nlin.AO
7 postsarXiv:2408.00109v3 Announce Type: replace-cross Abstract: Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general--they are destroyed by most infinitesimal changes of the dynamical law that defines them. This fragility limits their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We observe that the bifurcations from continuous attractors in theoretical neuroscience models display various structurally stable forms. Although their asymptotic behaviors to maintain memory are categorically distinct, their finite-time behaviors are similar. We build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the persistent manifold that survives the seemingly destructive bifurcation. Moreover, recurrent neural networks trained on analog memory tasks display approximate continuous attractors with predicted slow manifold structures. Therefore, continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory.
arXiv:2501.11835v1 Announce Type: new Abstract: Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing operational conditions, unknown interactions, excitations, and parametric drift. While data-based models can capture the current state of complex systems, they face significant challenges, including excessive data dependence, limited generalizability to changing conditions, and inability to predict parametric dependence. This has led to combining physics and data in modeling, termed physics-infused machine learning, often using numerical simulations from physics-based models. This paper introduces a novel approach that departs from standard techniques by uncovering information from nonlinear dynamical modeling and embedding it in data-based models. The goal is to create a hybrid adaptive modeling framework that integrates data-based modeling with newly measured data and analytical nonlinear dynamical models for enhanced accuracy, parametric dependence, and improved generalizability. By explicitly incorporating nonlinear dynamic phenomena through perturbation methods, the predictive capabilities are more realistic and insightful compared to knowledge obtained from brute-force numerical simulations. In particular, perturbation methods are utilized to derive asymptotic solutions which are parameterized to generate frequency responses. Frequency responses provide comprehensive insights into dynamics and nonlinearity which are quantified and extracted as high-quality features. A machine-learning model, trained by these features, tracks parameter variations and updates the mismatched model. The results demonstrate that this adaptive modeling method outperforms numerical gray box models in prediction accuracy and computational efficiency.
arXiv:2312.15141v2 Announce Type: replace Abstract: Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks (ESNs), a type of reservoir computer, mirror neural networks but simplify training. They apply fixed, random linear transformations to the internal state, followed by nonlinear changes. This process, guided by input signals and linear regression, adapts the system to match target characteristics, reducing computational demands. A potential drawback of ESNs is that the fixed reservoir may not offer the complexity needed for specific problems. While directly altering (training) the internal ESN would reintroduce the computational burden, an indirect modification can be achieved by redirecting some output as input. This feedback can influence the internal reservoir state, yielding ESNs with enhanced complexity suitable for broader challenges. In this paper, we demonstrate that by feeding some component of the reservoir state back into the network through the input, we can drastically improve upon the performance of a given ESN. We rigorously prove that, for any given ESN, feedback will almost always improve the accuracy of the output. For a set of three tasks, each representing different problem classes, we find that with feedback the average error measures are reduced by $30\%-60\%$. Remarkably, feedback provides at least an equivalent performance boost to doubling the initial number of computational nodes, a computationally expensive and technologically challenging alternative. These results demonstrate the broad applicability and substantial usefulness of this feedback scheme.
arXiv:2501.00160v1 Announce Type: new Abstract: Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution of multi-component systems over time, has uncovered some of the underlying dynamics by constructing deterministic approximation models of stochastic algorithms. In this work, we demonstrate that even in the simplest case of independent Q-learning with a Boltzmann exploration policy, significant discrepancies arise between the actual algorithm and previous approximations. We elaborate why these models actually approximate interesting variants rather than the original incremental algorithm. To explain the discrepancies, we introduce a new discrete-time approximation model that explicitly accounts for agents' update frequencies within the learning process and show that its dynamics fundamentally differ from the simplified dynamics of prior models. We illustrate the usefulness of our approach by applying it to the question of spontaneous cooperation in social dilemmas, specifically the Prisoner's Dilemma as the simplest case study. We identify conditions under which the learning behaviour appears as long-term stable cooperation from an external perspective. However, our model shows that this behaviour is merely a metastable transient phase and not a true equilibrium, making it exploitable. We further exemplify how specific parameter settings can significantly exacerbate the moving target problem in independent learning. Through a systematic analysis of our model, we show that increasing the discount factor induces oscillations, preventing convergence to a joint policy. These oscillations arise from a supercritical Neimark-Sacker bifurcation, which transforms the unique stable fixed point into an unstable focus surrounded by a stable limit cycle.
arXiv:2412.18549v1 Announce Type: cross Abstract: The collection of updated data on social contact patterns following the COVID-19 pandemic disruptions is crucial for future epidemiological assessments and evaluating non-pharmaceutical interventions (NPIs) based on physical distancing. We conducted two waves of an online survey in March 2022 and March 2023 in Italy, gathering data from a representative population sample on direct (verbal/physical interactions) and indirect (prolonged co-location in indoor spaces) contacts. Using a generalized linear mixed model, we examined determinants of individuals' total social contacts and evaluated the potential impact of work-from-home and distance learning on the transmissibility of respiratory pathogens. In-person attendance at work or school emerged as a primary driver of social contacts. Adults attending in person reported a mean of 1.69 (95% CI: 1.56-1.84) times the contacts of those staying home; among children and adolescents, this ratio increased to 2.38 (95% CI: 1.98-2.87). We estimated that suspending all non-essential work alone would marginally reduce transmissibility. However, combining distance learning for all education levels with work-from-home policies could decrease transmissibility by up to 23.7% (95% CI: 18.2%-29.0%). Extending these measures to early childcare services would yield only minimal additional benefits. These results provide useful data for modelling the transmission of respiratory pathogens in Italy after the end of the COVID-19 emergency. They also provide insights into the potential epidemiological effectiveness of social distancing interventions targeting work and school attendance, supporting considerations on the balance between the expected benefits and their heavy societal costs.
arXiv:2403.17392v3 Announce Type: replace Abstract: Cyborg insects refer to hybrid robots that integrate living insects with miniature electronic controllers to enable robotic-like programmable control. These creatures exhibit advantages over conventional robots in adaption to complex terrain and sustained energy efficiency. Nevertheless, there is a lack of literature on the control of multi-cyborg systems. This research gap is due to the difficulty in coordinating the movements of a cyborg system under the presence of insects' inherent individual variability in their reactions to control input. Regarding this issue, we propose a swarm navigation algorithm and verify it under experiments. This research advances swarm robotics by integrating biological organisms with control theory to develop intelligent autonomous systems for real-world applications.
arXiv:2412.16249v1 Announce Type: new Abstract: Behavioral experiments on the ultimatum game (UG) reveal that we humans prefer fair acts, which contradicts the prediction made in orthodox Economics. Existing explanations, however, are mostly attributed to exogenous factors within the imitation learning framework. Here, we adopt the reinforcement learning paradigm, where individuals make their moves aiming to maximize their accumulated rewards. Specifically, we apply Q-learning to UG, where each player is assigned two Q-tables to guide decisions for the roles of proposer and responder. In a two-player scenario, fairness emerges prominently when both experiences and future rewards are appreciated. In particular, the probability of successful deals increases with higher offers, which aligns with observations in behavioral experiments. Our mechanism analysis reveals that the system undergoes two phases, eventually stabilizing into fair or rational strategies. These results are robust when the rotating role assignment is replaced by a random or fixed manner, or the scenario is extended to a latticed population. Our findings thus conclude that the endogenous factor is sufficient to explain the emergence of fairness, exogenous factors are not needed.