Related papers: Stability of Localized Patterns in Neural Fields
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…
We study the optimization landscape and the stability properties of training problems with squared loss for neural networks and general nonlinear conic approximation schemes. It is demonstrated that, if a nonlinear conic approximation…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
Localized receptive fields -- neurons that are selective for certain contiguous spatiotemporal features of their input -- populate early sensory regions of the mammalian brain. Unsupervised learning algorithms that optimize explicit…
Neural fields, which represent signals as a function parameterized by a neural network, are a promising alternative to traditional discrete vector or grid-based representations. Compared to discrete representations, neural representations…
The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…
We consider the static domain wall braneworld scenario constructed from the Palatini formalism $f(\mathcal{R})$ theory. We check the self-consistency under scalar perturbations. By using the scalar-tensor formalism we avoid dealing with the…
We investigate the energetic ground states of a model two-phase system with 1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous formation of two kinds of periodic domain structure. A striped domain structure is…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…
Recent advances in machine learning have created increasing interest in solving visual computing problems using a class of coordinate-based neural networks that parametrize physical properties of scenes or objects across space and time.…
In this paper we address the issue of output instability of deep neural networks: small perturbations in the visual input can significantly distort the feature embeddings and output of a neural network. Such instability affects many deep…
Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…
In this article, two types of methods from different perspectives based on spectral normalization are described for ensuring the stability of the system controlled by a neural network. The first one is that the L2 gain of the feedback…
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of…
We examine the instabilities of a confined active nematic subjected to an orienting field using a low Reynolds number Ericksen-Leslie framework with active stresses and field-induced torques. Linear analysis reveals two distinct modes, with…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…