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To do so, these networks produce localized bumps of activity that move coherently in response to velocity inputs. In the brain, continuous attractors are believed to underlie grid cells and head direction cells, which maintain periodic representations of position and orientation, respectively. These representations can be achieved with any number of activity bumps, and the consequences of having more or fewer bumps are unclear. We address this knowledge gap by constructing 1D ring attractor networks with different bump numbers and characterizing their responses to three types of noise: fluctuating inputs, spiking noise, and deviations in connectivity away from ideal attractor configurations. Across all three types, networks with more bumps experience less noise-driven deviations in bump motion. This translates to more robust encodings of linear coordinates, like position, assuming that each neuron represents a fixed length no matter the bump number. Alternatively, we consider encoding a circular coordinate, like orientation, such that the network distance between adjacent bumps always maps onto 360 degrees. Under this mapping, bump number does not significantly affect the amount of error in the coordinate readout. Our simulation results are intuitively explained and quantitatively matched by a unified theory for path integration and noise in multi-bump networks. Thus, to suppress the effects of biologically relevant noise, continuous attractor networks can employ more bumps when encoding linear coordinates; this advantage disappears when encoding circular coordinates. Our findings provide motivation for multiple bumps in the mammalian grid network.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010547","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T13:53:49Z","timestamp":1665410029000},"page":"e1010547","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":9,"title":["Multiple bumps can enhance robustness to noise in continuous attractor networks"],"prefix":"10.1371","volume":"18","author":[{"given":"Raymond","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5702-2740","authenticated-orcid":true,"given":"Louis","family":"Kang","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,10,10]]},"reference":[{"issue":"2","key":"pcbi.1010547.ref001","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BF00337259","article-title":"Dynamics of pattern formation in lateral-inhibition type neural fields","volume":"27","author":"Si Amari","year":"1977","journal-title":"Biol Cybern"},{"issue":"3","key":"pcbi.1010547.ref002","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF00336965","article-title":"A mathematical theory of visual hallucination patterns","volume":"34","author":"GB Ermentrout","year":"1979","journal-title":"Biol Cybern"},{"issue":"2","key":"pcbi.1010547.ref003","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/BF01212280","article-title":"On the concept of attractor","volume":"99","author":"J Milnor","year":"1985","journal-title":"Commun Math Phys"},{"issue":"2","key":"pcbi.1010547.ref004","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF00320393","article-title":"A proposed neural network for the integrator of the oculomotor system","volume":"49","author":"SC Cannon","year":"1983","journal-title":"Biol Cybern"},{"issue":"2","key":"pcbi.1010547.ref005","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1162\/jocn.1991.3.2.190","article-title":"Dead reckoning, landmark learning, and the sense of direction: a neurophysiological and computational hypothesis","volume":"3","author":"BL McNaughton","year":"1991","journal-title":"J Cognit Neurosci"},{"issue":"23","key":"pcbi.1010547.ref006","doi-asserted-by":"crossref","first-page":"13339","DOI":"10.1073\/pnas.93.23.13339","article-title":"How the brain keeps the eyes still","volume":"93","author":"HS Seung","year":"1996","journal-title":"Proc Natl Acad Sci USA"},{"issue":"2","key":"pcbi.1010547.ref007","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1523\/JNEUROSCI.10-02-00420.1990","article-title":"Head-direction cells recorded from the postsubiculum in freely moving rats. 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