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. 2020 Sep 22;11:4783. doi: 10.1038/s41467-020-18254-6

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — a Inferring the existence of unobserved edges (links). Left—the task: The agents had to indicate which of two nodes (pictures) has smaller number of links to the target. With only observed links, the number of links to the target was identical. Right—red edges indicates missing links on the graph. For example, the two nodes that are marked with light blue have the same number of observed links to the target node (marked with dark blue circle), while the number of links that connect these two nodes to the target is different on the complete graph. b When learning from pairs that were sampled randomly (not in succession) while some of the links (pairs) were never observed, simple associative models as learning transition matrix (DA) or simple SR (SR-online: learning using TD-SR⁴⁴, SR-A: calculating SR from the learnt transition matrix) could not infer the existence of the unobserved links and solve the task (it in fact solves it worse than chance). Agents that use a filtered SR representation (SRreg) could answer these questions better than chance. Shadows are the standard errors of the mean (SEM), the centre is the mean. c When learning from pairs that were sampled randomly (not in succession) while some of the links (pairs) were never observed), the basis set agent, that transfers abstract structural knowledge, was able to infer the structural form (Supplementary Fig. 2) and graph size correctly. d Further, the agent was able to infer the existence of links that were never observed and determined correctly, which of two pictures is closer to a target picture, according to the complete graph (green). The agent could do so even though the number of observed links between the two pictures and the target was identical (p(cor) corresponds to the average fraction of correct answers out of 40 questions in each block). When the agent was forced to infer a community structure (red), it answered these questions worse than chance. Shadows are the standard errors of the mean, the centre is the mean.