Attractor and integrator networks in the brain — part 10/10

Cleaned-text code points [129522, 140478). Bibliography omitted here; source.md includes it.

[219] HS Kudrimoti, CA Barnes, and BL McNaughton. Reactivation of hippocampal cell assem-
blies: effects of behavioral state, experience, and eeg dynamics. J Neurosci, 19(10):4090–
101, May 15 1999.
[220] Thomas J Davidson, Fabian Kloosterman, and Matthew A Wilson. Hippocampal replay of
extended experience. Neuron, 63(4):497–507, Aug 2009.
[221] Brad E Pfeiffer and David J Foster . Hippocampal place-cell sequences depict future paths
to remembered goals. Nature, 497(7447):74–9, May 2013.
[222] Daniel W Moran and Andrew B Schwartz. Motor cortical representation of speed and
direction during reaching. Journal of neurophysiology , 82(5):2676–2692, 1999.
[223] Krishna V Shenoy , Maneesh Sahani, and Mark M Churchland. Cortical control of arm
movements: a dynamical systems perspective. Annual review of neuroscience , 36:337–359,
2013.
[224] Juan A Gallego, Matthew G Perich, Stephanie N Naufel, Christian Ethier , Sara A Solla, and
Lee E Miller . Cortical population activity within a preserved neural manifold underlies
multiple motor behaviors. Nature communications, 9(1):1–13, 2018.
[225] Juan A Gallego, Matthew G Perich, Raeed H Chowdhury , Sara A Solla, and Lee E Miller .
Long-term stability of cortical population dynamics underlying consistent behavior . Nature
Neuroscience, pages 1–11, 2020.
[226] Michael Wehr and Gilles Laurent. Odour encoding by temporal sequences of firing in os-
cillating neural assemblies. Nature, 384(6605):162–166, 1996.
[227] Uri Rokni and Haim Sompolinsky . How the brain generates movement.Neural computation,
24(2):289–331, 2012.
[228] Dmitry Kobak, Wieland Brendel, Christos Constantinidis, Claudia E Feierstein, Adam
Kepecs, Zachary F Mainen, Xue-Lian Qi, Ranulfo Romo, Naoshige Uchida, and Chris-
tian K Machens. Demixed principal component analysis of neural population data. Elife,
5:e10989, 2016.
[229] Mirko Klukas, Marcus Lewis, and Ila Fiete. Efficient and flexible representation of higher-
dimensional cognitive variables with grid cells. PLoS Comput Biol , 16(4):e1007796, 04
2020.
[230] Andrea Banino, Caswell Barry , Benigno Uria, Charles Blundell, Timothy Lillicrap, Pi-
otr Mirowski, Alexander Pritzel, Martin J Chadwick, Thomas Degris, Joseph Modayil,
et al. V ector-based navigation using grid-like representations in artificial agents. Nature,
557(7705):429–433, 2018.
[231] James C R Whittington, Timothy H Muller , Shirley Mark, Guifen Chen, Caswell Barry ,
Neil Burgess, and Timothy E J Behrens. The tolman-eichenbaum machine: Unifying
space and relational memory through generalization in the hippocampal formation. Cell,
183(5):1249–1263.e23, Nov 2020.
[232] Honi Sanders, Matthew A Wilson, and Samuel J Gershman. Hippocampal remapping as
hidden state inference. Elife, 9, 06 2020.
40

[233] Nathaniel J Killian, Michael J Jutras, and Elizabeth A Buffalo. A map of visual space in the
primate entorhinal cortex. Nature, 491(7426):761–764, 2012.
[234] Dmitriy Aronov , Rhino Nevers, and David W T ank. Mapping of a non-spatial dimension by
the hippocampal–entorhinal circuit. Nature, 543(7647):719–722, 2017.
[235] Alexandra O Constantinescu, Jill X O’Reilly , and Timothy EJ Behrens. Organizing concep-
tual knowledge in humans with a gridlike code. Science, 352(6292):1464–1468, 2016.
[236] Elizabeth Gardner . The space of interactions in neural network models. Journal of physics
A: Mathematical and general , 21(1):257, 1988.
[237] Robert J McEliece, Edward C Posner , Eugene R Rodemich, and Santosh S V enkatesh. The
capacity of the Hopfield associative memory . Information Theory, IEEE Transactions on ,
33(4):461–482, 1987.
[238] Daniel J Amit, Hanoch Gutfreund, and H Sompolinsky . Statistical mechanics of neural
networks near saturation. Annals of Physics , 173(1):30–67, 1987.
[239] Y aser S Abu-Mostafa and J St Jacques. Information capacity of the hopfield model. Infor-
mation Theory, IEEE Transactions on , 31(4):461–464, 1985.
[240] Hanne Stensola, T or Stensola, Trygve Solstad, Kristian Frøland, May-Britt Moser , and Ed-
vard I Moser . The entorhinal grid map is discretized. Nature, 492(7427):72, 2012.
[241] Christopher J Hillar and Ngoc M Tran. Robust exponential memory in hopfield networks.
The Journal of Mathematical Neuroscience , 8(1):1, 2018.
[242] IR Fiete, DS Schwab, and Ngoc Mai Tran. A binary hopfield network with information rate
and applications to grid cell decoding. In Proceedings of the 2nd Workshop on Biological
Distributed Algorithms, 2014.
[243] Noga Mosheiff and Y oram Burak. V elocity coupling of grid cell modules enables stable
embedding of a low dimensional variable in a high dimensional neural attractor . eLife, 8,
2019.
[244] Vincent Gripon and Claude Berrou. Sparse neural networks with large learning diversity .
IEEE transactions on neural networks , 22(7):1087–1096, 2011.
[245] Samuel P Muscinelli, Wulfram Gerstner , and Johanni Brea. Exponentially long orbits in
hopfield neural networks. Neural computation, 29(2):458–484, 2017.
[246] A. Mathis, A. Herz, and M. Stemmler . Optimal population codes for space: grid cells out-
perform place cells. Neural Comp., 24:2280–2317, 2012.
[247] Rishidev Chaudhuri and Ila Fiete. Bipartite expander hopfield networks as self-decoding
high-capacity error correcting codes. In H. Wallach, H. Larochelle, A. Beygelzimer ,
F . dAlché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing
Systems, volume 32, 2019.
[248] Man Yi Yim, Lorenzo A Sadun, Ila R Fiete, and Thibaud T aillefumier . Place-cell capacity
and volatility with grid-like inputs. Elife, 10, May 2021.
41

[249] H. C. LONGUET -HIGGINS. Holographic model of temporal recall. Nature, 217(5123):104–
104, jan 1968.
[250] A Korpel. Gabor: frequency , time, and memory . Appl Opt, 21(20):3624–32, Oct 1982.
[251] Niru Maheswaranathan, Alex H Williams, Matthew D Golub, Surya Ganguli, and David
Sussillo. Reverse engineering recurrent networks for sentiment classification reveals line
attractor dynamics. Advances in neural information processing systems , 32:15696, 2019.
[252] I. Kanitscheider and I. R. Fiete. Training recurrent networks to generate hypotheses about
how the brain solves hard navigation problems. Advances in Neural Information Processing
Systems (NeurIPS), 2017.
[253] Ingmar Kanitscheider and Ila Fiete. Emergence of dynamically reconfigurable hippocampal
responses by learning to perform probabilistic spatial reasoning. bioRxiv, page 231159,
2017.
[254] Ben Sorscher , Gabriel Mel, Surya Ganguli, and Samuel Ocko. A unified theory for the
origin of grid cells through the lens of pattern formation. In Advances in Neural Information
Processing Systems, pages 10003–10013, 2019.
[255] Rylan Schaeffer , Mikail Khona, Leenoy Meshulam, Ila Rani Fiete, et al. Reverse-engineering
recurrent neural network solutions to a hierarchical inference task for mice. bioRxiv, 2020.
[256] Xiao-Jing Wang. Synaptic basis of cortical persistent activity: the importance of nmda
receptors to working memory . Journal of Neuroscience , 19(21):9587–9603, 1999.
[257] G Bard Ermentrout and Nancy Kopell. Multiple pulse interactions and averaging in systems
of coupled neural oscillators. Journal of Mathematical Biology , 29(3):195–217, 1991.
[258] Martin Boerlin, Christian K Machens, and Sophie Denève. Predictive coding of dynamical
variables in balanced spiking networks. PLoS computational biology , 9(11), 2013.
[259] E Paxon Frady and Friedrich T Sommer . Robust computation with rhythmic spike patterns.
Proceedings of the National Academy of Sciences , 116(36):18050–18059, 2019.
[260] Ran Darshan and Alexander Rivkind. Learning to represent continuous variables in hetero-
geneous neural networks. bioRxiv, 2021.
[261] D. B. Arnold and D. A. Robinson. A learning network model of the neural integrator of the
oculomotor system. Biological Cybernetics, 64(6):447–454, Apr 1991.
[262] Richard H. R. Hahnloser , H. Sebastian Seung, and Jean-Jacques Slotine. Permitted and
forbidden sets in symmetric threshold-linear networks. Neural Computation , 15(3):621–
638, 2010/12/06 2003/03/01.
[263] H Sebastian Seung. Learning continuous attractors in recurrent networks. In Advances in
neural information processing systems , pages 654–660, 1998.
[264] V alerio Mante, David Sussillo, Krishna V Shenoy , and William T Newsome. Context-
dependent computation by recurrent dynamics in prefrontal cortex. Nature, 503(7474):78–
84, Nov 2013.
42

[265] Christopher J. Cueva and Xue-Xin Wei. Emergence of grid-like representations by training
recurrent neural networks to perform spatial localization. In International Conference on
Learning Representations, 2018.
[266] Logan Grosenick, James H Marshel, and Karl Deisseroth. Closed-loop and activity-guided
optogenetic control. Neuron, 86(1):106–39, Apr 2015.
[267] Peter E Latham, Sophie Deneve, and Alexandre Pouget. Optimal computation with attractor
networks. J Physiol Paris , 97(4-6):683–694, 2003.
[268] Timothy J. Buschman Flora Bouchacourt. A flexible model of working memory . bioRxiv
doi.org/10.1101/407700, 2018.
[269] Andrea Hasenstaub, Robert N S Sachdev , and David A McCormick. State changes rapidly
modulate cortical neuronal responsiveness. J Neurosci, 27(36):9607–22, Sep 2007.
[270] E Aksay , R Baker , H S Seung, and D W T ank. Anatomy and discharge properties of pre-
motor neurons in the goldfish medulla that have eye-position signals during fixations. J
Neurophysiol, 84(2):1035–49, Aug 2000.
[271] Emile Godaux, Philippe Mettens, and Guy Chéron. Differential effect of injections of kainic
acid into the prepositus and the vestibular nuclei of the cat. The Journal of physiology ,
472(1):459–482, 1993.
[272] Guy Major , Robert Baker , Emre Aksay , H Sebastian Seung, and David W T ank. Plasticity
and tuning of the time course of analog persistent firing in a neural integrator . Proc Natl
Acad Sci U S A , 101(20):7745–50, May 2004.
[273] C Shan Xu, Michal Januszewski, Zhiyuan Lu, Shin-ya T akemura, Kenneth Hayworth, Gary
Huang, Kazunori Shinomiya, Jeremy Maitin-Shepard, David Ackerman, Stuart Berg, et al.
A connectome of the adult drosophila central brain. bioRxiv, 2020.
[274] Yi Gu, Sam Lewallen, Amina A Kinkhabwala, Cristina Domnisoru, Kijung Y oon, Jeffrey L
Gauthier , Ila R Fiete, and David W T ank. A map-like micro-organization of grid cells in the
medial entorhinal cortex. Cell, 175(3):736–750.e30, Oct 2018.
[275] Alexei A Koulakov and Dmitri B Chklovskii. Orientation preference patterns in mammalian
visual cortex: a wire length minimization approach. Neuron, 29(2):519–527, 2001.
[276] T om J Wills, Francesca Cacucci, Neil Burgess, and John O’Keefe. Development of the hip-
pocampal cognitive map in preweanling rats. Science, 328(5985):1573–1576, Jun 2010.
[277] Rosamund F Langston, James A Ainge, Jonathan J Couey , Cathrin B Canto, T ale L Bjerk-
nes, Menno P Witter , Edvard I Moser , and May-Britt Moser . Development of the spatial
representation system in the rat. Science, 328(5985):1576–1580, 2010.
43