Topic: continuous attractors

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 structurall

Attractor dynamics are essential components of neural computation— they have given rise to elegant, interpretable models of population coding and working memory. Frequently, attractors are classified based on whether their invariant manifolds can represent discrete/continuous variables, with point attractors being an example of the former and ‘continuous attractors’ of the latter. Here we highlight that ‘learnability’ is another quality that may serve to differentiate neural dynamics while offering novel insight. Counterintuitively, good working memory does not necessarily imply that a well-de

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for arbitrarily long time intervals. Unfortunately, because continuous attractors are not structurally stable, they 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 bifurcations from and approximations of continuous attractors i

Continuous attractors offer a unique class of dynamical systems solutions for storing continuous-valued variables in recurrent neural 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 may limit their utility especially in biological systems as their recurrent dynamics are subject to constant perturbations. We indeed observe that the bifurcations from continuous attractors in theoretical neuroscience models

Though continuous attractors are believed to underlie working memory in the brain, learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of lea

Recent research involving bats navigating lengthy tunnels has confirmed that hippocampal place cells can be active at multiple locations, with considerable variability in place field size and peak rate. In a recurrent networks, such variability implies quenched disorder in the synaptic weights, impeding the establishment of a continuous manifold of fixed points. If most positions in space are not any longer fixed points, is the popular notion of continuous attractors still relevant? What would be the neural dynamics underlying retrieval of spatial representations?We study the dynamics of recur