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Learning accurate path integration in ring attractor models of the head direction system

Vafidis, Pantelis and Owald, David and D’Albis, Tiziano and Kempter, Richard (2022) Learning accurate path integration in ring attractor models of the head direction system. eLife, 11 . Art. No. e69841. ISSN 2050-084X. PMCID PMC9286743. doi:10.7554/eLife.69841.

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Ring attractor models for angular path integration have received strong experimental support. To function as integrators, head direction circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila head direction system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading in flies, and where the network remaps to integrate with different gains in rodents. Our model predicts that path integration requires self-supervised learning during a developmental phase, and proposes a general framework to learn to path-integrate with gain-1 even in architectures that lack the physical topography of a ring.

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URLURL TypeDescription Paper ItemCode ItemFiles required to reproduce the figures CentralArticle
Vafidis, Pantelis0000-0002-9768-0609
Owald, David0000-0001-7747-7884
D’Albis, Tiziano0000-0003-1585-1433
Kempter, Richard0000-0002-5344-2983
Alternate Title:Learning accurate path integration in a ring attractor model of the head direction system
Additional Information:© 2022, Vafidis et al. This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited. Preprinted: 12 March 2021; Received: 28 April 2021; Accepted: 17 June 2022; Published: 20 June 2022. We thank Raquel Suárez-Grimalt and Marcel Heim for helpful discussions and Louis Kang for comments on the manuscript. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation; SFB 1315 – project-ID 327654276 to RK and DO; and the Emmy Noether Programme 282979116 to DO and Germany´s Excellence Strategy – EXC-2049 – 390688087 to DO), the German Federal Ministry for Education and Research (BMBF; Grant 01GQ1705 to RK), and the Onassis Foundation (PV). The funding sources were not involved in study design, data collection and interpretation, or the decision to submit the work for publication. Author contributions: Pantelis Vafidis, Conceived the study, Performed analyses, Wrote the initial draft of the manuscript, Wrote the manuscript; David Owald, Supervised the research, Wrote the manuscript; Tiziano D'Albis, Conceived the study, Contributed to analyses, Supervised the research, Wrote the manuscript; Richard Kempter, Conceived the study, Supervised the research, Wrote the manuscript. The authors declare that no competing interests exist. Data availability: All code used in this work is available at, (copy archived at swh:1:rev:c6e354f80bf435114e577af70892db41c3ce5315). The files required to reproduce the figures can be found at
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB 1315
Deutsche Forschungsgemeinschaft (DFG)327654276
Deutsche Forschungsgemeinschaft (DFG)282979116
Deutsche Forschungsgemeinschaft (DFG)EXC-2049 – 390688087
Bundesministerium für Bildung und Forschung (BMBF)01GQ1705
Onassis FoundationUNSPECIFIED
Subject Keywords:path integration, head direction cells, recurrent neural networks, synaptic plasticity, compartmentalized neuron, self-supervised learning, predictive coding, inductive bias
PubMed Central ID:PMC9286743
Record Number:CaltechAUTHORS:20210419-171909265
Persistent URL:
Official Citation:Learning accurate path integration in ring attractor models of the head direction system. Vafidis et al. eLife 2022; 11:e69841. DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108763
Deposited By: Tony Diaz
Deposited On:22 Apr 2021 17:26
Last Modified:26 Jul 2022 20:33

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