The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond | Paper Citation Record

Observation 8275d2f1-7d92-48d1-b06e-bfd196520304 · outbound

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond From the neuron doctrine to neural networks.Nature reviews neuroscience, 16(8):487–497, 2015

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This paper cites Computation through neural population dynamics.Annual review of neuroscience, 43(1):249–275, 2020.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Computation through neural population dynamics.Annual review of neuroscience, 43(1):249–275, 2020

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This paper cites Neural tuning and representational geometry.Nature Reviews Neuroscience, 22(11):703–718, 2021.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Neural tuning and representational geometry.Nature Reviews Neuroscience, 22(11):703–718, 2021

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Observation 9962b709-2ca4-4260-ace3-23973f3f4095 · outbound

This paper cites Aneuralmanifoldviewofthebrain.NatureNeuroscience, pages 1–16, 2025.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Aneuralmanifoldviewofthebrain.NatureNeuroscience, pages 1–16, 2025

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This paper cites Large-scale neural recordings call for new insights to link brain and behavior.Nature neuroscience, 25(1):11–19, 2022.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Large-scale neural recordings call for new insights to link brain and behavior.Nature neuroscience, 25(1):11–19, 2022

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Observation 18467938-d9fa-487d-9216-08fd120a872d · outbound

This paper cites Neural population dynamics during reaching.Nature, 487(7405):51–56, 2012.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Neural population dynamics during reaching.Nature, 487(7405):51–56, 2012

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Observation 3dfce388-30b2-448c-aebd-0f605f25a2f0 · outbound

This paper cites Towardstheneuralpopulationdoctrine.Currentopinioninneurobiology, 55:103–111, 2019.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Towardstheneuralpopulationdoctrine.Currentopinioninneurobiology, 55:103–111, 2019

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Observation 8c38a751-f79c-45be-afb3-b8d49ff0f251 · outbound

This paper cites A unifying perspective on neural manifolds and circuits for cognition.Nature Reviews Neuroscience, 24(6):363–377, 2023.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond A unifying perspective on neural manifolds and circuits for cognition.Nature Reviews Neuroscience, 24(6):363–377, 2023

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Observation 0db61b56-b2d3-46da-93d5-dce15e9cbaea · outbound

This paper cites Spatial representation in the entorhinal cortex.Science, 305(5688):1258–1264, 2004.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Spatial representation in the entorhinal cortex.Science, 305(5688):1258–1264, 2004

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Observation b8e4860c-e4bd-4130-976b-b1d239045200 · outbound

This paper cites Microstructure of a spatial map in the entorhinal cortex.Nature, 436(7052):801–806, 2005.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Microstructure of a spatial map in the entorhinal cortex.Nature, 436(7052):801–806, 2005

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Observation fb4253ee-9891-493c-b405-b2aae8db0d2d · outbound

This paper cites Conjunctive representation of position, direction, and velocity in entorhinal cortex.Science, 312(5774):758–762, 2006.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Conjunctive representation of position, direction, and velocity in entorhinal cortex.Science, 312(5774):758–762, 2006

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Observation 4c9cde59-6a1b-4812-985d-cfea2b016afc · outbound

This paper cites Toroidal topology of population activity in grid cells.Nature, 602(7895):123–128, 2022.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Toroidal topology of population activity in grid cells.Nature, 602(7895):123–128, 2022

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Observation 1a655883-bc8c-4a15-9a35-33204ed8d253 · outbound

This paper cites Path integration and the neural basis of the’cognitive map’.Nature Reviews Neuroscience, 7(8):663–678, 2006.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Path integration and the neural basis of the’cognitive map’.Nature Reviews Neuroscience, 7(8):663–678, 2006

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This paper cites Accuratepathintegrationincontinuousattractornetworkmodelsofgridcells.PLoS computational biology, 5(2):e1000291, 2009.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Accuratepathintegrationincontinuousattractornetworkmodelsofgridcells.PLoS computational biology, 5(2):e1000291, 2009

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This paper cites Impairedpathintegrationinmicewithdisruptedgridcellfiring.Natureneuroscience,21(1):81–91,2018.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Impairedpathintegrationinmicewithdisruptedgridcellfiring.Natureneuroscience,21(1):81–91,2018

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Observation bd4c5522-414b-446c-be1c-5b6e1b381202 · outbound

This paper cites A metric for space.Hippocampus, 18(12):1142–1156, 2008.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond A metric for space.Hippocampus, 18(12):1142–1156, 2008

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Observation 27e25033-3fd7-4c46-934e-5501d7ce020a · outbound

This paper cites Are grid cells used for navigation? on local metrics, subjective spaces, and black holes.Neuron, 111(12):1858–1875, 2023.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Are grid cells used for navigation? on local metrics, subjective spaces, and black holes.Neuron, 111(12):1858–1875, 2023

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Observation f6112475-ef4b-45c7-8e48-3033f67e563a · outbound

This paper cites The hippocampus as a predictive map.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond The hippocampus as a predictive map

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Observation e7bb5a99-8201-44ad-a6fb-df7da4c5a24a · outbound

This paper cites Vector-based navigation using grid-like representations in artificial agents.Nature, 557(7705):429–433, 2018.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Vector-based navigation using grid-like representations in artificial agents.Nature, 557(7705):429–433, 2018

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Observation 1ca22d36-e865-4611-8d06-5d81d616614a · outbound

This paper cites Emergence of grid-like representations by training recurrent neural networks to perform spatial localization.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Emergence of grid-like representations by training recurrent neural networks to perform spatial localization

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Observation eb5005cc-4d11-4edc-9f9f-18b8e1b68f9a · outbound

This paper cites A unified theory for the origin of grid cells through the lens of pattern formation.Advances in neural information processing systems, 32, 2019.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond A unified theory for the origin of grid cells through the lens of pattern formation.Advances in neural information processing systems, 32, 2019

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Observation 1a15939e-c4a2-49e9-a0ea-ad2caea692c3 · outbound

This paper cites The tolman-eichenbaum machine: unifying space and relational memory through generalization in the hippocampal formation.Cell, 183(5):1249–1263, 2020.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond The tolman-eichenbaum machine: unifying space and relational memory through generalization in the hippocampal formation.Cell, 183(5):1249–1263, 2020

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Observation 9866accc-e327-45bd-b7e6-47a3ec812706 · outbound

This paper cites On path integration of grid cells: group representation and isotropic scaling.Advances in Neural Information Processing Systems, 34:28623–28635, 2021.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond On path integration of grid cells: group representation and isotropic scaling.Advances in Neural Information Processing Systems, 34:28623–28635, 2021

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Observation 8ea7cedf-81a6-4ff9-afad-eec207ed6803 · outbound

This paper cites Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells

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Observation 0623f463-79e3-4816-9dc4-942de130c5fb · outbound

This paper cites Actionable Neural Representations: Grid Cells from Minimal Constraints.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Actionable Neural Representations: Grid Cells from Minimal Constraints

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Observation 7bbdeb7c-911b-4563-9f4d-e15fcb49a7f0 · outbound

This paper cites an unresolved cited work.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Unresolved cited work

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Observation 04e4f306-a002-4a36-ad72-6b3958814799 · outbound

This paper cites Coherently remapping toroidal cells but not grid cells are responsible for path integration in virtual agents.Iscience, 26(11), 2023.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Coherently remapping toroidal cells but not grid cells are responsible for path integration in virtual agents.Iscience, 26(11), 2023

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This paper cites A unified theory for the computational and mechanistic origins of grid cells.Neuron, 111(1):121–137, 2023.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond A unified theory for the computational and mechanistic origins of grid cells.Neuron, 111(1):121–137, 2023

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Self-supervised learningofrepresentationsforspacegeneratesmulti-modulargridcells.AdvancesinNeuralInformationProcessing Systems, 36:23140–23157, 2023

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This paper cites Self-supervised grid cells without path integration.bioRxiv, pages 2024–05, 2024.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Self-supervised grid cells without path integration.bioRxiv, pages 2024–05, 2024

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond On conformal isometry of grid cells: Learning distance-preserving position embedding

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Some informational aspects of visual perception.Psychological review, 61(3):183, 1954

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Possible principles underlying the transformation of sensory messages.Sensory communication, 1(01):217–233, 1961

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Second-order isomorphism of internal representations: Shapes of states

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Representation is representation of similarities.Behavioral and brain sciences, 21(4):449–467, 1998

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond No free lunch theorems for optimization.IEEE transactions on evolutionary computation, 1(1):67–82, 1997

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Representation learning: A review and new perspectives

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Getting aligned on representational alignment

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond What grid cells convey about rat location.Journal of Neuroscience, 28(27):6858–6871, 2008

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Observation 3926f411-1180-4f04-bd63-3f1dd0aadc2e · outbound

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond PrincetonUniversity Press, 2021

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Cambridge University Press, 2002

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Grid cells generate an analog error-correcting code for singularly precise neural computation.Nature neuroscience, 14(10):1330–1337, 2011

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond The elementary geometric structure of compact lie groups

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Head-directioncellsinthedeeplayersofdorsalpresubiculumoffreelymovingrats

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Locally ordered representation of 3d space in the entorhinal cortex.Nature, 596(7872):404–409, 2021

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Irregular distribution of grid cell firing fields in rats exploring a 3d volumetric space.Nature neuroscience, 24(11):1567–1573, 2021

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond A model of the neural basis of the rat’s sense of direction.Advances in neural information processing systems, 7, 1994

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory.Journal of Neuroscience, 16(6):2112–2126, 1996

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Grid cell symmetry is shaped by environmental geometry.Nature, 518(7538):232–235, 2015

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Local transformations of the hippocampal cognitive map.Science, 359(6380):1143–1146, 2018

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Shearing-induced asymmetry in entorhinal grid cells.Nature, 518(7538):207–212, 2015

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The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Information processing with population codes.Nature Reviews Neuroscience, 1(2):125–132, 2000

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This paper cites Connecting multiple spatial scales to decode the population activity of grid cells.Science Advances, 1(11):e1500816, 2015.

The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond Connecting multiple spatial scales to decode the population activity of grid cells.Science Advances, 1(11):e1500816, 2015

Reference 54

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