相关论文: Guerra interpolation for place cells

The entorhinal-hippocampal circuit plays a critical role in higher brain functions, especially spatial cognition. Grid cells in the medial entorhinal cortex (MEC) periodically fire with different grid spacing and orientation, which makes a…

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…

Place cells in the hippocampus are active when an animal visits a certain location (referred to as a place field) within an environment. Grid cells in the medial entorhinal cortex (MEC) respond at multiple locations, with firing fields that…

In practice, deep neural networks are often able to easily interpolate their training data. To understand this phenomenon, many works have aimed to quantify the memorization capacity of a neural network architecture: the largest number of…

Over the brief time intervals available for processing retinal output, roughly 50 to 300 msec, the number of extra spikes generated by individual ganglion cells can be quite variable. Here, computer-generated spike trains were used to…

We present a hidden Markov model that describes variation in an animal's position associated with varying levels of activity in action potential spike trains of individual place cell neurons. The model incorporates a coarse-graining of…

Discussions of the hippocampus often focus on place cells, but many neurons are not place cells in any given environment. Here we describe the collective activity in such mixed populations, treating place and non-place cells on the same…

New results about Poisson-Dirichlet point processes and Derrida-Ruelle cascades allow us to express Guerra's interpolation entirely in the language of Derrida-Ruelle cascades and to streamline Guerra's computations. Moreover, our approach…

A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…

The mammalian hippocampus plays a principal role in producing a cognitive map of space---an internalized representation of the animal's environment. The neuronal mechanisms producing this map depend primarily on the temporal structure of…

In the mammalian brain, many neuronal ensembles are involved in representing spatial structure of the environment. In particular, there exist cells that encode the animal's location and cells that encode head direction. A number of studies…

There has been a long history of works showing that neural networks have hard time extrapolating beyond the training set. A recent study by Balestriero et al. (2021) challenges this view: defining interpolation as the state of belonging to…

Hippocampal place cells can encode spatial locations of an animal in physical or task-relevant spaces. We simulated place cell populations that encoded either Euclidean- or graph-based positions of a rat navigating to goal nodes in a maze…

The entorhinal-hippocampal formation is the mammalian brain's navigation system, encoding both physical and abstract spaces via grid cells. This system is well-studied in neuroscience, and its efficiency and versatility make it attractive…

In this paper we explain the strikingly regular activity of the 'grid' cells in rodent dorsal medial entorhinal cortex (dMEC) and the spatially localized activity of the hippocampal place cells in CA3 and CA1 by assuming that the…

In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…

Fourier-like summation of several grid cell modules with different spatial frequencies in the medial entorhinal cortex (MEC) has long been proposed to form the contours of place firing fields. Recent experiments largely, but not completely,…

The hippocampus is often attributed to episodic memory formation and storage in the mammalian brain; in particular, Alme et al. showed that hippocampal area CA3 forms statistically independent representations across a large number of…

Evidence accumulation models of simple decision-making have long assumed that the brain estimates a scalar decision variable corresponding to the log-likelihood ratio of the two alternatives. Typical neural implementations of this…

Lattices abound in nature - from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. Such regular arrangements provide solutions for optimally dense packings, efficient resource…