Related papers: Synchronization and Noise: A Mechanism for Regular…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
Neural spikes in the brain form stochastic sequences, i.e., belong to the class of pulse noises. This stochasticity is a counterintuitive feature because extracting information - such as the commonly supposed neural information of mean…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a…
Loss of plasticity is a phenomenon where neural networks can become more difficult to train over the course of learning. Continual learning algorithms seek to mitigate this effect by sustaining good performance while maintaining network…
In this paper we address the rotation synchronization problem, where the objective is to recover absolute rotations starting from pairwise ones, where the unknowns and the measures are represented as nodes and edges of a graph,…
Human reasoning can often be understood as an interplay between two systems: the intuitive and associative ("System 1") and the deliberative and logical ("System 2"). Neural sequence models -- which have been increasingly successful at…
This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
In recent years, the machine learning community has seen a continuous growing interest in research aimed at investigating dynamical aspects of both training procedures and machine learning models. Of particular interest among recurrent…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
A trained neural network can be interpreted as a structural causal model (SCM) that provides the effect of changing input variables on the model's output. However, if training data contains both causal and correlational relationships, a…
Neural abstractive summarization methods often require large quantities of labeled training data. However, labeling large amounts of summarization data is often prohibitive due to time, financial, and expertise constraints, which has…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
In this study, we apply a mean field theory to the neural network model with two periodic inputs in order to clarify the conditions of synchronies. This mean field theory yields a self-consistent condition for the synchrony and enables us…
In an attempt to better understand generalization in deep learning, we study several possible explanations. We show that implicit regularization induced by the optimization method is playing a key role in generalization and success of deep…
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of the training loss. Previous works indicate that the noise is…
Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical…