Related papers: Place Cells as Multi-Scale Position Embeddings: Ra…
Structural and functional heterogeneity are hallmarks of cortical circuits, from broad degree distributions in the mouse connectome to diverse intrinsic neuronal timescales. Yet a mechanistic link between connectivity heterogeneity and…
Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes…
In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…
Learning representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work embeds coordinates using sine…
Human proximity networks are temporal networks representing the close-range proximity among humans in a physical space. They have been extensively studied in the past 15 years as they are critical for understanding the spreading of diseases…
The mammalian spatial navigation system makes use of several different sensory information channels. This information is then converted into a neural code that represents the animal's current position in space by engaging place cell, grid…
Grid cells enable the brain to model the physical space of the world and navigate effectively via path integration, updating self-position using information from self-movement. Recent proposals suggest that the brain might use similar…
Recent years brought advancements in using neural networks for representation learning of various language or visual phenomena. New methods freed data scientists from hand-crafting features for common tasks. Similarly, problems that require…
In real-world sequential decision making tasks like autonomous driving, robotics, and healthcare, learning from observed state-action trajectories is critical for tasks like imitation, classification, and clustering. For example,…
The emerging field of diverse intelligence seeks an integrated view of problem-solving in agents of very different provenance, composition, and substrates. From subcellular chemical networks to swarms of organisms, and across evolved,…
Grid cells play a principal role in enabling mammalian cognitive representations of ambient environments. The key property of these cells -- the regular arrangement of their firing fields -- is commonly viewed as means for establishing…
We view random walks as the paths of foraging animals, perhaps searching for food or avoiding predators while forming a mental map of their surroundings. The formation of such maps requires them to memorise the locations they have visited.…
The time evolutions of discrete-time quantum walks on graphs are determined by the local adjacency relations of the graphs. In this paper, first, we construct a discrete-time quantum walk model that reflects the embedding on the surface so…
Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility.…
Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Positional encodings (PEs) are essential for building powerful and expressive graph neural networks and graph transformers, as they effectively capture the relative spatial relationships between nodes. Although extensive research has been…