V Srinivasa Chakravarthy

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.

Grid cells are a special class of spatial cells found in the medial entorhinal cortex (MEC) characterized by their strikingly regular hexagonal firing fields. This spatially periodic firing pattern is originally considered to be independent of the geometric properties of the environment. However, this notion was contested by examining the grid cell periodicity in environments with different polarity (Krupic et al., 2015) and in connected environments (Carpenter et al., 2015). Aforementioned experimental results demonstrated the dependence of grid cell activity on environmental geometry. Analysis of grid cell periodicity on practically infinite variations of environmental geometry imposes a limitation on the experimental study. Hence we analyze the dependence of grid cell periodicity on the environmental geometry purely from a computational point of view. We use a hierarchical oscillatory network model where velocity inputs are presented to a layer of Head Direction cells, outputs of which are projected to a Path Integration layer. The Lateral Anti-Hebbian Network (LAHN) is used to perform feature extraction from the Path Integration neurons thereby producing a spectrum of spatial cell responses. We simulated the model in five types of environmental geometries such as: (1) connected environments, (2) convex shapes, (3) concave shapes, (4) regular polygons with varying number of sides, and (5) transforming environment. Simulation results point to a greater function for grid cells than what was believed hitherto. Grid cells in the model encode not just the local position but also more global information like the shape of the environment. Furthermore, the model is able to capture the invariant attributes of the physical space ingrained in its LAHN layer, thereby revealing its ability to classify an environment using this information. The proposed model is interesting not only because it is able to capture the experimental results but, more importantly, it is able to make many important predictions on the effect of the environmental geometry on the grid cell periodicity and suggesting the possibility of grid cells encoding the invariant properties of an environment.

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

Oscillatory phenomena are ubiquitous in the brain. Although there are oscillator-based models of brain dynamics, their universal computational properties have not been explored much unlike in the case of rate-coded and spiking neuron network models. Use of oscillator-based models is often limited to special phenomena like locomotor rhythms and oscillatory attractor-based memories. If neuronal ensembles are taken to be the basic functional units of brain dynamics, it is desirable to develop oscillator-based models that can explain a wide variety of neural phenomena. Autoencoders are a special type of feed forward networks that have been used for construction of large-scale deep networks. Although autoencoders based on rate-coded and spiking neuron networks have been proposed, there are no autoencoders based on oscillators. We propose here an oscillatory neural network model that performs the function of an autoencoder. The model is a hybrid of rate-coded neurons and neural oscillators. Input signals modulate the frequency of the neural encoder oscillators. These signals are then multiplexed using a network of rate-code neurons that has afferent Hebbian and lateral anti-Hebbian connectivity, termed as Lateral Anti Hebbian Network (LAHN). Finally the LAHN output is de-multiplexed using an output neural layer which is a combination of adaptive Hopf and Kuramoto oscillators for the signal reconstruction. The Kuramoto-Hopf combination performing demodulation is a novel way of describing a neural phase-locked loop. The proposed model is tested using both synthetic signals and real world EEG signals. The proposed model arises out of the general motivation to construct biologically inspired, oscillatory versions of some of the standard neural network models, and presents itself as an autoencoder network based on oscillatory neurons applicable to time series signals. As a demonstration, the model is applied to compression of EEG signals.

Area V5 or Middle Temporal (MT) area of the primate brain is said to be involved in visual motion perception. Physiological studies indicate that the neurons in MT respond selectively to the direction of moving stimuli. However in response to the complex stimuli containing multiple oriented components, a set of MT neurons are selective to the direction of the component motion whereas the other set of MT neurons are selectively respond to the direction of the whole pattern motion. This paper discusses a two layer LISSOM model (Laterally Interconnected Synergetically Self-Organizing Map) which is analogous to neurons in the cortical areas V1 as well as MT. The adaptive Hebbian learning technique has been used to train the network with sequences of moving square stimuli and observed the following: i) afferent weight connections of V1 neurons are tuned as orientation detectors and ii) neurons at MT is tuned to the whole pattern motion. Lateral connections in each layer mediate the competition between the neurons which results in a topographic map. The results from the two layer LISSOM model was found to be in-line with that of well known experimental studies results.

Head direction (HD) cells, grid cells, and place cells, often dubbed spatial cells, are neural correlates of spatial navigation. We propose a computational model to study the influence of multisensory modalities, especially vision, and proprioception on responses of these cells. A virtual animal was made to navigate within a square box along a synthetic trajectory. Visual information was obtained via a cue card placed at a specific location in the environment, while proprioceptive information was derived from curvature-modulated limb oscillations associated with the gait of the virtual animal. A self-organizing layer was used to encode HD information from both sensory streams. The sensory integration (SI) of HD from both modalities was performed using a continuous attractor network with local connectivity, followed by oscillatory path integration and lateral anti-Hebbian network, where spatial cell responses were observed. The model captured experimental findings which investigated the role of visual manipulation (cue card removal and cue card rotation) on these spatial cells. The model showed a more stable formation of spatial representations via the visual pathway compared to the proprioceptive pathway, emphasizing the role of visual input as an anchor for HD, grid, and place responses. The model suggests the need for SI at the HD level for formation of such stable representations of space essential for effective navigation.

Grid cells and place cells are believed to be cellular substrates for the spatial navigation functions of hippocampus as experimental animals physically navigated in 2D and 3D spaces. However, a recent saccade study on head fixated monkey has also reported grid-like representations on saccadic trajectory while the animal scanned the images on a computer screen. We present two computational models that explain the formation of grid patterns on saccadic trajectory formed on the novel Images. The first model named Saccade Velocity Driven Oscillatory Network-Direct PCA (SVDON—DPCA) explains how grid patterns can be generated on saccadic space using Principal Component Analysis (PCA) like learning rule. The model adopts a hierarchical architecture. We extend this to a network model viz. Saccade Velocity Driven Oscillatory Network—Network PCA (SVDON-NPCA) where the direct PCA stage is replaced by a neural network that can implement PCA using a neurally plausible algorithm. This gives the leverage to study the formation of grid cells at a network level. Saccade trajectory for both models is generated based on an attention model which attends to the salient location by computing the saliency maps of the images. Both models capture the spatial characteristics of grid cells such as grid scale variation on the dorso-ventral axis of Medial Entorhinal cortex. Adding one more layer of LAHN over the SVDON-NPCA model predicts the Place cells in saccadic space, which are yet to be discovered experimentally. To the best of our knowledge, this is the first attempt to model grid cells and place cells from saccade trajectory.