"2022","unstructured":"Esmanhotto, E. et al. Experimental demonstration of multilevel resistive random access memory programming for up to two months stable neural networks inference accuracy. Adv. Intell. Syst. 4, 2200145 (2022).","journal-title":"Adv. Intell. Syst."},{"key":"360_CR34","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-024-44766-6","volume":"15","author":"F Jebali","year":"2024","unstructured":"Jebali, F. et al. Powering AI at the edge: a robust, memristor-based binarized neural network with near-memory computing and miniaturized solar cell. Nat. Commun. 15, 741 (2024).","journal-title":"Nat. Commun."},{"key":"360_CR35","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.3389\/fnins.2019.01383","volume":"13","author":"T Hirtzlin","year":"2020","unstructured":"Hirtzlin, T. et al. Digital biologically plausible implementation of binarized neural networks with differential hafnium oxide resistive memory arrays. Front. Neurosci. 13, 1383 (2020).","journal-title":"Front. Neurosci."},{"key":"360_CR36","doi-asserted-by":"publisher","first-page":"3784","DOI":"10.1109\/TMAG.2009.2024325","volume":"45","author":"W Zhao","year":"2009","unstructured":"Zhao, W., Chappert, C., Javerliac, V. & Noziere, J.-P. High speed, high stability and low power sensing amplifier for MTJ\/CMOS hybrid logic circuits. IEEE Trans. Magn. 45, 3784\u20133787 (2009).","journal-title":"IEEE Trans. Magn."},{"key":"360_CR37","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1109\/TCSII.2014.2319692","volume":"61","author":"W Zhao","year":"2014","unstructured":"Zhao, W. et al. Synchronous non-volatile logic gate design based on resistive switching memories. IEEE Trans. Circuits Syst. I: Regul. Pap. 61, 443\u2013454 (2014).","journal-title":"IEEE Trans. Circuits Syst. I: Regul. Pap."},{"key":"360_CR38","doi-asserted-by":"publisher","unstructured":"Devuyst, S., Dutoit, T. & Kerkhofs, M. The dreams databases and assessment algorithm. [data set]. Zenodo https:\/\/doi.org\/10.5281\/zenodo.2650142 (Zenodo, Geneva, Switzerland, 2005).","DOI":"10.5281\/zenodo.2650142"},{"key":"360_CR39","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-43317-9","volume":"14","author":"D Bonnet","year":"2023","unstructured":"Bonnet, D. et al. Bringing uncertainty quantification to the extreme-edge with memristor-based Bayesian neural networks. Nat. Commun. 14, 7530 (2023).","journal-title":"Nat. Commun."}],"container-title":["Communications Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s44172-025-00360-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s44172-025-00360-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s44172-025-00360-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,26]],"date-time":"2025-02-26T16:25:13Z","timestamp":1740587113000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s44172-025-00360-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,26]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["360"],"URL":"https:\/\/doi.org\/10.1038\/s44172-025-00360-2","relation":{},"ISSN":["2731-3395"],"issn-type":[{"value":"2731-3395","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,26]]},"assertion":[{"value":"21 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Damien Querlioz is an Editorial Board Member for Communications Engineering but was not involved in the editorial review of, nor the decision to publish this article. All other authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"35"}}