arXiv subjects

Marco Cafiso

Publications and source records attributed to Marco Cafiso.

5 recordsLinked to original sources

arXiv2026

Temporal Complexity and Self-Organization in an Exponential Dense Associative Memory Model

Dense Associative Memory (DAM) models generalize the classical Hopfield model by incorporating n-body or exponential interactions that greatly enhance storage capacity. While the criticality of DAM models has been largely investigated, mainly within a statistical equilibrium picture, little attention has been devoted to the temporal self-organizing behavior induced by learning. In this work, we investigate the behavior of a stochastic exponential DAM (SEDAM) model through the lens of Temporal Complexity (TC), a framework that characterizes complex systems by intermittent transition events between order and disorder and by scale-free temporal statistics. Transition events associated with birth-death of neural avalanche structures are exploited for the TC analyses and compared with analogous transition events based on coincidence structures. We systematically explore how TC indicators depend on control parameters, i.e., noise intensity and memory load. Our results reveal that the SEDAM model exhibits regimes of complex intermittency characterized by nontrivial temporal correlations and scale-free behavior, indicating the spontaneous emergence of self-organizing dynamics. Notably, such regimes arise over finite intervals of noise intensity rather than at a single critical point, consistent with the concept of extended criticality. Further, the noise intensity range needed to reach the critical region, where self-organizing behavior emerges, slightly decreases as the memory load increases. This study highlights the relevance of TC as a complementary framework for understanding learning and information processing in artificial and biological neural systems, revealing the link between the memory load and the self-organizing capacity of the network.

nlin.AO↗

arXiv2025

Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies

Neural network models capable of storing memory have been extensively studied in computer science and computational neuroscience. The Hopfield network is a prototypical example of a model designed for associative, or content-addressable, memory and has been analyzed in many forms. Further, ideas and methods from complex network theory have been incorporated into artificial neural networks and learning, emphasizing their structural properties. Nevertheless, the temporal dynamics also play a vital role in biological neural networks, whose temporal structure is a crucial feature to examine. Biological neural networks display complex intermittency and, thus, can be studied through the lens of the temporal complexity (TC) theory. The TC approach look at the metastability of self-organized states, characterized by a power-law decay in the inter-event time distribution and in the total activity distribution or a scaling behavior in the corresponding event-driven diffusion processes. In this study, we present a temporal complexity (TC) analysis of a biologically-inspired Hopfield-type neural network model. We conducted a comparative assessment between scale-free and random network topologies, with particular emphasis on their global activation patterns. Our parametric analysis revealed comparable dynamical behaviors across both neural network architectures. Furthermore, our investigation into temporal complexity characteristics uncovered that seemingly distinct dynamical patterns exhibit similar temporal complexity behaviors. In particular, similar power-law decay in the activity distribution and similar complexity levels are observed in both topologies, but with a much reduced noise in the scale-free topology. Notably, most of the complex dynamical profiles were consistently observed in scale-free network configurations, thus confirming the crucial role of hubs in neural network dynamics.

q-bio.NC↗

arXiv2025

Criticality of a Stochastic Dense Associative Memory Model with Exponential Interaction Function

The Hopfield network (HN) is a classical model of associative memory with stored patterns encoded as minima of an energy function shaped by a Hebbian learning rule. Dense Associative Memory (DAM) models introduce n-body interactions among neurons with n greater than 2 and, more recently, also exponential interaction functions, which significantly improve the network's storing capacity. While the emergence of phase transitions in HN and DAM were extensively studied, the investigation of exponential DAM is still in its early stages. Further, an equilibrium thermodynamical condition is typically assumed, while out-of-equilibrium dynamics are not considered. Here, we study the temporal dynamics of a stochastic exponential DAM (SEDAM) with a multiplicative salt-and-pepper noise and trained on the MNIST dataset. While taking the noise probability p as control parameter, the time-averaged overlap Q and the diffusion scaling H are taken as order parameters, being H related to the network's time correlation features. The MNIST-based SEDAM is also compared with a SEDAM trained on standard Rademacher patterns and with a stochastic HN (SHN). We found the emergence of a phase transition in both Q and H, with the critical noise level pc decreasing as the load K increases. For each load K, Q highlights a transition between a sub-critical and a super-critical regime, both with short-time correlated dynamics. Conversely, in the critical regime of the MNIST-based SEDAM the network displays long-time correlated dynamics with highly persistent temporal memory marked by the high value H around 1.25. Similar behaviors are observed for both models trained with Rademacher patterns, but with a slightly higher temporal memory index H around 1.5.

physics.app-ph↗

arXiv2025

Robustness of complexity estimation in event-driven signals against accuracy of event detection method

Complexity has gained recent attention in machine learning for its ability to extract synthetic information from large datasets. Complex dynamical systems are characterized by temporal complexity associated with intermittent birth-death events of self-organizing behavior. These rapid transition events (RTEs) can be modelled as a stochastic point process on the time axis, with inter-event times (IETs) revealing rich dynamics. In particular, IETs with power-law distribution mark a departure from the Poisson statistics and indicate the presence of nontrivial complexity that is quantified by the power-law exponent $\mu$ of the IET distribution. However, detection of RTEs in noisy signals remains a challenge, since false positives can obscure the statistical structure of the underlying process. In this paper, we address the problem of quantifying the effect of the event detection tool on the accuracy of complexity estimation. This is reached through a systematic evaluation of the Event-Driven Diffusion Scaling (EDDiS) algorithm, a tool exploiting event-driven diffusion to estimate temporal complexity.After introducing the event detection method RTE-Finder (RTEF), we assess the performance of the RTEF-EDDiS pipeline using event-driven synthetic signals. The reliability of the RTEF is found to strongly depend on parameters such as the percentile and the number of false positives can be much higher than the number of genuine complex events. Despite this, we found that the complexity estimation is quite robust with respect to the rate of false positives. For the power-law distributed IETs with $\mu\le2.5$, the second moment scaling $H$ appears to even improve as the rate of false positives increases, reaching estimation errors of about 4-7%.

physics.comp-ph↗

arXiv2024

Temporal Complexity of a Hopfield-Type Neural Model in Random and Scale-Free Graphs

The Hopfield network model and its generalizations were introduced as a model of associative, or content-addressable, memory. They were widely investigated both as an unsupervised learning method in artificial intelligence and as a model of biological neural dynamics in computational neuroscience. The complexity features of biological neural networks have attracted the scientific community's interest for the last two decades. More recently, concepts and tools borrowed from complex network theory were applied to artificial neural networks and learning, thus focusing on the topological aspects. However, the temporal structure is also a crucial property displayed by biological neural networks and investigated in the framework of systems displaying complex intermittency. The Intermittency-Driven Complexity (IDC) approach indeed focuses on the metastability of self-organized states, whose signature is a power-decay in the inter-event time distribution or a scaling behaviour in the related event-driven diffusion processes. The investigation of IDC in neural dynamics and its relationship with network topology is still in its early stages. In this work, we present the preliminary results of an IDC analysis carried out on a bio-inspired Hopfield-type neural network comparing two different connectivities, i.e., scale-free vs. random network topology. We found that random networks can trigger complexity features similar to that of scale-free networks, even if with some differences and for different parameter values, in particular for different noise levels

q-bio.NC↗