Related papers: Geometric Phase Transition Enables Extreme Hippoca…
The nervous system, more specifically, the brain, is capable of solving complex problems simply and efficiently, far surpassing modern computers. In this regard, neuromorphic engineering is a research field that focuses on mimicking the…
We study the storage of multiple phase-coded patterns as stable dynamical attractors in recurrent neural networks with sparse connectivity. To determine the synaptic strength of existent connections and store the phase-coded patterns, we…
High-capacity kernel Hopfield networks exhibit a \textit{Ridge of Optimization} characterized by extreme stability. While previously linked to \textit{Spectral Concentration}, its origin remains elusive. Here, we analyze the network…
We study a simple extended model of oscillator neural networks capable of storing sparsely coded phase patterns, in which information is encoded both in the mean firing rate and in the timing of spikes. Applying the methods of statistical…
The compression of geometric structures is a relatively new field of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are…
Contemporary ML separates the static structure of parameters from the dynamic flow of inference, yielding systems that lack the sample efficiency and thermodynamic frugality of biological cognition. In this theoretical work, we propose…
Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…
Hippocampal neurons exhibit precise phase locking to network oscillations, but the computational principle governing this temporal precision is still unclear. Neural information is conveyed jointly by firing rates and spike timing, but…
Attractor neural network is an important theoretical scenario for modeling memory function in the hippocampus and in the cortex. In these models, memories are stored in the plastic recurrent connections of neural populations in the form of…
In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms…
Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…
We model a direct solid-state phase transition through a nucleation-and-growth process in which plates have simple, regular shapes - squares, cubes, or square-faced lamellae - and grow homothetically (self-similarly) until they either reach…
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…
Topographic maps are a brain structure connecting pre-synpatic and post-synaptic brain regions. Topographic development is dependent on Hebbian-based plasticity mechanisms working in conjunction with spontaneous patterns of neural activity…
Mammalian brains span about 4 orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral…
Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal…
We propose a formal foundation for cognition rooted in algebraic topology, built on a Homological Parity Principle. This posits that even-dimensional homology represents stable Structure/Context (e.g., generative models), while…
Crumpling an ordinary thin sheet transforms it into a structure with unusual mechanical behaviors, such as enhanced rigidity, emission of crackling noise, slow relaxations, and memory retention. A central challenge in explaining these…