A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space

Modeling hippocampal spatial cells in rodents navigating in 3D environments

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.

Grid cells, border cells, and discrete complex analysis

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.

Grid Cells, Border Cells and Discrete Complex Analysis

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.

Brain inspired path planning algorithms for drones

Introduction

With the development of artificial intelligence and brain science, brain-inspired navigation and path planning has attracted widespread attention.

Methods

In this paper, we present a place cell based path planning algorithm that utilizes spiking neural network (SNN) to create efficient routes for drones. First, place cells are characterized by the leaky integrate-and-fire (LIF) neuron model. Then, the connection weights between neurons are trained by spike-timing-dependent plasticity (STDP) learning rules. Afterwards, a synaptic vector field is created to avoid obstacles and to find the shortest path.

Results

Finally, simulation experiments both in a Python simulation environment and in an Unreal Engine environment are conducted to evaluate the validity of the algorithms.

Discussion

Experiment results demonstrate the validity, its robustness and the computational speed of the proposed model.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.

A Plane-Dependent Model of 3D Grid Cells for Representing Both 2D and 3D Spaces Under Various Navigation Modes

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.

Modeling the grid cell activity on non-horizontal surfaces based on oscillatory interference modulated by gravity

Internal representation of the space is a fundamental and crucial function of the animal's brain. Grid cells in the medial entorhinal cortex are thought to provide an environment-invariant metric system for the navigation of the animal. Most experimental and theoretical studies have focused on the horizontal planar codes of grid cell, while how this metric coordinate system is configured in the actual three-dimensional space remains unclear. Evidence has implied the spatial cognition may not be fully volumetric. We proposed an oscillatory interference model with a novel gravity and body plane modulation to simulate grid cell activity in complex space for rodents. The animal can perceive the rotation of its body plane along the local surface by sensing the gravity, causing the modulation to the dendritic oscillations. The results not only reproduce the firing patterns of the grid cell recorded from known experiments, but also predict the grid codes in novel environments. It further demonstrates that the gravity signal is indispensable for the animal's navigation, and supports the hypothesis that the periodic firing of the grid cell is intrinsically not a volumetric code in three-dimensional space. This will provide new insights to understand the spatial representation of the actual world in the brain.

Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space

We investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment's structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation

We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation.

NeuroSLAM: a brain-inspired SLAM system for 3D environments

Roboticists have long drawn inspiration from nature to develop navigation and simultaneous localization and mapping (SLAM) systems such as RatSLAM. Animals such as birds and bats possess superlative navigation capabilities, robustly navigating over large, three-dimensional environments, leveraging an internal neural representation of space combined with external sensory cues and self-motion cues. This paper presents a novel neuro-inspired 4DoF (degrees of freedom) SLAM system named NeuroSLAM, based upon computational models of 3D grid cells and multilayered head direction cells, integrated with a vision system that provides external visual cues and self-motion cues. NeuroSLAM's neural network activity drives the creation of a multilayered graphical experience map in a real time, enabling relocalization and loop closure through sequences of familiar local visual cues. A multilayered experience map relaxation algorithm is used to correct cumulative errors in path integration after loop closure. Using both synthetic and real-world datasets comprising complex, multilayered indoor and outdoor environments, we demonstrate NeuroSLAM consistently producing topologically correct three-dimensional maps.