Related papers: Memory as Structured Trajectories: Persistent Homo…
Humans learn multiple tasks in succession with minimal mutual interference, through the context gating mechanism in the prefrontal cortex (PFC). The brain-inspired models of spiking neural networks (SNN) have drawn massive attention for…
A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of…
This study is focused on the development of the cortex-like visual object recognition system. We propose a general framework, which consists of three hierarchical levels (modules). These modules functionally correspond to the V1, V4 and IT…
Several guiding principles for thought processes are proposed and a neural-network-type model implementing these principles is presented and studied. We suggest to consider thinking within an associative network built-up of overlapping…
Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful…
Neural circuits in the brain perform a variety of essential functions, including input classification, pattern completion, and the generation of rhythms and oscillations that support processes such as breathing and locomotion. There is also…
Hopfield networks and their generalizations have established deep connections among biological associative memories, statistical physics, and transformers. Yet most models treat retrieval as a fixed query-to-memory mapping, ignoring the…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…
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…
Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
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…
Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
The functional network of the brain continually adapts to changing environmental demands. The environmental changes closely connect with changes of active cognitive processes. In recent years, the network approach has emerged as a promising…
Fascinating and puzzling phenomena, such as landmark vector cells, splitter cells, and event-specific representations to name a few, are regularly discovered in the hippocampus. Without a unifying principle that can explain these divergent…
Spatial awareness in mammals is based on internalized representations of the environment---cognitive maps---encoded by networks of spiking neurons. Although behavioral studies suggest that these maps can remain stable for long periods, it…
We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim…
Memory retention mechanisms play a central role in determining the efficiency of computational architectures designed for processing extended sequences. Conventional methods for token management often impose fixed retention thresholds or…