Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

How to build a cognitive map

Abstract

Learning and interpreting the structure of the environment is an innate feature of biological systems, and is integral to guiding flexible behaviors for evolutionary viability. The concept of a cognitive map has emerged as one of the leading metaphors for these capacities, and unraveling the learning and neural representation of such a map has become a central focus of neuroscience. In recent years, many models have been developed to explain cellular responses in the hippocampus and other brain areas. Because it can be difficult to see how these models differ, how they relate and what each model can contribute, this Review aims to organize these models into a clear ontology. This ontology reveals parallels between existing empirical results, and implies new approaches to understand hippocampal–cortical interactions and beyond.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The cognitive mapping problem: generalization and latent states.
Fig. 2: Representing latent states.
Fig. 3: Integrating different cognitive map models and new predictions.
Fig. 4: Representing time and hierarchies of abstraction in cognitive maps.

Similar content being viewed by others

Data availability

No data were generated in this Review.

Code availability

Python and TensorFlow code are available at https://github.com/djcrw/generalising-structural-knowledge.

References

  1. Scoville, W. B. & Milner, B. Loss of recent memory after bilateral hippocampal lesions. J. Neurol. Neurosurg. Psychiatry 20, 11–21 (1957).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Cohen, N. J. & Squire, L. R. Preserved learning and retention of pattern-analyzing skill in amnesia: dissociation of knowing how and knowing that. Science 210, 207–210 (1980).

    Article  CAS  PubMed  Google Scholar 

  3. O’Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Oxford Univ. Press, 1978).

  4. Hafting, T., Fyhn, M., Molden, S., Moser, M. B. & Moser, E. I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005).

    Article  CAS  PubMed  Google Scholar 

  5. Hassabis, D., Kumaran, D., Vann, S. D. & Maguire, E. A. Patients with hippocampal amnesia cannot imagine new experiences. Proc. Natl Acad. Sci. USA 104, 1726–1731 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Tolman, E. C. Cognitive maps in rats and men. Psychol. Rev. 55, 189–208 (1948).

    Article  CAS  PubMed  Google Scholar 

  7. Turner, C. H. The homing of ants: an experimental study of ant behavior. J. Comp. Neurol. Psychol. 17, 367–434 (1907).

  8. Zanforlin, M. & Poli, G. The burrowing rat: a new technique to study place learning and orientation. Acti. Memorie 82, 653–670 (1970).

    Google Scholar 

  9. Behrens, T. E. J. et al. What is a cognitive map? Organizing knowledge for flexible behavior. Neuron 100, 490–509 (2018).

    Article  CAS  PubMed  Google Scholar 

  10. Tenenbaum, J. B., Kemp, C., Griffiths, T. L. & Goodman, N. D. How to grow a mind: statistics, structure and abstraction. Science 331, 1279–1285 (2011).

    Article  CAS  PubMed  Google Scholar 

  11. Bartlett, F. C. & Burt, C. Remembering: a study in experimental and social psychology. Br. J. Educ. Psychol. 3, 187–192 (1932).

    Article  Google Scholar 

  12. Harlow, H. F. The formation of learning sets. Psychological Rev. 56, 51–65 (1949).

    Article  CAS  Google Scholar 

  13. Moser, E. I., Moser, M.-B. & McNaughton, B. L. Spatial representation in the hippocampal formation: a history. Nat. Neurosci. 20, 1448–1464 (2017).

    Article  CAS  PubMed  Google Scholar 

  14. Aronov, D., Nevers, R. & Tank, D. W. Mapping of a non-spatial dimension by the hippocampal–entorhinal circuit. Nature 543, 719–722 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Knudsen, E. B. & Wallis, J. D. Hippocampal neurons construct a map of an abstract value space. Cell 184, 4640–4650 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Nieh, E. H. et al. Geometry of abstract learned knowledge in the hippocampus. Nature https://doi.org/10.1038/s41586-021-03652-7 (2021).

  17. Doeller, C. F., Barry, C. & Burgess, N. Evidence for grid cells in a human memory network. Nature 463, 657–661 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Constantinescu, A. O. et al. Organizing conceptual knowledge in humans with a gridlike code. Science 352, 1464–1468 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Bao, X. et al. Grid-like neural representations support olfactory navigation of a two-dimensional odor space. Neuron 102, 1066–1075 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Park, S. A., Miller, D. S., Nili, H., Ranganath, C. & Boorman, E. D. Map making: constructing, combining and inferring on abstract cognitive maps. Neuron 107, 1226–1238 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Bongioanni, A. et al. Activation and disruption of a neural mechanism for novel choice in monkeys. Nature 591, 270–274 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Rueckemann, J. W., Sosa, M., Giocomo, L. M. & Buffalo, E. A. The grid code for ordered experience. Nat. Rev. Neurosci. 22, 637–649 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Radulescu, A., Shin, Y. S. & Niv, Y. Human representation learning. Annu. Rev. Neurosci. 44, 253–273 (2021).

    Article  CAS  PubMed  Google Scholar 

  24. Sanders, H., Wilson, M. A. & Gershman, S. J. Hippocampal remapping as hidden state inference. eLife 9, e51140 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  25. Stoianov, I., Maisto, D. & Pezzulo, G. The hippocampal formation as a hierarchical generative model supporting generative replay and continual learning. Prog. Neurobiol. 217, 102329 (2022).

    Article  PubMed  Google Scholar 

  26. Niv, Y. Learning task-state representations. Nat. Neurosci. 22, 1544–1553 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Sutton, R. S. & Barto, A. G. Reinforcement learning: an introduction. in IEEE Transactions on Neural Networks https://doi.org/10.1109/TNN.1998.712192 (2017).

  28. Bellman, R. A Markovian decision process. J. Math. Mech. 6, 679–684 (1957).

  29. Gershman, S. J. & Niv, Y. Learning latent structure: carving nature at its joints. Curr. Opin. Neurobiol. 20, 251–256 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Wilson, R. C., Takahashi, Y. K., Schoenbaum, G. & Niv, Y. Orbitofrontal cortex as a cognitive map of task space. Neuron 81, 267–278 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Watkins, C. J. C. H. & Dayan, P. Technical note: Q-learning. Mach. Learn. 8, 279–292 (1992).

    Article  Google Scholar 

  32. Tolman, E. C., Ritchie, B. F. & Kalish, D. Studies in spatial learning. I. Orientation and the short-cut. J. Exp. Psychol. 36, 13–24 (1946).

    Article  CAS  PubMed  Google Scholar 

  33. Bush, D., Barry, C., Manson, D. & Burgess, N. Using grid cells for navigation. Neuron 87, 507–520 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  34. Stemmler, M., Mathis, A. & Herz, A. V. M. Connecting multiple spatial scales to decode the population activity of grid cells. Sci. Adv. 1, e1500816 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Foster, D. J., Morris, R. G. M. & Dayan, P. A model of hippocampally dependent navigation, using the temporal difference learning rule. Hippocampus 10, 1–16 (2000).

    Article  CAS  PubMed  Google Scholar 

  36. Gustafson, N. J. & Daw, N. D. Grid cells, place cells and geodesic generalization for spatial reinforcement learning. PLoS Comput. Biol. 7, e1002235 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Stachenfeld, K. L., Botvinick, M. M. & Gershman, S. J. The hippocampus as a predictive map. Nat. Neurosci. 20, 1643–1653 (2017).

    Article  CAS  PubMed  Google Scholar 

  38. Piray, P. & Daw, N. D. A model for learning based on the joint estimation of stochasticity and volatility. Nat. Commun. 12, 6587 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Dusek, J. A. & Eichenbaum, H. The hippocampus and memory for orderly stimulus relations. Proc. Natl Acad. Sci. USA 94, 7109–7114 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Wood, E. R., Dudchenko, P. A., Robitsek, R. J. & Eichenbaum, H. Hippocampal neurons encode information about different types of memory episodes occurring in the same location. Neuron 27, 623–633 (2000).

    Article  CAS  PubMed  Google Scholar 

  41. Frank, L. M., Brown, E. N. & Wilson, M. Trajectory encoding in the hippocampus and entorhinal cortex. Neuron 27, 169–178 (2000).

    Article  CAS  PubMed  Google Scholar 

  42. Komorowski, R. W., Manns, J. R. & Eichenbaum, H. Robust conjunctive item-place coding by hippocampal neurons parallels learning what happens where. J. Neurosci. 29, 9918–9929 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Carpenter, F., Manson, D., Jeffery, K., Burgess, N. & Barry, C. Grid cells form a global representation of connected environments. Curr. Biol. 25, 1176–1182 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Grieves, R. M., Wood, E. R. & Dudchenko, P. A. Place cells on a maze encode routes rather than destinations. eLife 5, 1–24 (2016).

    Article  Google Scholar 

  45. Sun, C., Yang, W., Martin, J. & Tonegawa, S. Hippocampal neurons represent events as transferable units of experience. Nat. Neurosci. 23, 651–663 (2020).

    Article  CAS  PubMed  Google Scholar 

  46. Taube, J., Muller, R. & Ranck, J. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420–435 (1990).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Darwin, C. Origin of certain instincts. Nature 7, 417–418 (1873).

    Article  Google Scholar 

  48. Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980).

    Article  Google Scholar 

  49. Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).

    Article  PubMed  Google Scholar 

  50. Loomis, J. M. et al. Nonvisual navigation by blind and sighted: assessment of path integration ability. J. Exp. Psychol. 122, 73–91 (1993).

    Article  CAS  Google Scholar 

  51. Maaswinkel, H., Jarrard, L. E. & Whishaw, I. Q. Hippocampectomized rats are impaired in homing by path integration. Hippocampus 9, 553–561 (1999).

    Article  CAS  PubMed  Google Scholar 

  52. Sreenivasan, S. & Fiete, I. Grid cells generate an analog error-correcting code for singularly precise neural computation. Nat. Neurosci. 14, 1330–1337 (2011).

    Article  CAS  PubMed  Google Scholar 

  53. Mathis, A., Herz, A. V. M. & Stemmler, M. Optimal population codes for space: grid cells outperform place cells. Neural Comput. 24, 2280–2317 (2012).

    Article  PubMed  Google Scholar 

  54. Chen, G., Lu, Y., King, J. A., Cacucci, F. & Burgess, N. Differential influences of environment and self-motion on place and grid cell firing. Nat. Commun. 10, 630 (2019).

  55. Anderson, M. I. & Jeffery, K. J. Heterogeneous modulation of place cell firing by changes in context. J. Neurosci. 23, 8827–8835 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Bostock, E., Muller, R. U. & Kubie, J. L. Experience-dependent modifications of hippocampal place cell firing. Hippocampus 1, 193–205 (1991).

    Article  CAS  PubMed  Google Scholar 

  57. Muller, R. U. & Kubie, J. L. The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968 (1987).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Fyhn, M., Hafting, T., Treves, A., Moser, M. B. & Moser, E. I. Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446, 190–194 (2007).

    Article  CAS  PubMed  Google Scholar 

  59. Yoon, K. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nat. Neurosci. 16, 1077–1084 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Manns, J. R. & Eichenbaum, H. Evolution of declarative memory. Hippocampus 16, 795–808 (2006).

    Article  PubMed  Google Scholar 

  61. Whittington, J. C. R. et al. The Tolman–Eichenbaum machine: unifying space and relational memory through generalization in the hippocampal formation. Cell 183, 1249–1263 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. Mark, S., Moran, R., Parr, T., Kennerley, S. W. & Behrens, T. E. J. Transferring structural knowledge across cognitive maps in humans and models. Nat. Commun. 11, 4783 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Kemp, C. & Tenenbaum, J. B. The discovery of structural form. Proc. Natl Acad. Sci. USA 105, 10687–10692 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Høydal, Ø. A., Skytøen, E. R., Andersson, S. O., Moser, M. -B. & Moser, E. I. Object-vector coding in the medial entorhinal cortex. Nature 568, 400–404 (2019).

    Article  PubMed  Google Scholar 

  65. Hartley, T., Burgess, N., Lever, C., Cacucci, F. & O’Keefe, J. Modeling place fields in terms of the cortical inputs to the hippocampus. Hippocampus 10, 369–379 (2000).

    Article  CAS  PubMed  Google Scholar 

  66. Becker, S. & Burgess, N. Modelling spatial recall, mental imagery and neglect. Adv. Neural Inf. Process. Syst. 13, 96–102 (2001).

    Google Scholar 

  67. Barry, C. et al. The boundary vector cell model of place cell firing and spatial memory. Rev. Neurosci. 17, 71–97 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  68. Solstad, T., Boccara, C. N., Kropff, E., Moser, M.-B. & Moser, E. I. Representation of geometric borders in the entorhinal cortex. Science 322, 1865–1868 (2008).

    Article  CAS  PubMed  Google Scholar 

  69. Lever, C., Burton, S., Jeewajee, A., O’Keefe, J. & Burgess, N. Boundary vector cells in the subiculum of the hippocampal formation. J. Neurosci. 29, 9771–9777 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Gauthier, J. L. & Tank, D. W. A dedicated population for reward coding in the hippocampus. Neuron 99, 179–193 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Sarel, A., Finkelstein, A., Las, L. & Ulanovsky, N. Vectorial representation of spatial goals in the hippocampus of bats. Science 355, 176–180 (2017).

    Article  CAS  PubMed  Google Scholar 

  72. Grieves, R. M. & Jeffery, K. J. The representation of space in the brain. Behav. Processes 135, 113–131 (2017).

    Article  PubMed  Google Scholar 

  73. Eichenbaum, H. Time cells in the hippocampus: a new dimension for mapping memories. Nat. Rev. Neurosci. 15, 732–744 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  74. George, D. et al. Clone-structured graph representations enable flexible learning and vicarious evaluation of cognitive maps. Nat. Commun. 12, 2392 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Uria, B. et al. The spatial memory pipeline: a model of egocentric to allocentric understanding in mammalian brains. Preprint at bioRxiv https://doi.org/10.1101/2020.11.11.378141 (2020).

  76. Botvinick, M. & Toussaint, M. Planning as inference. Trends Cogn. Sci. 16, 485–488 (2012).

    Article  PubMed  Google Scholar 

  77. Friston, K. The free-energy principle: a rough guide to the brain? Trends Cogn. Sci. 13, 293–301 (2009).

    Article  PubMed  Google Scholar 

  78. Banino, A. et al. Vector-based navigation using grid-like representations in artificial agents. Nature 557, 429–433 (2018).

    Article  CAS  PubMed  Google Scholar 

  79. Dordek, Y., Soudry, D., Meir, R. & Derdikman, D. Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis. eLife 5, 1–36 (2016).

    Article  Google Scholar 

  80. McNamee, D. C., Stachenfeld, K. L., Botvinick, M. M. & Gershman, S. J. Flexible modulation of sequence generation in the entorhinal–hippocampal system. Nat. Neuro. https://doi.org/10.1038/s41593-021-00831-7 (2021).

  81. Pfeiffer, B. E. & Foster, D. J. Autoassociative dynamics in the generation of sequences of hippocampal place cells. Science 349, 180–183 (2015).

    Article  CAS  PubMed  Google Scholar 

  82. Baram, A. B., Muller, T. H., Whittington, J. C. R. & Behrens, T. E. J. Intuitive planning: global navigation through cognitive maps based on grid-like codes. Preprint at bioRxiv https://doi.org/10.1101/421461 (2018).

  83. Yu, C., Behrens, T. E. J. & Burgess, N. Prediction and generalisation over directed actions by grid cells. International Conference on Learning Representations (2021).

  84. O’Keefe, J. & Recce, M. L. Phase relationship between hippocampal place units and the EEG theta rhythm. Hippocampus 3, 317–330 (1993).

    Article  PubMed  Google Scholar 

  85. Burgess, N., Barry, C. & O’Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2009).

    Article  Google Scholar 

  86. Burak, Y. & Fiete, I. Do we understand the emergent dynamics of grid cell activity? J. Neurosci. 26, 9352–9354 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Wang, J. X. et al. Prefrontal cortex as a meta-reinforcement learning system. Nat. Neurosci. 21, 860–868 (2018).

    Article  CAS  PubMed  Google Scholar 

  88. Chen, L. et al. Decision transformer: reinforcement learning via sequence modeling. Preprint at https://arxiv.org/abs/2106.01345 (2021).

  89. Janner, M., Li, Q. & Levine, S. Offline reinforcement learning as one big sequence modeling problem. Preprint at https://arxiv.org/abs/2106.02039 (2021).

  90. Foster, D. J. & Wilson, M. A. Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature 440, 680–683 (2006).

    Article  CAS  PubMed  Google Scholar 

  91. Deshmukh, S. S. & Knierim, J. J. Influence of local objects on hippocampal representations: landmark vectors and memory. Hippocampus 23, 253–267 (2013).

    Article  PubMed  Google Scholar 

  92. Evans, T. & Burgess, N. Coordinated hippocampal-entorhinal replay as structural inference. Adv. Neural Inf. Process. Syst. 32, 1731–1743 (2019).

    Google Scholar 

  93. Mattar, M. G. & Daw, N. D. Prioritized memory access explains planning and hippocampal replay. Nat. Neurosci. 21, 1609–1617 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  94. Momennejad, I. et al. The successor representation in human reinforcement learning. Nat. Hum. Behav. 1, 680–692 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Ólafsdóttir, H. F., Carpenter, F. & Barry, C. Coordinated grid and place cell replay during rest. Nat. Neurosci. 19, 792–794 (2016).

    Article  PubMed  Google Scholar 

  96. Kaefer, K., Nardin, M., Blahna, K. & Csicsvari, J. Replay of behavioral sequences in the medial prefrontal cortex during rule switching. Neuron 106, 154–165 (2020).

    Article  CAS  PubMed  Google Scholar 

  97. Boccara, C. N., Nardin, M., Stella, F., O’Neill, J. & Csicsvari, J. The entorhinal cognitive map is attracted to goals. Science 363, 1443–1447 (2019).

    Article  CAS  PubMed  Google Scholar 

  98. Butler, W. N., Hardcastle, K. & Giocomo, L. M. Remembered reward locations restructure entorhinal spatial maps. Science 363, 1447–1452 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  99. Ziv, Y. et al. Long-term dynamics of CA1 hippocampal place codes. Nat. Neurosci. 16, 264–266 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Driscoll, L. N., Pettit, N. L., Minderer, M., Chettih, S. N. & Harvey, C. D. Dynamic reorganization of neuronal activity patterns in parietal cortex. Cell 170, 986–999 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Rule, M. E., O’Leary, T. & Harvey, C. D. Causes and consequences of representational drift. Curr. Opin. Neurobiol. 58, 141–147 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Rubin, A., Geva, N., Sheintuch, L. & Ziv, Y. Hippocampal ensemble dynamics timestamp events in long-term memory. eLife 4, e12247 (2015).

  103. Pastalkova, E., Itskov, V., Amarasingham, A. & Buzsaki, G. Internally generated cell assembly sequences in the rat hippocampus. Science 321, 1322–1327 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. MacDonald, C. J., Lepage, K. Q., Eden, U. T. & Eichenbaum, H. Hippocampal ‘time cells’ bridge the gap in memory for discontiguous events. Neuron 71, 737–749 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Zhou, J. et al. Evolving schema representations in orbitofrontal ensembles during learning. Nature 590, 606–611 (2021).

    Article  CAS  PubMed  Google Scholar 

  106. Zhou, J. et al. Complementary task structure representations in hippocampus and orbitofrontal cortex during an odor sequence task. Curr. Biol. 29, 3402–3409 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Miller, E. K. & Cohen, J. D. An integrative theory of prefrontal cortex function. Annu. Rev. Neurosci. 24, 167–202 (2001).

    Article  CAS  PubMed  Google Scholar 

  108. Bernardi, S. et al. The geometry of abstraction in the hippocampus and prefrontal cortex. Cell 183, 954–967 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  109. Morton, N. W., Schlichting, M. L. & Preston, A. R. Representations of common event structure in medial temporal lobe and frontoparietal cortex support efficient inference. Proc. Natl Acad. Sci. USA 117, 29338–29345 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  110. Samborska, V., Butler, J. L., Walton, M. E., Behrens, T. E. & Akam, T. Complementary task representations in hippocampus and prefrontal cortex for generalizing the structure of problems. Nat. Neurosci. (in the press).

  111. Schuck, N. W., Cai, M. B., Wilson, R. C. & Niv, Y. Human orbitofrontal cortex represents a cognitive map of state space. Neuron 91, 1402–1412 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  112. Yu, J. Y., Liu, D. F., Loback, A., Grossrubatscher, I. & Frank, L. M. Specific hippocampal representations are linked to generalized cortical representations in memory. Nat. Commun. 9, 2209 (2018).

  113. Hawkins, J., Lewis, M., Klukas, M., Purdy, S. & Ahmad, S. A framework for intelligence and cortical function based on grid cells in the neocortex. Front. Neural Circuits 12, 121 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  114. Lewis, M. Hippocampal spatial mapping as fast graph learning. Preprint at https://arxiv.org/abs/2107.00567 (2021).

  115. Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9, 17351780 (1997).

    Article  Google Scholar 

  116. Vaswani, A. et al. Attention is all you need. Adv. Neural Inf. Process. Syst. 20, 5999–6009 (2017).

    Google Scholar 

  117. Brown, T. B. et al. Language models are few-shot learners. Preprint at https://arxiv.org/abs/2005.14165 (2020).

  118. Dosovitskiy, A. et al. An image is worth 16x16 words: transformers for image recognition at scale. Preprint at https://arxiv.org/abs/2010.11929 (2020).

  119. Amalric, M. & Dehaene, S. Origins of the brain networks for advanced mathematics in expert mathematicians. Proc. Natl Acad. Sci. USA 113, 4909–4917 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  120. Whittington, J. C. R., Warren, J. & Behrens, T. E. J. Relating transformers to models and neural representations of the hippocampal formation. In International Conference on Learning Representations (2022).

  121. Higgins, I. et al. β-VAE: learning basic visual concepts with a constrained variational framework. In International Conference on Learning Representations (2017).

  122. Higgins, I. et al. Towards a definition of disentangled representations. Preprint at https://arxiv.org/abs/1812.02230 (2018).

  123. Killian, N. J. & Buffalo, E. A. Grid cells map the visual world. Nat. Neurosci. 21, 161–162 (2018).

    Article  CAS  PubMed  Google Scholar 

  124. Nau, M., Navarro Schröder, T., Bellmund, J. L. S. & Doeller, C. F. Hexadirectional coding of visual space in human entorhinal cortex. Nat. Neurosci. 21, 188–190 (2018).

    Article  CAS  PubMed  Google Scholar 

  125. Julian, J. B., Keinath, A. T., Frazzetta, G. & Epstein, R. A. Human entorhinal cortex represents visual space using a boundary-anchored grid. Nat. Neurosci. 21, 191–194 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. Schwartenbeck, P. et al. Generative replay for compositional visual understanding in the prefrontal-hippocampal circuit. Preprint at bioRxiv https://doi.org/10.1101/2021.06.06.447249 (2021).

  127. Bellmund, J. L. S., Gärdenfors, P., Moser, E. I. & Doeller, C. F. Navigating cognition: spatial codes for human thinking. Science 362, eaat6766 (2018).

    Article  PubMed  Google Scholar 

  128. Salz, D. M. et al. Time cells in hippocampal area CA3. J. Neurosci. 36, 7476–7484 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  129. Dayan, P. Improving generalization for temporal difference learning: the successor representation. Neural Comput. 5, 613–624 (1993).

    Article  Google Scholar 

  130. Mehta, M. R., Quirk, M. C. & Wilson, M. A. Experience-dependent asymmetric shape of hippocampal receptive fields. Neuron 25, 707–715 (2000).

    Article  CAS  PubMed  Google Scholar 

  131. Derdikman, D. et al. Fragmentation of grid cell maps in a multicompartment environment. Nat. Neurosci. 12, 1325–1332 (2009).

    Article  CAS  PubMed  Google Scholar 

  132. Krupic, J., Burgess, N. & O’Keefe, J. Neural representations of location composed of spatially periodic bands. Science 337, 853–857 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  133. Garvert, M. M., Dolan, R. J. & Behrens, T. E. A map of abstract relational knowledge in the human hippocampal–entorhinal cortex. eLife 6, e17086 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  134. Schapiro, A. C., Turk-browne, N. B., Botvinick, M. M., Norman, K. A. & Schapiro, A. C. Complementary learning systems within the hippocampus: a neural network modelling approach to reconciling episodic memory with statistical learning. Philos. Trans. R. Soc. Lond. B Biol. Sci. 372, 20160049 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  135. Momennejad, I. Learning structures: predictive representations, replay, and generalization. Curr. Opin. Behav. Sci. 32, 155–166 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  136. Todorov, E. Linearly solvable Markov decision problems. In Advances in Neural Information Processing Systems 1369–1376 https://doi.org/10.7551/mitpress/7503.003.0176 (2007).

  137. Cormack, G. V. & Horspool, R. N. S. Data compression using dynamic Markov modelling. Comput. J. 30, 541–550 (1987).

    Article  Google Scholar 

  138. Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. 39, 1–22 (1977).

    Google Scholar 

  139. Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Skaggs, W. E., Knierim, J. J., Kudrimoti, H. S. & McNaughton, B. L. A model of the neural basis of the rat’s sense of direction. Adv. neural Inf. Process. Syst. 7, 173–180 (1995).

    CAS  PubMed  Google Scholar 

  141. Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  142. Tsodyks, M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).

    Article  CAS  PubMed  Google Scholar 

  143. Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  144. Ben-Yishai, R., Bar-Or, R. L. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Natl Acad. Sci. USA 92, 3844–3848 (1995).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  145. Kim, S. S., Rouault, H., Druckmann, S. & Jayaraman, V. Ring attractor dynamics in the Drosophila central brain. Science 356, 849–853 (2017).

    Article  CAS  PubMed  Google Scholar 

  146. Gardner, R. J. et al. Toroidal topology of population activity in grid cells. Nature 602, 123–128 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  147. Cueva, C. J. & Wei, X. -X. Emergence of grid-like representations by training recurrent neural networks to perform spatial localization. Peeprint at https://arxiv.org/abs/1803.07770 (2018).

  148. Sorscher, B., Mel, G. C., Ganguli, S. & Ocko, S. A. A unified theory for the origin of grid cells through the lens of pattern formation. Adv. Neural Inf. Process. Syst. 32, 10003–10013 (2019).

    Google Scholar 

  149. Pritzel, A. et al. Neural episodic control. Preprint at https://arxiv.org/abs/1703.01988 (2017).

  150. Hebb, D. O. The Organization of Behavior; a Neuropsychological Theory (Wiley, 1949).

  151. Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities (associative memory/parallel processing/categorization/content-addressable memory/fail-soft devices). Biophysics 79, 2554–2558 (1982).

    CAS  Google Scholar 

  152. McKenzie, S. et al. Hippocampal representation of related and opposing memories develop within distinct, hierarchically organized neural schemas. Neuron 83, 202–215 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  153. Bunsey, M. & Eichenbaum, H. Conservation of hippocampal memory function in rats and humans. Nature 379, 255–257 (1996).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank N. Burgess and C. Sun for helpful comments on earlier drafts of the manuscript. We thank the following funding sources: Sir Henry Wellcome Post-doctoral Fellowship (222817/Z/21/Z) to J.C.R.W.; Wellcome Trust DPhil Scholarship to D.M.; and Wellcome Principal Research Fellowship (219525/Z/19/Z), Wellcome Collaborator award (214314/Z/18/Z), and JS McDonnell Foundation award (JSMF220020372) to T.E.J.B.. The Wellcome Centre for Integrative Neuroimaging and Wellcome Centre for Human Neuroimaging are each supported by core funding from the Wellcome Trust (203139/Z/16/Z, 203147/Z/16/Z).

Author information

Authors and Affiliations

Authors

Contributions

J.C.R.W. and T.E.J.B. conceptualized the manuscript. J.C.R.W. and D.M. performed simulations. J.C.R.W. drafted the manuscript with input from D.M. J.C.R.W. and T.E.J.B. edited the manuscript with input from D.M. and J.J.W.B.

Corresponding author

Correspondence to James C. R. Whittington.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Neuroscience thanks the anonymous reviewers for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1 and 2

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Whittington, J.C.R., McCaffary, D., Bakermans, J.J.W. et al. How to build a cognitive map. Nat Neurosci 25, 1257–1272 (2022). https://doi.org/10.1038/s41593-022-01153-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41593-022-01153-y

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing