Megamap: flexible representation of a large space embedded with nonspatial information by a hippocampal attractor network

State transitions in the statistically stable place cell population correspond to rate of perceptual change

The hippocampus occupies a central role in mammalian navigation and memory. Yet an understanding of the rules that govern the statistics and granularity of the spatial code, as well as its interactions with perceptual stimuli, is lacking. We analyzed CA1 place cell activity recorded while rats foraged in different large-scale environments. We found that place cell activity was subject to an unexpected but precise homeostasis—the distribution of activity in the population as a whole being constant at all locations within and between environments. Using a virtual reconstruction of the largest environment, we showed that the rate of transition through this statistically stable population matches the rate of change in the animals’ visual scene. Thus, place fields near boundaries were small but numerous, while in the environment’s interior, they were larger but more dispersed. These results indicate that hippocampal spatial activity is governed by a small number of simple laws and, in particular, suggest the presence of an information-theoretic bound imposed by perception on the fidelity of the spatial memory system.

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Neural activity in rodent CA1 place cell populations is homeostatically balanced

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Hippocampal place field size and frequency are governed by proximity to boundaries

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Transition rate through place cell population matches rate of change in visual scene

Dorsal CA1 hippocampal place cells form a multi-scale representation of megaspace

Spatially firing "place cells" within the hippocampal CA1 region form internal maps of the environment necessary for navigation and memory. In rodents, these neurons have been almost exclusively studied in small environments (<4 m²). It remains unclear how place cells encode a very large open 2D environment that is commensurate with the natural environments experienced by rodents and other mammals. Such an ethologically realistic environment would require a complex spatial representation, capable of simultaneously representing space at multiple overlapping fine-to-coarse informational scales. Here, we show that in a "megaspace" (18.6 m²), the majority of dorsal CA1 place cells exhibited multiple place subfields of different sizes, akin to those observed along the septo-temporal axis. Furthermore, the total area covered by the subfields of each cell was not correlated with the number of subfields, and increased with the scale of the environment. The multiple different-sized subfields exhibited by place cells in the megaspace suggest that the ensemble population of subfields form a multi-scale representation of space within the dorsal hippocampus. Our findings point to a new dorsal hippocampus ensemble coding scheme that simultaneously supports navigational processes at both fine- and coarse-grained resolutions. VIDEO ABSTRACT.

Experience-dependent contextual codes in the hippocampus

The hippocampus contains neural representations capable of supporting declarative memory. Hippocampal place cells are one such representation, firing in one or few locations in a given environment. Between environments, place cell firing fields remap (turning on/off or moving to a new location) to provide a population-wide code for distinct contexts. However, the manner by which contextual features combine to drive hippocampal remapping remains a matter of debate. Using large-scale in vivo two-photon intracellular calcium recordings in mice during virtual navigation, we show that remapping in the hippocampal region CA1 is driven by prior experience regarding the frequency of certain contexts and that remapping approximates an optimal estimate of the identity of the current context. A simple associative-learning mechanism reproduces these results. Together, our findings demonstrate that place cell remapping allows an animal to simultaneously identify its physical location and optimally estimate the identity of the environment.

Biomimetic FPGA-based spatial navigation model with grid cells and place cells

The mammalian spatial navigation system is characterized by an initial divergence of internal representations, with disparate classes of neurons responding to distinct features including location, speed, borders and head direction; an ensuing convergence finally enables navigation and path integration. Here, we report the algorithmic and hardware implementation of biomimetic neural structures encompassing a feed-forward trimodular, multi-layer architecture representing grid-cell, place-cell and decoding modules for navigation. The grid-cell module comprised of neurons that fired in a grid-like pattern, and was built of distinct layers that constituted the dorsoventral span of the medial entorhinal cortex. Each layer was built as an independent continuous attractor network with distinct grid-field spatial scales. The place-cell module comprised of neurons that fired at one or few spatial locations, organized into different clusters based on convergent modular inputs from different grid-cell layers, replicating the gradient in place-field size along the hippocampal dorso-ventral axis. The decoding module, a two-layer neural network that constitutes the convergence of the divergent representations in preceding modules, received inputs from the place-cell module and provided specific coordinates of the navigating object. After vital design optimizations involving all modules, we implemented the tri-modular structure on Zynq Ultrascale+ field-programmable gate array silicon chip, and demonstrated its capacity in precisely estimating the navigational trajectory with minimal overall resource consumption involving a mere 2.92% Look Up Table utilization. Our implementation of a biomimetic, digital spatial navigation system is stable, reliable, reconfigurable, real-time with execution time of about 32 s for 100k input samples (in contrast to 40 minutes on Intel Core i7-7700 CPU with 8 cores clocking at 3.60 GHz) and thus can be deployed for autonomous-robotic navigation without requiring additional sensors.

Cognitive swarming in complex environments with attractor dynamics and oscillatory computing

Neurobiological theories of spatial cognition developed with respect to recording data from relatively small and/or simplistic environments compared to animals' natural habitats. It has been unclear how to extend theoretical models to large or complex spaces. Complementarily, in autonomous systems technology, applications have been growing for distributed control methods that scale to large numbers of low-footprint mobile platforms. Animals and many-robot groups must solve common problems of navigating complex and uncertain environments. Here, we introduce the NeuroSwarms control framework to investigate whether adaptive, autonomous swarm control of minimal artificial agents can be achieved by direct analogy to neural circuits of rodent spatial cognition. NeuroSwarms analogizes agents to neurons and swarming groups to recurrent networks. We implemented neuron-like agent interactions in which mutually visible agents operate as if they were reciprocally connected place cells in an attractor network. We attributed a phase state to agents to enable patterns of oscillatory synchronization similar to hippocampal models of theta-rhythmic (5-12 Hz) sequence generation. We demonstrate that multi-agent swarming and reward-approach dynamics can be expressed as a mobile form of Hebbian learning and that NeuroSwarms supports a single-entity paradigm that directly informs theoretical models of animal cognition. We present emergent behaviors including phase-organized rings and trajectory sequences that interact with environmental cues and geometry in large, fragmented mazes. Thus, NeuroSwarms is a model artificial spatial system that integrates autonomous control and theoretical neuroscience to potentially uncover common principles to advance both domains.

An uncertainty principle for neural coding: Conjugate representations of position and velocity are mapped onto firing rates and co-firing rates of neural spike trains

The hippocampal system contains neural populations that encode an animal's position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R) conveyed by within‐cell spike intervals, and a co‐firing rate code (R˙) conveyed by between‐cell spike intervals. These two codes behave as conjugates of one another, obeying an analog of the uncertainty principle from physics: information conveyed in R comes at the expense of information in R˙, and vice versa. An exception to this trade‐off occurs when spike trains encode a pair of conjugate variables, such as position and velocity, which do not compete for capacity across R and R˙. To illustrate this, we describe two biologically inspired methods for decoding R and R˙, referred to as sigma and sigma‐chi decoding, respectively. Simulations of head direction and grid cells show that if firing rates are tuned for position (but not velocity), then position is recovered by sigma decoding, whereas velocity is recovered by sigma‐chi decoding. Conversely, simulations of oscillatory interference among theta‐modulated “speed cells” show that if co‐firing rates are tuned for position (but not velocity), then position is recovered by sigma‐chi decoding, whereas velocity is recovered by sigma decoding. Between these two extremes, information about both variables can be distributed across both channels, and partially recovered by both decoders. These results suggest that populations with different spatial and temporal tuning properties—such as speed versus grid cells—might not encode different information, but rather, distribute similar information about position and velocity in different ways across R and R˙. Such conjugate coding of position and velocity may influence how hippocampal populations are interconnected to form functional circuits, and how biological neurons integrate their inputs to decode information from firing rates and spike correlations.

Can Grid Cell Ensembles Represent Multiple Spaces?

The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Unlike hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low-dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute, using two alternative mathematical models, the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple noncongruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.

Memory System Neurons Represent Gaze Position and the Visual World

The entorhinal cortex, a brain area critical for memory, contains neurons that fire when a rodent is in a certain location (eg, grid cells), or when a monkey looks at certain locations. In rodents, these spatial representations align to visual objects in the environment by firing when the animal is in a preferred location defined by relative position of visual environmental features. Recently, our laboratory found that simultaneously recorded entorhinal neurons in monkeys can exhibit different spatial reference frames for gaze position, including a reference frame of visual environmental features. We also discovered that most of the neurons represent gaze position. These results suggest that gaze information in multiple spatial reference frames is a potent signal used in the primate memory system. Here, I describe how these findings support three underappreciated views of the hippocampal memory system.

Analysis of an Attractor Neural Network's Response to Conflicting External Inputs

The theory of attractor neural networks has been influential in our understanding of the neural processes underlying spatial, declarative, and episodic memory. Many theoretical studies focus on the inherent properties of an attractor, such as its structure and capacity. Relatively little is known about how an attractor neural network responds to external inputs, which often carry conflicting information about a stimulus. In this paper we analyze the behavior of an attractor neural network driven by two conflicting external inputs. Our focus is on analyzing the emergent properties of the megamap model, a quasi-continuous attractor network in which place cells are flexibly recombined to represent a large spatial environment. In this model, the system shows a sharp transition from the winner-take-all mode, which is characteristic of standard continuous attractor neural networks, to a combinatorial mode in which the equilibrium activity pattern combines embedded attractor states in response to conflicting external inputs. We derive a numerical test for determining the operational mode of the system a priori. We then derive a linear transformation from the full megamap model with thousands of neurons to a reduced 2-unit model that has similar qualitative behavior. Our analysis of the reduced model and explicit expressions relating the parameters of the reduced model to the megamap elucidate the conditions under which the combinatorial mode emerges and the dynamics in each mode given the relative strength of the attractor network and the relative strength of the two conflicting inputs. Although we focus on a particular attractor network model, we describe a set of conditions under which our analysis can be applied to more general attractor neural networks.

An Energy Model of Place Cell Network in Three Dimensional Space

Place cells are important elements in the spatial representation system of the brain. A considerable amount of experimental data and classical models are achieved in this area. However, an important question has not been addressed, which is how the three dimensional space is represented by the place cells. This question is preliminarily surveyed by energy coding method in this research. Energy coding method argues that neural information can be expressed by neural energy and it is convenient to model and compute for neural systems due to the global and linearly addable properties of neural energy. Nevertheless, the models of functional neural networks based on energy coding method have not been established. In this work, we construct a place cell network model to represent three dimensional space on an energy level. Then we define the place field and place field center and test the locating performance in three dimensional space. The results imply that the model successfully simulates the basic properties of place cells. The individual place cell obtains unique spatial selectivity. The place fields in three dimensional space vary in size and energy consumption. Furthermore, the locating error is limited to a certain level and the simulated place field agrees to the experimental results. In conclusion, this is an effective model to represent three dimensional space by energy method. The research verifies the energy efficiency principle of the brain during the neural coding for three dimensional spatial information. It is the first step to complete the three dimensional spatial representing system of the brain, and helps us further understand how the energy efficiency principle directs the locating, navigating, and path planning function of the brain.

Neurons in Primate Entorhinal Cortex Represent Gaze Position in Multiple Spatial Reference Frames

Primates rely predominantly on vision to gather information from the environment and neurons representing visual space and gaze position are found in many brain areas. Within the medial temporal lobe, a brain region critical for memory, neurons in the entorhinal cortex of macaque monkeys exhibit spatial selectivity for gaze position. Specifically, the firing rate of single neurons reflects fixation location within a visual image (Killian et al., 2012). In the rodents, entorhinal cells such as grid cells, border cells, and head direction cells show spatial representations aligned to visual environmental features instead of the body (Hafting et al., 2005; Sargolini et al., 2006; Solstad et al., 2008; Diehl et al., 2017). However, it is not known whether similar allocentric representations exist in primate entorhinal cortex. Here, we recorded neural activity in the entorhinal cortex in two male rhesus monkeys during a naturalistic, free-viewing task. Our data reveal that a majority of entorhinal neurons represent gaze position and that simultaneously recorded neurons represent gaze position relative to distinct spatial reference frames, with some neurons aligned to the visual image and others aligned to the monkey's head position. Our results also show that entorhinal neural activity can be used to predict gaze position with a high degree of accuracy. These findings demonstrate that visuospatial representation is a fundamental property of entorhinal neurons in primates and suggest that entorhinal cortex may support relational memory and motor planning by coding attentional locus in distinct, behaviorally relevant frames of reference.SIGNIFICANCE STATEMENT The entorhinal cortex, a brain area important for memory, shows striking spatial activity in rodents through grid cells, border cells, head direction cells, and nongrid spatial cells. The majority of entorhinal neurons signal the location of a rodent relative to visual environmental cues, representing the location of the animal relative to space in the world instead of the body. Recently, we found that entorhinal neurons can signal location of gaze while a monkey explores images visually. Here, we report that spatial entorhinal neurons are widespread in the monkey and these neurons are capable of showing a world-based spatial reference frame locked to the bounds of explored images. These results help connect the extensive findings in rodents to the primate.

Theta-paced flickering between place-cell maps in the hippocampus: A model based on short-term synaptic plasticity

Hippocampal place cells represent different environments with distinct neural activity patterns. Following an abrupt switch between two familiar configurations of visual cues defining two environments, the hippocampal neural activity pattern switches almost immediately to the corresponding representation. Surprisingly, during a transient period following the switch to the new environment, occasional fast transitions between the two activity patterns (flickering) were observed (Jezek, Henriksen, Treves, Moser, & Moser, 2011). Here we show that an attractor neural network model of place cells with connections endowed with short‐term synaptic plasticity can account for this phenomenon. A memory trace of the recent history of network activity is maintained in the state of the synapses, allowing the network to temporarily reactivate the representation of the previous environment in the absence of the corresponding sensory cues. The model predicts that the number of flickering events depends on the amplitude of the ongoing theta rhythm and the distance between the current position of the animal and its position at the time of cue switching. We test these predictions with new analysis of experimental data. These results suggest a potential role of short‐term synaptic plasticity in recruiting the activity of different cell assemblies and in shaping hippocampal activity of behaving animals.