Related papers: Grade Inflation in Generative Models

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Evaluating the performance of generative models in image synthesis is a challenging task. Although the Fr\'echet Inception Distance is a widely accepted evaluation metric, it integrates different aspects (e.g., fidelity and diversity) of…

Endogeneity bias and instrument variable validation have always been important topics in statistics and econometrics. In the era of big data, such issues typically combine with dimensionality issues and, hence, require even more attention.…

We propose to learn a generative model via entropy interpolation with a Schr\"{o}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the…

The ensemble smoother with multiple data assimilation (ES-MDA) is becoming a popular assisted history matching method. In its standard form, the method requires the specification of the number of iterations in advance. If the selected…

An alternative scenario about the phenomenology of primordial Universe is k-inflation. According to this concept, inflation can be achieved by nonstandard kinetic term of scalar field, namely the inflaton. In this project we focus on…

Implicit generative modeling (IGM) aims to produce samples of synthetic data matching the characteristics of a target data distribution. Recent work (e.g. score-matching networks, diffusion models) has approached the IGM problem from the…

The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystem, and brain network. Measuring…

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function…

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…

The inflationary paradigm has transformed our understanding of the early universe; yet most inflationary models are considered geodesically past-incomplete, suggesting a beginning of time or a primordial Big Bang singularity. The…

We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established…

The variational lower bound (a.k.a. ELBO or free energy) is the central objective for many established as well as for many novel algorithms for unsupervised learning. Such algorithms usually increase the bound until parameters have…

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…

The incorporation of generative models as regularisers within variational formulations for inverse problems has proven effective across numerous image reconstruction tasks. However, the resulting optimisation problem is often non-convex and…

A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…

While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…

We study a new ensemble of random correlation matrices related to multivariate Student (or more generally elliptic) random variables. We establish the exact density of states of empirical correlation matrices that generalizes the…

Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a…