A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

A theory of hippocampal function: New developments

We develop further here the only quantitative theory of the storage of information in the hippocampal episodic memory system and its recall back to the neocortex. The theory is upgraded to account for a revolution in understanding of spatial representations in the primate, including human, hippocampus, that go beyond the place where the individual is located, to the location being viewed in a scene. This is fundamental to much primate episodic memory and navigation: functions supported in humans by pathways that build 'where' spatial view representations by feature combinations in a ventromedial visual cortical stream, separate from those for 'what' object and face information to the inferior temporal visual cortex, and for reward information from the orbitofrontal cortex. Key new computational developments include the capacity of the CA3 attractor network for storing whole charts of space; how the correlations inherent in self-organizing continuous spatial representations impact the storage capacity; how the CA3 network can combine continuous spatial and discrete object and reward representations; the roles of the rewards that reach the hippocampus in the later consolidation into long-term memory in part via cholinergic pathways from the orbitofrontal cortex; and new ways of analysing neocortical information storage using Potts networks.

Computing with Residue Numbers in High-Dimensional Representation

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.

Computational cross-species views of the hippocampal formation

The discovery of place cells and head direction cells in the hippocampal formation of freely foraging rodents has led to an emphasis of its role in encoding allocentric spatial relationships. In contrast, studies in head-fixed primates have additionally found representations of spatial views. We review recent experiments in freely moving monkeys that expand upon these findings and show that postural variables such as eye/head movements strongly influence neural activity in the hippocampal formation, suggesting that the function of the hippocampus depends on where the animal looks. We interpret these results in the light of recent studies in humans performing challenging navigation tasks which suggest that depending on the context, eye/head movements serve one of two roles-gathering information about the structure of the environment (active sensing) or externalizing the contents of internal beliefs/deliberation (embodied cognition). These findings prompt future experimental investigations into the information carried by signals flowing between the hippocampal formation and the brain regions controlling postural variables, and constitute a basis for updating computational theories of the hippocampal system to accommodate the influence of eye/head movements.

The chicken and egg problem of grid cells and place cells

Place cells and grid cells are major building blocks of the hippocampal cognitive map. The prominent forward model postulates that grid-cell modules are generated by a continuous attractor network; that a velocity signal evoked during locomotion moves entorhinal activity bumps; and that place-cell activity constitutes summation of entorhinal grid-cell modules. Experimental data support the first postulate, but not the latter two. Several families of solutions that depart from these postulates have been put forward. We suggest a modified model (spatial modulation continuous attractor network; SCAN), whereby place cells are generated from spatially selective nongrid cells. Locomotion causes these cells to move the hippocampal activity bump, leading to movement of the entorhinal manifolds. Such inversion accords with the shift of hippocampal thought from navigation to more abstract functions.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

Place cells dynamically refine grid cell activities to reduce error accumulation during path integration in a continuous attractor model

Navigation is one of the most fundamental skills of animals. During spatial navigation, grid cells in the medial entorhinal cortex process speed and direction of the animal to map the environment. Hippocampal place cells, in turn, encode place using sensory signals and reduce the accumulated error of grid cells for path integration. Although both cell types are part of the path integration system, the dynamic relationship between place and grid cells and the error reduction mechanism is yet to be understood. We implemented a realistic model of grid cells based on a continuous attractor model. The grid cell model was coupled to a place cell model to address their dynamic relationship during a simulated animal's exploration of a square arena. The grid cell model processed the animal's velocity and place field information from place cells. Place cells incorporated salient visual features and proximity information with input from grid cells to define their place fields. Grid cells had similar spatial phases but a diversity of spacings and orientations. To determine the role of place cells in error reduction for path integration, the animal's position estimates were decoded from grid cell activities with and without the place field input. We found that the accumulated error was reduced as place fields emerged during the exploration. Place fields closer to the animal's current location contributed more to the error reduction than remote place fields. Place cells' fields encoding space could function as spatial anchoring signals for precise path integration by grid cells.

Noise-driven bifurcations in a neural field system modelling networks of grid cells

The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity generated by networks of grid cells emerge from the instability of homogeneous activity for small levels of noise. This is carried out by analysing the robustness of network activity patterns with respect to noise in an upscaled noisy grid cell model in the form of a system of partial differential equations. Inhomogeneous network patterns are numerically understood as branches bifurcating from unstable homogeneous states for small noise levels. We show that there is a phase transition occurring as the level of noise decreases. Our numerical study also indicates the presence of hysteresis phenomena close to the precise critical noise value.

Grid-cell modules remain coordinated when neural activity is dissociated from external sensory cues

The representation of an animal’s position in the medial entorhinal cortex (MEC) is distributed across several modules of grid cells, each characterized by a distinct spatial scale. The population activity within each module is tightly coordinated and preserved across environments and behavioral states. Little is known, however, about the coordination of activity patterns across modules. We analyzed the joint activity patterns of hundreds of grid cells simultaneously recorded in animals that were foraging either in the light, when sensory cues could stabilize the representation, or in darkness, when such stabilization was disrupted. We found that the states of different modules are tightly coordinated, even in darkness, when the internal representation of position within the MEC deviates substantially from the true position of the animal. These findings suggest that internal brain mechanisms dynamically coordinate the representation of position in different modules, ensuring that they jointly encode a coherent and smooth trajectory.

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Hundreds of grid cells were recorded simultaneously from multiple grid modules

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Coordination between grid modules was assessed in rats that foraged in darkness

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Coordination persists despite relative drift of the represented versus true position

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This suggests that internal network mechanisms maintain inter-module coordination

Entorhinal-hippocampal interactions lead to globally coherent representations of space

The firing maps of grid cells in the entorhinal cortex are thought to provide an efficient metric system capable of supporting spatial inference in all environments. However, whether spatial representations of grid cells are determined by local environment cues or are organized into globally coherent patterns remains undetermined. We propose a navigation model containing a path integration system in the entorhinal cortex and a cognitive map system in the hippocampus. In the path integration system, grid cell network and head direction (HD) cell network integrate movement and visual information, and form attractor states to represent the positions and head directions of the animal. In the cognitive map system, a topological map is constructed capturing the attractor states of the path integration system as nodes and the transitions between attractor states as links. On loop closure, when the animal revisits a familiar place, the topological map is calibrated to minimize odometry errors. The change of the topological map is mapped back to the path integration system, to correct the states of the grid cells and the HD cells. The proposed model was tested on iRat, a rat-like miniature robot, in a realistic maze. Experimental results showed that, after familiarization of the environment, both grid cells and HD cells develop globally coherent firing maps by map calibration and activity correction. These results demonstrate that the hippocampus and the entorhinal cortex work together to form globally coherent metric representations of the environment. The underlying mechanisms of the hippocampal-entorhinal circuit in capturing the structure of the environment from sequences of experience are critical for understanding episodic memory.

Has the hippocampus really forgotten about space?

Several lines of evidence, including the discovery of place cells, have contributed to the notion that the hippocampus serves primarily to navigate the environment, as a repository of spatial memories, like a drawer full of charts; and that in some species it has exapted on this original one an episodic memory function. We argue that recent evidence questions the primacy of space, and points at memory load, whether spatial or not, as the challenge that mammalian hippocampal circuitry has evolved to meet.

Deep entorhinal cortex: from circuit organization to spatial cognition and memory

The deep layers of the entorhinal cortex are important for spatial cognition, as well as memory storage, consolidation and retrieval. A long-standing hypothesis is that deep-layer neurons relay spatial and memory-related signals between the hippocampus and telencephalon. We review the implications of recent circuit-level analyses that suggest more complex roles. The organization of deep entorhinal layers is consistent with multi-stage processing by specialized cell populations; in this framework, hippocampal, neocortical, and subcortical inputs are integrated to generate representations for use by targets in the telencephalon and for feedback to the superficial entorhinal cortex and hippocampus. Addressing individual sublayers of the deep entorhinal cortex in future experiments and models will be important for establishing systems-level mechanisms for spatial cognition and episodic memory.

Spiking Neural Networks and Hippocampal Function: A Web-Accessible Survey of Simulations, Modeling Methods, and Underlying Theories

Computational modeling has contributed to hippocampal research in a wide variety of ways and through a large diversity of approaches, reflecting the many advanced cognitive roles of this brain region. The intensively studied neuron type circuitry of the hippocampus is a particularly conducive substrate for spiking neural models. Here we present an online knowledge base of spiking neural network simulations of hippocampal functions. First, we overview theories involving the hippocampal formation in subjects such as spatial representation, learning, and memory. Then we describe an original literature mining process to organize published reports in various key aspects, including: (i) subject area (e.g., navigation, pattern completion, epilepsy); (ii) level of modeling detail (Hodgkin-Huxley, integrate-and-fire, etc.); and (iii) theoretical framework (attractor dynamics, oscillatory interference, self-organizing maps, and others). Moreover, every peer-reviewed publication is also annotated to indicate the specific neuron types represented in the network simulation, establishing a direct link with the Hippocampome.org portal. The web interface of the knowledge base enables dynamic content browsing and advanced searches, and consistently presents evidence supporting every annotation. Moreover, users are given access to several types of statistical reports about the collection, a selection of which is summarized in this paper. This open access resource thus provides an interactive platform to survey spiking neural network models of hippocampal functions, compare available computational methods, and foster ideas for suitable new directions of research.

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

Learning an Efficient Hippocampal Place Map from Entorhinal Inputs Using Non-Negative Sparse Coding

Cells in the entorhinal cortex (EC) contain rich spatial information and project strongly to the hippocampus where a cognitive map is supposedly created. These cells range from cells with structured spatial selectivity, such as grid cells in the medial EC (MEC) that are selective to an array of spatial locations that form a hexagonal grid, to weakly spatial cells, such as non-grid cells in the MEC and lateral EC (LEC) that contain spatial information but have no structured spatial selectivity. However, in a small environment, place cells in the hippocampus are generally selective to a single location of the environment, while granule cells in the dentate gyrus of the hippocampus have multiple discrete firing locations but lack spatial periodicity. Given the anatomic connection from the EC to the hippocampus, how the hippocampus retrieves information from upstream EC remains unclear. Here, we propose a unified learning model that can describe the spatial tuning properties of both hippocampal place cells and dentate gyrus granule cells based on non-negative sparse coding from EC inputs. Sparse coding plays an important role in many cortical areas and is proposed here to have a key role in the hippocampus. Our results show that the hexagonal patterns of MEC grid cells with various orientations, grid spacings and phases are necessary for the model to learn different place cells that efficiently tile the entire spatial environment. However, if there is a lack of diversity in any grid parameters or a lack of hippocampal cells in the network, this will lead to the emergence of hippocampal cells that have multiple firing locations. More surprisingly, the model can also learn hippocampal place cells even when weakly spatial cells, instead of grid cells, are used as the input to the hippocampus. This work suggests that sparse coding may be one of the underlying organizing principles for the navigational system of the brain.

Place-cell capacity and volatility with grid-like inputs

What factors constrain the arrangement of the multiple fields of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell’s repertoire – how many field arrangements it can realize without external cues while its grid inputs are unique – and derive its capacity – the spatial range over which it can achieve any field arrangement. We show that the repertoire is very large and relatively noise-robust. However, the repertoire is a vanishing fraction of all arrangements, while capacity scales only as the sum of the grid periods so field arrangements are constrained over larger distances. Thus, grid-driven place field arrangements define a large response scaffold that is strongly constrained by its structured inputs. Finally, we show that altering grid-place weights to generate an arbitrary new place field strongly affects existing arrangements, which could explain the volatility of the place code.