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In an era where visual content generation is increasingly driven by machine learning, the integration of human feedback into generative models presents significant opportunities for enhancing user experience and output quality. This study…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform…
The Regge-Gribov model of the pomeron and odderon in the non-trivial transverse space is studied by the renormalization group technique. The single loop approximation is adopted. Five real fixed points are found and the high-energy…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…
A consumer Behaviour model is considered in the context of a network of interacting individuals in an energy market. We propose and analyse a simple dynamical model of an ensemble of coupled active elements mimicking consumers' Behaviour,…
Recently there has been significant progress in the field of dialogue system thanks to the introduction of training paradigms such as fine-tune and prompt learning. Persona can function as the prior knowledge for maintaining the personality…
Recent advances in autoregressive neural surrogate models have enabled orders-of-magnitude speedups in simulating dynamical systems. However, autoregressive models are generally prone to distribution drift: compounding errors in…
Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…
The goal of the present paper is to explore the long-time behavior of the growth-fragmentation equation formulated in the case of equal mitosis and variability in growth rate, under fairly general assumptions on the coefficients. The first…
Personalized image synthesis has emerged as a pivotal application in text-to-image generation, enabling the creation of images featuring specific subjects in diverse contexts. While diffusion models have dominated this domain,…
Recent generative adversarial networks (GANs) are able to generate impressive photo-realistic images. However, controllable generation with GANs remains a challenging research problem. Achieving controllable generation requires semantically…
Modern generative machine learning models demonstrate surprising ability to create realistic outputs far beyond their training data, such as photorealistic artwork, accurate protein structures, or conversational text. These successes…
Generative reward models (GRMs) have emerged as a promising approach for aligning Large Language Models (LLMs) with human preferences by offering greater representational capacity and flexibility than traditional scalar reward models.…
Growth models with internal habit formation have been studied in various settings under the assumption of deterministic dynamics. The purpose of this paper is to explore a stochastic version of the model in Carroll et al. [1997, 2000], one…
In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…
There are many natural, physical, and biological systems that exhibit multiple time scales. For example, the dynamics of a population of ticks can be described in continuous time during their individual life cycle yet discrete time is used…
Behaviour change lies at the heart of many observable collective phenomena such as the transmission and control of infectious diseases, adoption of public health policies, and migration of animals to new habitats. Representing the process…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…