1
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Thompson JC, Parkinson C. Interactions between neural representations of the social and spatial environment. Philos Trans R Soc Lond B Biol Sci 2024; 379:20220522. [PMID: 39230453 DOI: 10.1098/rstb.2022.0522] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 05/07/2024] [Accepted: 05/14/2024] [Indexed: 09/05/2024] Open
Abstract
Even in our highly interconnected modern world, geographic factors play an important role in human social connections. Similarly, social relationships influence how and where we travel, and how we think about our spatial world. Here, we review the growing body of neuroscience research that is revealing multiple interactions between social and spatial processes in both humans and non-human animals. We review research on the cognitive and neural representation of spatial and social information, and highlight recent findings suggesting that underlying mechanisms might be common to both. We discuss how spatial factors can influence social behaviour, and how social concepts modify representations of space. In so doing, this review elucidates not only how neural representations of social and spatial information interact but also similarities in how the brain represents and operates on analogous information about its social and spatial surroundings.This article is part of the theme issue 'The spatial-social interface: a theoretical and empirical integration'.
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Affiliation(s)
- James C Thompson
- Department of Psychology, and Center for Adaptive Systems of Brain-Body Interactions, George Mason University, MS3F5 4400 University Drive, Fairfax, VA 22030, USA
| | - Carolyn Parkinson
- Department of Psychology, University of California, Los Angeles, Los Angeles, CA, USA
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2
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Aziz A, Patil BK, Lakshmikanth K, Sreeharsha PSS, Mukhopadhyay A, Chakravarthy VS. Modeling hippocampal spatial cells in rodents navigating in 3D environments. Sci Rep 2024; 14:16714. [PMID: 39030197 PMCID: PMC11271631 DOI: 10.1038/s41598-024-66755-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2024] [Accepted: 07/03/2024] [Indexed: 07/21/2024] Open
Abstract
Studies on the neural correlates of navigation in 3D environments are plagued by several issues that need to be solved. For example, experimental studies show markedly different place cell responses in rats and bats, both navigating in 3D environments. In this study, we focus on modelling the spatial cells in rodents in a 3D environment. We propose a deep autoencoder network to model the place and grid cells in a simulated agent navigating in a 3D environment. The input layer to the autoencoder network model is the HD layer, which encodes the agent's HD in terms of azimuth (θ) and pitch angles (ϕ). The output of this layer is given as input to the Path Integration (PI) layer, which computes displacement in all the preferred directions. The bottleneck layer of the autoencoder model encodes the spatial cell-like responses. Both grid cell and place cell-like responses are observed. The proposed model is verified using two experimental studies with two 3D environments. This model paves the way for a holistic approach using deep neural networks to model spatial cells in 3D navigation.
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Affiliation(s)
- Azra Aziz
- Computational Neuroscience Lab, Indian Institute of Technology Madras, Chennai, 600036, India
| | - Bharat K Patil
- Computational Neuroscience Lab, Indian Institute of Technology Madras, Chennai, 600036, India
| | - Kailash Lakshmikanth
- Computational Neuroscience Lab, Indian Institute of Technology Madras, Chennai, 600036, India
| | | | - Ayan Mukhopadhyay
- Department of Physics, Indian Institute of Technology Madras, Chennai, 600036, India
- Instituto de Física, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - V Srinivasa Chakravarthy
- Computational Neuroscience Lab, Indian Institute of Technology Madras, Chennai, 600036, India.
- Center for Complex Systems and Dynamics, Indian Institute of Technology Madras, Chennai, 600036, India.
- Department of Biotechnology, Indian Institute of Technology Madras, Chennai, 600036, India.
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3
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Kymn CJ, Mazelet S, Thomas A, Kleyko D, Frady EP, Sommer FT, Olshausen BA. Binding in hippocampal-entorhinal circuits enables compositionality in cognitive maps. ARXIV 2024:arXiv:2406.18808v1. [PMID: 38979486 PMCID: PMC11230348] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in distributed representation. Spatial position is encoded in a residue number system, with individual residues represented by high-dimensional, complex-valued vectors. These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation. Self-consistency between the representations of the overall position and of the individual residues is enforced by a modular attractor network whose modules correspond to the grid cell modules in entorhinal cortex. The vector binding operation can also associate different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus. We show that the model achieves normative desiderata including superlinear scaling of patterns with dimension, robust error correction, and hexagonal, carry-free encoding of spatial position. These properties in turn enable robust path integration and association with sensory inputs. More generally, the model formalizes how compositional computations could occur in the hippocampal formation and leads to testable experimental predictions.
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Affiliation(s)
| | - Sonia Mazelet
- Redwood Center for Theoretical Neuroscience, UC Berkeley, Berkeley, USA
- Université Paris-Saclay, ENS Paris-Saclay, Gif-sur-Yvette, France
| | - Anthony Thomas
- Redwood Center for Theoretical Neuroscience, UC Berkeley, Berkeley, USA
| | - Denis Kleyko
- Centre for Applied Autonomous Sensor Systems, Örebro University, Örebro, Sweden
| | | | - Friedrich T Sommer
- Redwood Center for Theoretical Neuroscience, UC Berkeley, Berkeley, USA
- Intel Labs, Santa Clara, USA
| | - Bruno A Olshausen
- Redwood Center for Theoretical Neuroscience, UC Berkeley, Berkeley, USA
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4
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Hermansen E, Klindt DA, Dunn BA. Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior. Nat Commun 2024; 15:5429. [PMID: 38926360 PMCID: PMC11208534 DOI: 10.1038/s41467-024-49703-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 06/13/2024] [Indexed: 06/28/2024] Open
Abstract
Minimal experiments, such as head-fixed wheel-running and sleep, offer experimental advantages but restrict the amount of observable behavior, making it difficult to classify functional cell types. Arguably, the grid cell, and its striking periodicity, would not have been discovered without the perspective provided by free behavior in an open environment. Here, we show that by shifting the focus from single neurons to populations, we change the minimal experimental complexity required. We identify grid cell modules and show that the activity covers a similar, stable toroidal state space during wheel running as in open field foraging. Trajectories on grid cell tori correspond to single trial runs in virtual reality and path integration in the dark, and the alignment of the representation rapidly shifts with changes in experimental conditions. Thus, we provide a methodology to discover and study complex internal representations in even the simplest of experiments.
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Affiliation(s)
- Erik Hermansen
- Department of Mathematical Sciences, NTNU, Trondheim, Norway.
| | - David A Klindt
- Department of Mathematical Sciences, NTNU, Trondheim, Norway
- Cold Spring Harbor Laboratory, Cold Spring Harbor, Laurel Hollow, New York, USA
| | - Benjamin A Dunn
- Department of Mathematical Sciences, NTNU, Trondheim, Norway.
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Dietrich R, Waniek N, Stemmler M, Knoll A. Grid codes vs. multi-scale, multi-field place codes for space. Front Comput Neurosci 2024; 18:1276292. [PMID: 38707680 PMCID: PMC11066179 DOI: 10.3389/fncom.2024.1276292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 03/19/2024] [Indexed: 05/07/2024] Open
Abstract
Introduction Recent work on bats flying over long distances has revealed that single hippocampal cells have multiple place fields of different sizes. At the network level, a multi-scale, multi-field place cell code outperforms classical single-scale, single-field place codes, yet the performance boundaries of such a code remain an open question. In particular, it is unknown how general multi-field codes compare to a highly regular grid code, in which cells form distinct modules with different scales. Methods In this work, we address the coding properties of theoretical spatial coding models with rigorous analyses of comprehensive simulations. Starting from a multi-scale, multi-field network, we performed evolutionary optimization. The resulting multi-field networks sometimes retained the multi-scale property at the single-cell level but most often converged to a single scale, with all place fields in a given cell having the same size. We compared the results against a single-scale single-field code and a one-dimensional grid code, focusing on two main characteristics: the performance of the code itself and the dynamics of the network generating it. Results Our simulation experiments revealed that, under normal conditions, a regular grid code outperforms all other codes with respect to decoding accuracy, achieving a given precision with fewer neurons and fields. In contrast, multi-field codes are more robust against noise and lesions, such as random drop-out of neurons, given that the significantly higher number of fields provides redundancy. Contrary to our expectations, the network dynamics of all models, from the original multi-scale models before optimization to the multi-field models that resulted from optimization, did not maintain activity bumps at their original locations when a position-specific external input was removed. Discussion Optimized multi-field codes appear to strike a compromise between a place code and a grid code that reflects a trade-off between accurate positional encoding and robustness. Surprisingly, the recurrent neural network models we implemented and optimized for either multi- or single-scale, multi-field codes did not intrinsically produce a persistent "memory" of attractor states. These models, therefore, were not continuous attractor networks.
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Affiliation(s)
- Robin Dietrich
- School of Computation, Information and Technology, Technical University of Munich, Munich, Germany
- Kavli Institute for Systems Neuroscience, Norwegian University of Science and Technology, Trondheim, Norway
| | - Nicolai Waniek
- Kavli Institute for Systems Neuroscience, Norwegian University of Science and Technology, Trondheim, Norway
- Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
| | - Martin Stemmler
- Bernstein Center for Computational Neuroscience, Ludwig-Maximilians-Universität, Munich, Germany
| | - Alois Knoll
- School of Computation, Information and Technology, Technical University of Munich, Munich, Germany
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6
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Chen D, Axmacher N, Wang L. Grid codes underlie multiple cognitive maps in the human brain. Prog Neurobiol 2024; 233:102569. [PMID: 38232782 DOI: 10.1016/j.pneurobio.2024.102569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 01/07/2024] [Accepted: 01/10/2024] [Indexed: 01/19/2024]
Abstract
Grid cells fire at multiple positions that organize the vertices of equilateral triangles tiling a 2D space and are well studied in rodents. The last decade witnessed rapid progress in two other research lines on grid codes-empirical studies on distributed human grid-like representations in physical and multiple non-physical spaces, and cognitive computational models addressing the function of grid cells based on principles of efficient and predictive coding. Here, we review the progress in these fields and integrate these lines into a systematic organization. We also discuss the coordinate mechanisms of grid codes in the human entorhinal cortex and medial prefrontal cortex and their role in neurological and psychiatric diseases.
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Affiliation(s)
- Dong Chen
- CAS Key Laboratory of Mental Health, Institute of Psychology, 100101, Beijing, China; Department of Psychology, University of Chinese Academy of Sciences, 100101, Beijing, China
| | - Nikolai Axmacher
- Department of Neuropsychology, Institute of Cognitive Neuroscience, Faculty of Psychology, Ruhr University Bochum, 44801, Bochum, Germany
| | - Liang Wang
- CAS Key Laboratory of Mental Health, Institute of Psychology, 100101, Beijing, China; Department of Psychology, University of Chinese Academy of Sciences, 100101, Beijing, China.
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7
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Kymn CJ, Kleyko D, Frady EP, Bybee C, Kanerva P, Sommer FT, Olshausen BA. Computing with Residue Numbers in High-Dimensional Representation. ARXIV 2023:arXiv:2311.04872v1. [PMID: 37986727 PMCID: PMC10659444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Download PDF] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
We introduce Residue Hyperdimensional Computing, a computing framework that unifies residue number systems with an algebra defined over random, high-dimensional vectors. We show how residue numbers can be represented as high-dimensional vectors in a manner that allows algebraic operations to be performed with component-wise, parallelizable operations on the vector elements. The resulting framework, when combined with an efficient method for factorizing high-dimensional vectors, can represent and operate on numerical values over a large dynamic range using vastly fewer resources than previous methods, and it exhibits impressive robustness to noise. We demonstrate the potential for this framework to solve computationally difficult problems in visual perception and combinatorial optimization, showing improvement over baseline methods. More broadly, the framework provides a possible account for the computational operations of grid cells in the brain, and it suggests new machine learning architectures for representing and manipulating numerical data.
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Affiliation(s)
- Christopher J Kymn
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA
| | - Denis Kleyko
- Centre for Applied Autonomous Sensor Systems, Örebro University, Sweden
- Intelligent Systems Lab, Research Institutes of Sweden, Kista, Sweden
| | | | - Connor Bybee
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA
| | - Pentti Kanerva
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA
| | - Friedrich T Sommer
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA
- Neuromorphic Computing Lab, Intel, Santa Clara, CA
| | - Bruno A Olshausen
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA
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8
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Dabaghian Y. Grid cells, border cells, and discrete complex analysis. Front Comput Neurosci 2023; 17:1242300. [PMID: 37881247 PMCID: PMC10595009 DOI: 10.3389/fncom.2023.1242300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2023] [Accepted: 09/22/2023] [Indexed: 10/27/2023] Open
Abstract
We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity toward the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.
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Affiliation(s)
- Yuri Dabaghian
- Department of Neurology, The University of Texas, McGovern Medical Center at Houston, Houston, TX, United States
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9
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Dabaghian Y. Grid Cells, Border Cells and Discrete Complex Analysis. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.06.539720. [PMID: 37214803 PMCID: PMC10197584 DOI: 10.1101/2023.05.06.539720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We propose a mechanism enabling the appearance of border cells-neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows constructing discrete epitomes of complex-analytic functions and making use of their inherent ability to attain maximal values at the boundaries of generic lattice domains. As it turns out, certain elements of the discrete-complex framework readily appear in the oscillatory models of grid cells. We demonstrate that these models can extend further, producing cells that increase their activity towards the frontiers of the navigated environments. We also construct a network model of neurons with border-bound firing that conforms with the oscillatory models.
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Affiliation(s)
- Yuri Dabaghian
- Department of Neurology, The University of Texas McGovern Medical School, 6431 Fannin St, Houston, TX 77030
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10
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Linton P, Morgan MJ, Read JCA, Vishwanath D, Creem-Regehr SH, Domini F. New Approaches to 3D Vision. Philos Trans R Soc Lond B Biol Sci 2023; 378:20210443. [PMID: 36511413 PMCID: PMC9745878 DOI: 10.1098/rstb.2021.0443] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 10/25/2022] [Indexed: 12/15/2022] Open
Abstract
New approaches to 3D vision are enabling new advances in artificial intelligence and autonomous vehicles, a better understanding of how animals navigate the 3D world, and new insights into human perception in virtual and augmented reality. Whilst traditional approaches to 3D vision in computer vision (SLAM: simultaneous localization and mapping), animal navigation (cognitive maps), and human vision (optimal cue integration) start from the assumption that the aim of 3D vision is to provide an accurate 3D model of the world, the new approaches to 3D vision explored in this issue challenge this assumption. Instead, they investigate the possibility that computer vision, animal navigation, and human vision can rely on partial or distorted models or no model at all. This issue also highlights the implications for artificial intelligence, autonomous vehicles, human perception in virtual and augmented reality, and the treatment of visual disorders, all of which are explored by individual articles. This article is part of a discussion meeting issue 'New approaches to 3D vision'.
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Affiliation(s)
- Paul Linton
- Presidential Scholars in Society and Neuroscience, Center for Science and Society, Columbia University, New York, NY 10027, USA
- Italian Academy for Advanced Studies in America, Columbia University, New York, NY 10027, USA
- Visual Inference Lab, Zuckerman Mind Brain Behavior Institute, Columbia University, New York, NY 10027, USA
| | - Michael J. Morgan
- Department of Optometry and Visual Sciences, City, University of London, Northampton Square, London EC1V 0HB, UK
| | - Jenny C. A. Read
- Biosciences Institute, Newcastle University, Newcastle upon Tyne, Tyne & Wear NE2 4HH, UK
| | - Dhanraj Vishwanath
- School of Psychology and Neuroscience, University of St Andrews, St Andrews, Fife KY16 9JP, UK
| | | | - Fulvio Domini
- Department of Cognitive, Linguistic, and Psychological Sciences, Brown University, Providence, RI 02912-9067, USA
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11
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Sorscher B, Mel GC, Ocko SA, Giocomo LM, Ganguli S. A unified theory for the computational and mechanistic origins of grid cells. Neuron 2023; 111:121-137.e13. [PMID: 36306779 DOI: 10.1016/j.neuron.2022.10.003] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Revised: 05/05/2022] [Accepted: 10/03/2022] [Indexed: 02/05/2023]
Abstract
The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might emerge in a generic manner from neural circuits, and what their computational significance might be. Here, we forge a link between the problem of path integration and the existence of hexagonal grids, by demonstrating that such grids arise in neural networks trained to path integrate under simple biologically plausible constraints. Moreover, we develop a unifying theory for why hexagonal grids are ubiquitous in path-integrator circuits. Such trained networks also yield powerful mechanistic hypotheses, exhibiting realistic levels of biological variability not captured by hand-designed models. We furthermore develop methods to analyze the connectome and activity maps of our networks to elucidate fundamental mechanisms underlying path integration. These methods provide a road map to go from connectomic and physiological measurements to conceptual understanding in a manner that could generalize to other settings.
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Affiliation(s)
- Ben Sorscher
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - Gabriel C Mel
- Neurosciences PhD Program, Stanford University, Stanford, CA 94305, USA.
| | - Samuel A Ocko
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA
| | - Lisa M Giocomo
- Department of Neurobiology, Stanford University School of Medicine, Stanford, CA 94305, USA
| | - Surya Ganguli
- Department of Applied Physics, Stanford University, Stanford, CA 94305, USA; Department of Neurobiology, Stanford University School of Medicine, Stanford, CA 94305, USA
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12
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Wang J, Yan R, Tang H. Grid cell modeling with mapping representation of self-motion for path integration. Neural Comput Appl 2022. [DOI: 10.1007/s00521-021-06039-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Gong Z, Yu F. A Plane-Dependent Model of 3D Grid Cells for Representing Both 2D and 3D Spaces Under Various Navigation Modes. Front Comput Neurosci 2021; 15:739515. [PMID: 34630061 PMCID: PMC8493087 DOI: 10.3389/fncom.2021.739515] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2021] [Accepted: 08/20/2021] [Indexed: 11/30/2022] Open
Abstract
Grid cells are crucial in path integration and representation of the external world. The spikes of grid cells spatially form clusters called grid fields, which encode important information about allocentric positions. To decode the information, studying the spatial structures of grid fields is a key task for both experimenters and theorists. Experiments reveal that grid fields form hexagonal lattice during planar navigation, and are anisotropic beyond planar navigation. During volumetric navigation, they lose global order but possess local order. How grid cells form different field structures behind these different navigation modes remains an open theoretical question. However, to date, few models connect to the latest discoveries and explain the formation of various grid field structures. To fill in this gap, we propose an interpretive plane-dependent model of three-dimensional (3D) grid cells for representing both two-dimensional (2D) and 3D space. The model first evaluates motion with respect to planes, such as the planes animals stand on and the tangent planes of the motion manifold. Projection of the motion onto the planes leads to anisotropy, and error in the perception of planes degrades grid field regularity. A training-free recurrent neural network (RNN) then maps the processed motion information to grid fields. We verify that our model can generate regular and anisotropic grid fields, as well as grid fields with merely local order; our model is also compatible with mode switching. Furthermore, simulations predict that the degradation of grid field regularity is inversely proportional to the interval between two consecutive perceptions of planes. In conclusion, our model is one of the few pioneers that address grid field structures in a general case. Compared to the other pioneer models, our theory argues that the anisotropy and loss of global order result from the uncertain perception of planes rather than insufficient training.
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Affiliation(s)
- Ziyi Gong
- Center for Brain Inspired Computing Research, Tsinghua University, Beijing, China.,Department of Neurobiology, School of Medicine, Duke University, Durham, NC, United States
| | - Fangwen Yu
- Center for Brain Inspired Computing Research, Tsinghua University, Beijing, China
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14
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15
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How environmental movement constraints shape the neural code for space. Cogn Process 2021; 22:97-104. [PMID: 34351539 PMCID: PMC8423650 DOI: 10.1007/s10339-021-01045-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Accepted: 07/09/2021] [Indexed: 11/16/2022]
Abstract
Study of the neural code for space in rodents has many insights to offer for how mammals, including humans, construct a mental representation of space. This code is centered on the hippocampal place cells, which are active in particular places in the environment. Place cells are informed by numerous other spatial cell types including grid cells, which provide a signal for distance and direction and are thought to help anchor the place cell signal. These neurons combine self-motion and environmental information to create and update their map-like representation. Study of their activity patterns in complex environments of varying structure has revealed that this "cognitive map" of space is not a fixed and rigid entity that permeates space, but rather is variably affected by the movement constraints of the environment. These findings are pointing toward a more flexible spatial code in which the map is adapted to the movement possibilities of the space. An as-yet-unanswered question is whether these different forms of representation have functional consequences, as suggested by an enactivist view of spatial cognition.
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16
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Locally ordered representation of 3D space in the entorhinal cortex. Nature 2021; 596:404-409. [PMID: 34381211 DOI: 10.1038/s41586-021-03783-x] [Citation(s) in RCA: 40] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Accepted: 06/29/2021] [Indexed: 02/07/2023]
Abstract
As animals navigate on a two-dimensional surface, neurons in the medial entorhinal cortex (MEC) known as grid cells are activated when the animal passes through multiple locations (firing fields) arranged in a hexagonal lattice that tiles the locomotion surface1. However, although our world is three-dimensional, it is unclear how the MEC represents 3D space2. Here we recorded from MEC cells in freely flying bats and identified several classes of spatial neurons, including 3D border cells, 3D head-direction cells, and neurons with multiple 3D firing fields. Many of these multifield neurons were 3D grid cells, whose neighbouring fields were separated by a characteristic distance-forming a local order-but lacked any global lattice arrangement of the fields. Thus, whereas 2D grid cells form a global lattice-characterized by both local and global order-3D grid cells exhibited only local order, creating a locally ordered metric for space. We modelled grid cells as emerging from pairwise interactions between fields, which yielded a hexagonal lattice in 2D and local order in 3D, thereby describing both 2D and 3D grid cells using one unifying model. Together, these data and model illuminate the fundamental differences and similarities between neural codes for 3D and 2D space in the mammalian brain.
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17
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Why grid cells function as a metric for space. Neural Netw 2021; 142:128-137. [PMID: 34000560 DOI: 10.1016/j.neunet.2021.04.031] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2020] [Revised: 04/16/2021] [Accepted: 04/23/2021] [Indexed: 11/20/2022]
Abstract
The brain is able to calculate the distance and direction to the desired position based on grid cells. Extensive neurophysiological studies of rodent navigation have postulated the grid cells function as a metric for space, and have inspired many computational studies to develop innovative navigation approaches. Furthermore, grid cells may provide a general encoding scheme for high-order nonspatial information. Built upon existing neuroscience and machine learning work, this paper provides theoretical clarity on that the grid cell population codes can be taken as a metric for space. The metric is generated by a shift-invariant positive definite kernel via kernel distance method and embeds isometrically in a Euclidean space, and the inner product of the grid cell population code exponentially converges to the kernel. We also provide a method to learn the distribution of grid cell population efficiently. Grid cells, as a scalable position encoding method, can encode the spatial relationships of places and enable grid cells to outperform place cells in navigation. Further, we extend the grid cell to images encoding and find that grid cells embed images into a mental map, where geometric relationships are conceptual relationships of images. The theoretical model and analysis would contribute to establishing the grid cell code as a generic coding scheme for both spatial and conceptual spaces, and is promising for a multitude of problems across spatial cognition, machine learning and semantic cognition.
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18
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Baram AB, Muller TH, Nili H, Garvert MM, Behrens TEJ. Entorhinal and ventromedial prefrontal cortices abstract and generalize the structure of reinforcement learning problems. Neuron 2021; 109:713-723.e7. [PMID: 33357385 PMCID: PMC7889496 DOI: 10.1016/j.neuron.2020.11.024] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Revised: 10/09/2020] [Accepted: 11/19/2020] [Indexed: 11/25/2022]
Abstract
Knowledge of the structure of a problem, such as relationships between stimuli, enables rapid learning and flexible inference. Humans and other animals can abstract this structural knowledge and generalize it to solve new problems. For example, in spatial reasoning, shortest-path inferences are immediate in new environments. Spatial structural transfer is mediated by cells in entorhinal and (in humans) medial prefrontal cortices, which maintain their co-activation structure across different environments and behavioral states. Here, using fMRI, we show that entorhinal and ventromedial prefrontal cortex (vmPFC) representations perform a much broader role in generalizing the structure of problems. We introduce a task-remapping paradigm, where subjects solve multiple reinforcement learning (RL) problems differing in structural or sensory properties. We show that, as with space, entorhinal representations are preserved across different RL problems only if task structure is preserved. In vmPFC and ventral striatum, representations of prediction error also depend on task structure.
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Affiliation(s)
- Alon Boaz Baram
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, UK.
| | - Timothy Howard Muller
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, UK
| | - Hamed Nili
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, UK
| | - Mona Maria Garvert
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, UK; Max-Planck-Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, 04103, Leipzig, Germany
| | - Timothy Edward John Behrens
- Wellcome Centre for Integrative Neuroimaging, University of Oxford, John Radcliffe Hospital, Oxford OX3 9DU, UK; Wellcome Trust Centre for Neuroimaging, University College London, London WC1N 3AR, UK
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19
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Mok RM, Love BC. A non-spatial account of place and grid cells based on clustering models of concept learning. Nat Commun 2019; 10:5685. [PMID: 31831749 PMCID: PMC6908717 DOI: 10.1038/s41467-019-13760-8] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Accepted: 11/24/2019] [Indexed: 11/24/2022] Open
Abstract
One view is that conceptual knowledge is organized using the circuitry in the medial temporal lobe (MTL) that supports spatial processing and navigation. In contrast, we find that a domain-general learning algorithm explains key findings in both spatial and conceptual domains. When the clustering model is applied to spatial navigation tasks, so-called place and grid cell-like representations emerge because of the relatively uniform distribution of possible inputs in these tasks. The same mechanism applied to conceptual tasks, where the overall space can be higher-dimensional and sampling sparser, leading to representations more aligned with human conceptual knowledge. Although the types of memory supported by the MTL are superficially dissimilar, the information processing steps appear shared. Our account suggests that the MTL uses a general-purpose algorithm to learn and organize context-relevant information in a useful format, rather than relying on navigation-specific neural circuitry.
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Affiliation(s)
- Robert M Mok
- Department of Experimental Psychology, University College London, 26 Bedford Way, London, WC1H 0AP, UK.
| | - Bradley C Love
- Department of Experimental Psychology, University College London, 26 Bedford Way, London, WC1H 0AP, UK.
- The Alan Turing Institute, London, UK.
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20
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Dannenberg H, Alexander AS, Robinson JC, Hasselmo ME. The Role of Hierarchical Dynamical Functions in Coding for Episodic Memory and Cognition. J Cogn Neurosci 2019; 31:1271-1289. [PMID: 31251890 DOI: 10.1162/jocn_a_01439] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Behavioral research in human verbal memory function led to the initial definition of episodic memory and semantic memory. A complete model of the neural mechanisms of episodic memory must include the capacity to encode and mentally reconstruct everything that humans can recall from their experience. This article proposes new model features necessary to address the complexity of episodic memory encoding and recall in the context of broader cognition and the functional properties of neurons that could contribute to this broader scope of memory. Many episodic memory models represent individual snapshots of the world with a sequence of vectors, but a full model must represent complex functions encoding and retrieving the relations between multiple stimulus features across space and time on multiple hierarchical scales. Episodic memory involves not only the space and time of an agent experiencing events within an episode but also features shown in neurophysiological data such as coding of speed, direction, boundaries, and objects. Episodic memory includes not only a spatio-temporal trajectory of a single agent but also segments of spatio-temporal trajectories for other agents and objects encountered in the environment consistent with data on encoding the position and angle of sensory features of objects and boundaries. We will discuss potential interactions of episodic memory circuits in the hippocampus and entorhinal cortex with distributed neocortical circuits that must represent all features of human cognition.
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21
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Abstract
The brain’s spatial map is supported by place cells, encoding current location, and grid cells, which report horizontal distance traveled by producing evenly sized and spaced foci of activity (firing fields) that tile the environment surface. We investigated whether the metric properties of the cells’ activity are the same in vertical space as in horizontal. On a vertical wall, grid-cell firing fields were enlarged and more widely spaced, while place-cell firing fields were unchanged in size/shape but less prevalent. Sensitivity of single-cell and population field potential activity to running speed was reduced. Together, these results suggest that spatial encoding properties are determined by an interaction between the body-plane alignment and the gravity axis. Entorhinal grid cells integrate sensory and self-motion inputs to provide a spatial metric of a characteristic scale. One function of this metric may be to help localize the firing fields of hippocampal place cells during formation and use of the hippocampal spatial representation (“cognitive map”). Of theoretical importance is the question of how this metric, and the resulting map, is configured in 3D space. We find here that when the body plane is vertical as rats climb a wall, grid cells produce stable, almost-circular grid-cell firing fields. This contrasts with previous findings when the body was aligned horizontally during vertical exploration, suggesting a role for the body plane in orienting the plane of the grid cell map. However, in the present experiment, the fields on the wall were fewer and larger, suggesting an altered or absent odometric (distance-measuring) process. Several physiological indices of running speed in the entorhinal cortex showed reduced gain, which may explain the enlarged grid pattern. Hippocampal place fields were found to be sparser but unchanged in size/shape. Together, these observations suggest that the orientation and scale of the grid cell map, at least on a surface, are determined by an interaction between egocentric information (the body plane) and allocentric information (the gravity axis). This may be mediated by the different sensory or locomotor information available on a vertical surface and means that the resulting map has different properties on a vertical plane than a horizontal plane (i.e., is anisotropic).
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22
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Kim M, Maguire EA. Can we study 3D grid codes non-invasively in the human brain? Methodological considerations and fMRI findings. Neuroimage 2019; 186:667-678. [PMID: 30481593 PMCID: PMC6347569 DOI: 10.1016/j.neuroimage.2018.11.041] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 11/21/2018] [Accepted: 11/23/2018] [Indexed: 11/21/2022] Open
Abstract
Recent human functional magnetic resonance imaging (fMRI) and animal electrophysiology studies suggest that grid cells in entorhinal cortex are an efficient neural mechanism for encoding knowledge about the world, not only for spatial location but also for more abstract cognitive information. The world, be it physical or abstract, is often high-dimensional, but grid cells have been mainly studied on a simple two-dimensional (2D) plane. Recent theoretical studies have proposed how grid cells encode three-dimensional (3D) physical space, but it is unknown whether grid codes can be examined non-invasively in humans. Here, we investigated whether it was feasible to test different 3D grid models using fMRI based on the direction-modulated property of grid signals. In doing so, we developed interactive software to help researchers visualize 3D grid fields and predict grid activity in 3D as a function of movement directions. We found that a direction-modulated grid analysis was sensitive to one type of 3D grid model - a face-centred cubic (FCC) lattice model. As a proof of concept, we searched for 3D grid-like signals in human entorhinal cortex using a novel 3D virtual reality paradigm and a new fMRI analysis method. We found that signals in the left entorhinal cortex were explained by the FCC model. This is preliminary evidence for 3D grid codes in the human brain, notwithstanding the inherent methodological limitations of fMRI. We believe that our findings and software serve as a useful initial stepping-stone for studying grid cells in realistic 3D worlds and also, potentially, for interrogating abstract high-dimensional cognitive processes.
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Affiliation(s)
- Misun Kim
- Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London, WC1N 3AR, UK
| | - Eleanor A Maguire
- Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London, WC1N 3AR, UK.
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23
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A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space. Nat Commun 2018; 9:4046. [PMID: 30279469 PMCID: PMC6168468 DOI: 10.1038/s41467-018-06441-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2018] [Accepted: 09/05/2018] [Indexed: 11/30/2022] Open
Abstract
Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps. Neurons in the hippocampal formation encode diverse spatial properties. Here, the authors present a hierarchical network model for 3D spatial navigation that accounts for the observed neuronal representations and predict as yet unreported cell types with planar selectivity.
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24
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Abstract
The world has a complex, three-dimensional (3-D) spatial structure, but until recently the neural representation of space was studied primarily in planar horizontal environments. Here we review the emerging literature on allocentric spatial representations in 3-D and discuss the relations between 3-D spatial perception and the underlying neural codes. We suggest that the statistics of movements through space determine the topology and the dimensionality of the neural representation, across species and different behavioral modes. We argue that hippocampal place-cell maps are metric in all three dimensions, and might be composed of 2-D and 3-D fragments that are stitched together into a global 3-D metric representation via the 3-D head-direction cells. Finally, we propose that the hippocampal formation might implement a neural analogue of a Kalman filter, a standard engineering algorithm used for 3-D navigation.
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Affiliation(s)
- Arseny Finkelstein
- Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Liora Las
- Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Nachum Ulanovsky
- Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel;
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25
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Vágó L, Ujfalussy BB. Robust and efficient coding with grid cells. PLoS Comput Biol 2018; 14:e1005922. [PMID: 29309406 PMCID: PMC5774847 DOI: 10.1371/journal.pcbi.1005922] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2017] [Revised: 01/19/2018] [Accepted: 12/08/2017] [Indexed: 11/24/2022] Open
Abstract
The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise. We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments. We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases. Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules. Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies. Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system.
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Affiliation(s)
- Lajos Vágó
- NAP-B PATTERN Group, MTA Wigner Research Center for Physics, Budapest, Hungary
| | - Balázs B. Ujfalussy
- NAP-B PATTERN Group, MTA Wigner Research Center for Physics, Budapest, Hungary
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26
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Abstract
"Grid cells" encode an animal's location and direction of movement in 2D physical environments via regularly repeating receptive fields. Constantinescu et al. (2016) report the first evidence of grid cells for 2D conceptual spaces. The work has exciting implications for mental representation and shows how detailed neural-coding hypotheses can be tested with bulk population-activity measures.
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Affiliation(s)
- Nikolaus Kriegeskorte
- Medical Research Council Cognition and Brain Sciences Unit, 15 Chaucer Road, Cambridge CB2 7EF, UK.
| | - Katherine R Storrs
- Medical Research Council Cognition and Brain Sciences Unit, 15 Chaucer Road, Cambridge CB2 7EF, UK.
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27
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Herz AV, Mathis A, Stemmler M. Periodic population codes: From a single circular variable to higher dimensions, multiple nested scales, and conceptual spaces. Curr Opin Neurobiol 2017; 46:99-108. [PMID: 28888183 DOI: 10.1016/j.conb.2017.07.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Revised: 07/06/2017] [Accepted: 07/19/2017] [Indexed: 12/27/2022]
Abstract
Across the nervous system, neurons often encode circular stimuli using tuning curves that are not sine or cosine functions, but that belong to the richer class of von Mises functions, which are periodic variants of Gaussians. For a population of neurons encoding a single circular variable with such canonical tuning curves, computing a simple population vector is the optimal read-out of the most likely stimulus. We argue that the advantages of population vector read-outs are so compelling that even the neural representation of the outside world's flat Euclidean geometry is curled up into a torus (a circle times a circle), creating the hexagonal activity patterns of mammalian grid cells. Here, the circular scale is not set a priori, so the nervous system can use multiple scales and gain fields to overcome the ambiguity inherent in periodic representations of linear variables. We review the experimental evidence for this framework and discuss its testable predictions and generalizations to more abstract grid-like neural representations.
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Affiliation(s)
- Andreas Vm Herz
- Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Grosshadernerstrasse 2, 82152 Planegg-Martinsried, Germany.
| | - Alexander Mathis
- Department of Molecular and Cellular Biology and Center for Brain Science, Harvard University, 16 Divinity Avenue, Cambridge, MA 02138, USA; Werner Reichardt Centre for Integrative Neuroscience and Institute for Theoretical Physics, University of Tübingen, 72076 Tübingen, Germany
| | - Martin Stemmler
- Bernstein Center for Computational Neuroscience Munich and Faculty of Biology, Ludwig-Maximilians-Universität München, Grosshadernerstrasse 2, 82152 Planegg-Martinsried, Germany
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28
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Mosheiff N, Agmon H, Moriel A, Burak Y. An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules. PLoS Comput Biol 2017; 13:e1005597. [PMID: 28628647 PMCID: PMC5495497 DOI: 10.1371/journal.pcbi.1005597] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2017] [Revised: 07/03/2017] [Accepted: 05/25/2017] [Indexed: 11/25/2022] Open
Abstract
Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.
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Affiliation(s)
- Noga Mosheiff
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel
| | - Haggai Agmon
- Edmond and Lily Safra Center for Brain Sciences, Hebrew University of Jerusalem, Jerusalem, Israel
| | - Avraham Moriel
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel
| | - Yoram Burak
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem, Israel
- Edmond and Lily Safra Center for Brain Sciences, Hebrew University of Jerusalem, Jerusalem, Israel
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29
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Victor JD, Rizvi SM, Conte MM. Two representations of a high-dimensional perceptual space. Vision Res 2017; 137:1-23. [PMID: 28549921 DOI: 10.1016/j.visres.2017.05.003] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2016] [Revised: 04/27/2017] [Accepted: 05/03/2017] [Indexed: 12/01/2022]
Abstract
A perceptual space is a mental workspace of points in a sensory domain that supports similarity and difference judgments and enables further processing such as classification and naming. Perceptual spaces are present across sensory modalities; examples include colors, faces, auditory textures, and odors. Color is perhaps the best-studied perceptual space, but it is atypical in two respects. First, the dimensions of color space are directly linked to the three cone absorption spectra, but the dimensions of generic perceptual spaces are not as readily traceable to single-neuron properties. Second, generic perceptual spaces have more than three dimensions. This is important because representing each distinguishable point in a high-dimensional space by a separate neuron or population is unwieldy; combinatorial strategies may be needed to overcome this hurdle. To study the representation of a complex perceptual space, we focused on a well-characterized 10-dimensional domain of visual textures. Within this domain, we determine perceptual distances in a threshold task (segmentation) and a suprathreshold task (border salience comparison). In N=4 human observers, we find both quantitative and qualitative differences between these sets of measurements. Quantitatively, observers' segmentation thresholds were inconsistent with their uncertainty determined from border salience comparisons. Qualitatively, segmentation thresholds suggested that distances are determined by a coordinate representation with Euclidean geometry. Border salience comparisons, in contrast, indicated a global curvature of the space, and that distances are determined by activity patterns across broadly tuned elements. Thus, our results indicate two representations of this perceptual space, and suggest that they use differing combinatorial strategies. SIGNIFICANCE STATEMENT To move from sensory signals to decisions and actions, the brain carries out a sequence of transformations. An important stage in this process is the construction of a "perceptual space" - an internal workspace of sensory information that captures similarities and differences, and enables further processing, such as classification and naming. Perceptual spaces for color, faces, visual and haptic textures and shapes, sounds, and odors (among others) are known to exist. How such spaces are represented is at present unknown. Here, using visual textures as a model, we investigate this. Psychophysical measurements suggest roles for two combinatorial strategies: one based on projections onto coordinate-like axes, and one based on patterns of activity across broadly tuned elements scattered throughout the space.
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Affiliation(s)
- Jonathan D Victor
- Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, 1300 York Avenue, New York, NY 10065, United States.
| | - Syed M Rizvi
- Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, 1300 York Avenue, New York, NY 10065, United States
| | - Mary M Conte
- Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, 1300 York Avenue, New York, NY 10065, United States
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30
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Dordek Y, Soudry D, Meir R, Derdikman D. Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis. eLife 2016; 5:e10094. [PMID: 26952211 PMCID: PMC4841785 DOI: 10.7554/elife.10094] [Citation(s) in RCA: 85] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Accepted: 03/08/2016] [Indexed: 11/13/2022] Open
Abstract
Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is -1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.
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Affiliation(s)
- Yedidyah Dordek
- Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel.,Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel
| | - Daniel Soudry
- Department of Statistics, Columbia University, New York, United States.,Center for Theoretical Neuroscience, Columbia University, New York, United States
| | - Ron Meir
- Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel
| | - Dori Derdikman
- Rappaport Faculty of Medicine and Research Institute, Technion - Israel Institute of Technology, Haifa, Israel
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31
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Yoon K, Lewallen S, Kinkhabwala AA, Tank DW, Fiete IR. Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice. Neuron 2016; 89:1086-99. [PMID: 26898777 PMCID: PMC5507689 DOI: 10.1016/j.neuron.2016.01.039] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2015] [Revised: 11/30/2015] [Accepted: 01/13/2016] [Indexed: 12/13/2022]
Abstract
Grid cells, defined by their striking periodic spatial responses in open 2D arenas, appear to respond differently on 1D tracks: the multiple response fields are not periodically arranged, peak amplitudes vary across fields, and the mean spacing between fields is larger than in 2D environments. We ask whether such 1D responses are consistent with the system's 2D dynamics. Combining analytical and numerical methods, we show that the 1D responses of grid cells with stable 1D fields are consistent with a linear slice through a 2D triangular lattice. Further, the 1D responses of comodular cells are well described by parallel slices, and the offsets in the starting points of the 1D slices can predict the measured 2D relative spatial phase between the cells. From these results, we conclude that the 2D dynamics of these cells is preserved in 1D, suggesting a common computation during both types of navigation behavior.
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Affiliation(s)
- KiJung Yoon
- Center for Learning and Memory, University of Texas at Austin, Austin, TX 78712, USA; Department of Neuroscience, University of Texas at Austin, Austin, TX 78712, USA
| | - Sam Lewallen
- Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA; Bezos Center for Neural Circuit Dynamics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA
| | - Amina A Kinkhabwala
- Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA
| | - David W Tank
- Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA; Bezos Center for Neural Circuit Dynamics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA.
| | - Ila R Fiete
- Center for Learning and Memory, University of Texas at Austin, Austin, TX 78712, USA; Department of Neuroscience, University of Texas at Austin, Austin, TX 78712, USA.
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32
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Hayman RMA, Casali G, Wilson JJ, Jeffery KJ. Grid cells on steeply sloping terrain: evidence for planar rather than volumetric encoding. Front Psychol 2015; 6:925. [PMID: 26236245 PMCID: PMC4502341 DOI: 10.3389/fpsyg.2015.00925] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2015] [Accepted: 06/22/2015] [Indexed: 11/29/2022] Open
Abstract
Neural encoding of navigable space involves a network of structures centered on the hippocampus, whose neurons –place cells – encode current location. Input to the place cells includes afferents from the entorhinal cortex, which contains grid cells. These are neurons expressing spatially localized activity patches, or firing fields, that are evenly spaced across the floor in a hexagonal close-packed array called a grid. It is thought that grids function to enable the calculation of distances. The question arises as to whether this odometry process operates in three dimensions, and so we queried whether grids permeate three-dimensional (3D) space – that is, form a lattice – or whether they simply follow the environment surface. If grids form a 3D lattice then this lattice would ordinarily be aligned horizontally (to explain the usual hexagonal pattern observed). A tilted floor would transect several layers of this putative lattice, resulting in interruption of the hexagonal pattern. We model this prediction with simulated grid lattices, and show that the firing of a grid cell on a 40°-tilted surface should cover proportionally less of the surface, with smaller field size, fewer fields, and reduced hexagonal symmetry. However, recording of real grid cells as animals foraged on a 40°-tilted surface found that firing of grid cells was almost indistinguishable, in pattern or rate, from that on the horizontal surface, with if anything increased coverage and field number, and preserved field size. It thus appears unlikely that the sloping surface transected a lattice. However, grid cells on the slope displayed slightly degraded firing patterns, with reduced coherence and slightly reduced symmetry. These findings collectively suggest that the grid cell component of the metric representation of space is not fixed in absolute 3D space but is influenced both by the surface the animal is on and by the relationship of this surface to the horizontal, supporting the hypothesis that the neural map of space is “multi-planar” rather than fully volumetric.
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Affiliation(s)
- Robin M A Hayman
- Department of Clinical and Experimental Epilepsy, Institute of Neurology, Faculty of Brain Sciences, University College London London, UK
| | - Giulio Casali
- Institute of Behavioural Neuroscience, Research Department of Experimental Psychology, Division of Psychology and Language Sciences, University College London London, UK
| | - Jonathan J Wilson
- Institute of Behavioural Neuroscience, Research Department of Experimental Psychology, Division of Psychology and Language Sciences, University College London London, UK
| | - Kate J Jeffery
- Institute of Behavioural Neuroscience, Research Department of Experimental Psychology, Division of Psychology and Language Sciences, University College London London, UK
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33
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Abstract
Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively quickly, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering.
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Affiliation(s)
- Federico Stella
- Cognitive Neuroscience, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
| | - Alessandro Treves
- Cognitive Neuroscience, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
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