Related papers: Topology of cognitive maps
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ 2D RNNs to investigate two prototypical…
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…
In this article, we show how the recent statistical techniques developed in Topological Data Analysis for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological…
Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that…
Data reconstruction is a widely used pre-training task to learn the generalized features for many downstream tasks. Although reconstruction tasks have been applied to neural signal completion and denoising, neural signal reconstruction is…
We introduce a novel Theory of Mind (ToM) framework inspired by dual-process theories from cognitive science, integrating a fast, habitual graph-based reasoning system (System 1), implemented via graph convolutional networks (GCNs), and a…
Functional networks provide a topological description of activity patterns in the brain, as they stem from the propagation of neural activity on the underlying anatomical or structural network of synaptic connections. This latter is well…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
Activity in the human brain moves between diverse functional states to meet the demands of our dynamic environment, but fundamental principles guiding these transitions remain poorly understood. Here, we capitalize on recent advances in…
In this paper we propose a neurogeometrical model of the behaviour of cells of the arm area of the primary motor cortex (M1). We mathematically express the hypercolumnar organization of M1 discovered by Georgopoulos, as a fiber bundle, as…
For many important network types (e.g., sensor networks in complex harsh environments and social networks) physical coordinate systems (e.g., Cartesian), and physical distances (e.g., Euclidean), are either difficult to discern or…
We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message…
Neural circuits comprise multiple interconnected regions, each with complex dynamics. The interplay between local and global activity is thought to underlie computational flexibility, yet the structure of multiregion neural activity and its…
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human…
Cognitive maps are a proposed concept on how the brain efficiently organizes memories and retrieves context out of them. The entorhinal-hippocampal complex is heavily involved in episodic and relational memory processing, as well as spatial…
We propose a framework for jointly modeling the geometry and functionality in high dimensional functional surfaces. The proposed mixed effects model characterizes effects of subject-specific covariates and exogenous stimuli on functional…
Inspired by research in psychology, we introduce a behavioral approach for visual navigation using topological maps. Our goal is to enable a robot to navigate from one location to another, relying only on its visual input and the…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…