Related papers: Back to the Continuous Attractor
We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors…
Maintaining stable internal representations of continuous variables is fundamental for effective robotic control. Continuous attractor networks provide a biologically inspired mechanism for encoding such variables, yet neuromorphic…
Continual Learning (CL) is a field dedicated to devise algorithms able to achieve lifelong learning. Overcoming the knowledge disruption of previously acquired concepts, a drawback affecting deep learning models and that goes by the name of…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
We analyze a multiparameter periodically-forced dynamical system inspired in the SIR endemic model. We show that the condition on the \emph{basic reproduction number} $\mathcal{R}_0 < 1$ is not sufficient to guarantee the elimination of…
Oscillators have two main limitations: their synchronization properties are limited (i.e they have a finite synchronization region) and they have no memory of past interactions (i.e. they return to their intrinsic frequency whenever the…
We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and…
We study the long time behavior of the solutions to the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ driven by additive noise and real linear multiplicative noise in the subcritical case (i.e. $\alpha>1/2$) by proving the…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
A large body of research in continual learning is devoted to overcoming the catastrophic forgetting of neural networks by designing new algorithms that are robust to the distribution shifts. However, the majority of these works are strictly…
Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…
Numerical bifurcation analysis, and in particular two-parameter continuation, is used in consort with numerical simulation to reveal complicated dynamics in the Mackey-Glass equation for moderate values of the delay close to the onset of…
Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we…
Weighted bipolar argumentation frameworks allow modeling decision problems and online discussions by defining arguments and their relationships. The strength of arguments can be computed based on an initial weight and the strength of…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
Continual learning is the ability to sequentially learn over time by accommodating knowledge while retaining previously learned experiences. Neural networks can learn multiple tasks when trained on them jointly, but cannot maintain…
Humans and animals learn throughout life. Such continual learning is crucial for intelligence. In this chapter, we examine the pivotal role plasticity mechanisms with complex internal synaptic dynamics could play in enabling this ability in…
We consider a population of agents competing for finite resources using strategies based on two channels of signals. The model is applicable to financial markets, ecosystems and computer networks. We find that the dynamics of the system is…