Estimation of animal location from grid cell populationactivity using persistent cohomology

Many cognitive functions are represented as cell assemblies. For example, the population activity of place cells in the hippocampus and grid cells in the entorhinal cortex represent self-location in the environment. The brain cannot directly observe self-location information in the environment. Instead, it relies on sensory information and memory to estimate self-location. Therefore, estimating low-dimensional dynamics, such as the movement trajectory of an animal exploring its environment, from only the high-dimensional neural activity is important in deciphering the information represented in the brain. Most previous studies have estimated the low-dimensional dynamics behind neural activity by unsupervised learning with dimensionality reduction using artificial neural networks or Gaussian processes. This paper shows theoretically and experimentally that these previous research approaches fail to estimate well when the nonlinearity between high-dimensional neural activity and low-dimensional dynamics becomes strong. We estimate the animals position in 2-D and 3-D space from the activity of grid cells using an unsupervised method based on persistent cohomology. The method using persistent cohomology estimates low-dimensional dynamics from the phases of manifolds created by neural activity. Much cognitive information, including self-location information, is expressed in the phases of the manifolds created by neural activity. The persistent cohomology may be useful for estimating these cognitive functions from neural population activity in an unsupervised manner. Author summaryHippocampal place cells fire only when the animal is in a specific position in the environment. Grid cells in entorhinal cortex fire to spatial locations in a repeating hexagonal grid. Information about self-location in the environment is expressed by the population activity of place cells and grid cells. The brain cannot directly observe the information of self-position in the environment but relies on the direction of movement, distance, and landmarks to estimate self-position. This corresponds to unsupervised learning. Estimating the position of an animal from neural activity alone, without using information about the animals position, is important for understanding the brains representation of information. Unsupervised learning methods using artificial neural networks and Gaussian processes have been used in previous studies to address this problem. However, we show that these previous studies cannot estimate the position of an animal in two dimensions from the population activity of grid cells. As an alternative to the previous studies, we used a topological method called persistent cohomolohy to estimate the animals position in 2D and 3D space from the population activity of grid cells. However, it was impossible to estimate the animals position from the population activity of place cells. We discussed the causes and solutions to this problem.