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The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…
Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper…
Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…
Generative foundation models like Stable Diffusion comprise a diverse spectrum of knowledge in computer vision with the potential for transfer learning, e.g., via generating data to train student models for downstream tasks. This could…
Machine learning is becoming increasingly important for nonlinear system identification, including dynamical systems with spatially distributed outputs. However, classical identification and forecasting approaches become markedly less…
Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for…
How diffusion models generalize beyond their training set is not known, and is somewhat mysterious given two facts: the optimum of the denoising score matching (DSM) objective usually used to train diffusion models is the score function of…
Diffusion Models generate data by reversing a stochastic diffusion process, progressively transforming noise into structured samples drawn from a target distribution. Recent theoretical work has shown that this backward dynamics can undergo…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…
Existing music generation models are mostly language-based, neglecting the frequency continuity property of notes, resulting in inadequate fitting of rare or never-used notes and thus reducing the diversity of generated samples. We argue…
Deep learning-based image generation has undergone a paradigm shift since 2021, marked by fundamental architectural breakthroughs and computational innovations. Through reviewing architectural innovations and empirical results, this paper…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
Diffusion models have achieved remarkable success in image and video generation. In this work, we demonstrate that diffusion models can also \textit{generate high-performing neural network parameters}. Our approach is simple, utilizing an…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…