Increasing evidence supports the hypothesis that the visual system employs a sparse code to represent visual stimuli, where information is encoded in an efficient way by a small population of cells that respond to sensory input at a given time. This includes simple cells in primary visual cortex (V1), which are defined by their linear spatial integration of visual stimuli. Various models of sparse coding have been proposed to explain physiological phenomena observed in simple cells. However, these models have usually made the simplifying assumption that inputs to simple cells already incorporate linear spatial summation. This overlooks the fact that these inputs are known to have strong non-linearities such the separation of ON and OFF pathways, or separation of excitatory and inhibitory neurons. Consequently these models ignore a range of important experimental phenomena that are related to the emergence of linear spatial summation from non-linear inputs, such as segregation of ON and OFF sub-regions of simple cell receptive fields, the push-pull effect of excitation and inhibition, and phase-reversed cortico-thalamic feedback. Here, we demonstrate that a two-layer model of the visual pathway from the lateral geniculate nucleus to V1 that incorporates these biological constraints on the neural circuits and is based on sparse coding can account for the emergence of these experimental phenomena, diverse shapes of receptive fields and contrast invariance of orientation tuning of simple cells when the model is trained on natural images. The model suggests that sparse coding can be implemented by the V1 simple cells using neural circuits with a simple biologically plausible architecture.

Learning an efficient hippocampal place map from entorhinal inputs using non-negative sparse codingAbbreviated title (50 character max): Learning an efficient place map

Experimental studies of grid cells in the Medial Entorhinal Cortex (MEC) have shown that they are selective to an array of spatial locations in the environment that form a hexagonal grid. However, place cells in the hippocampus are only 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 anatomical connection from MEC to the hippocampus, previous feedforward models of grid-to-place have been proposed. 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. Sparse coding plays an important role in many cortical areas and is proposed here to have a key role in the navigational system of the brain in the hippocampus.Our results show that the hexagonal patterns of grid cells with various orientations, grid spacings and phases are necessary for model cells to learn a single spatial field that efficiently tile the entire spatial environment. However, if there is a lack of diversity in any grid parameters or a lack of cells in the network, this will lead to the emergence of place cells that have multiple firing locations. More surprisingly, the model shows that place cells can also emerge even when non-negative sparse coding is used with weakly-tuned MEC cells, instead of MEC grid cells, as the input to place cells. This work suggests that sparse coding may be one of the underlying organizing principles for the navigational system of the brain.

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.

It is well known that hippocampal place cells have spatio-temporal properties, namely that they generally respond to a single spatial location of a small environment, and they also display the temporal response property of theta phase precession, namely that the phase of spiking relative to the theta wave shifts from the late phase to early phase as the animal crosses the place field. Grid cells in layer II of the medial entorhinal cortex (MEC) also have spatio-temporal properties similar to hippocampal place cells, except that grid cells respond to multiple spatial locations that form a hexagonal pattern. Because the entorhinal cortex (EC) is the upstream area that projects strongly to the hippocampus, a number of EC-hippocampus learning models have been proposed to explain how the spatial receptive field properties of place cells emerge via synaptic plasticity. However, the question of how the phase precession properties of place cells and grid cells are related has remained unclear. This study shows how theta phase precession in hippocampal place cells can emerge from MEC input as a result of synaptic plasticity, demonstrating that a learning model based on non-negative sparse coding can account for both the spatial and temporal properties of hippocampal place cells. Although both MEC grid cells and other EC spatial cells contribute to the spatial properties of hippocampal place cells, it is the MEC grid cells that predominantly determine the temporal response properties of hippocampal place cells displayed here.