Related papers: Encoding certainty in bump attractors
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…
Attractor neural network is an important theoretical scenario for modeling memory function in the hippocampus and in the cortex. In these models, memories are stored in the plastic recurrent connections of neural populations in the form of…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
Word embeddings have recently been shown to reflect many of the pronounced societal biases (e.g., gender bias or racial bias). Existing studies are, however, limited in scope and do not investigate the consistency of biases across relevant…
Working memory - the ability to remember recent events as they recede continuously into the past - requires the ability to represent any stimulus at any time delay. This property requires neurons coding working memory to show mixed…
Spike synchrony, which occurs in various cortical areas in response to specific perception, action and memory tasks, has sparked a long-standing debate on the nature of temporal organization in cortex. One prominent view is that this type…
Crucial problems of the quantum Internet are the derivation of stability properties of quantum repeaters and theory of entanglement rate maximization in an entangled network structure. The stability property of a quantum repeater entails…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant.…
The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…
Recently, encoder-decoder neural networks have shown impressive performance on many sequence-related tasks. The architecture commonly uses an attentional mechanism which allows the model to learn alignments between the source and the target…
In previous work, we have proposed an entanglement indicator for a general multiqubit state, which can be "learned" by a quantum system, acting as a neural network. The indicator can be used for a pure or a mixed state, and it need not be…
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…
Long, elastic filaments cross-linked and deformed by active molecular motors occur in various natural settings. The overall macroscopic mechanical response of such a composite network depends on the coupling between the active and the…
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…
As experiments advance to record from tens of thousands of neurons, statistical physics provides a framework for understanding how collective activity emerges from networks of fine-scale correlations. While modeling these populations is…
Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still…