Related papers: On Generation in Metric Spaces

This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an…

It can be difficult to tell whether a trained generative model has learned to generate novel examples or has simply memorized a specific set of outputs. In published work, it is common to attempt to address this visually, for example by…

The theory of $D$-norms is an offspring of multivariate extreme value theory. We present recent results on $D$-norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space…

There is a word metric $d$ on countably generated free group $\Gamma$ such that $(\Gamma,d)$ does not admit a coarse uniform embedding into a Hilbert space.

Expressive range analysis is a visualization-based technique used to evaluate the performance of generative models, particularly in game level generation. It typically employs two quantifiable metrics to position generated artifacts on a 2D…

Semantic word embeddings represent the meaning of a word via a vector, and are created by diverse methods. Many use nonlinear operations on co-occurrence statistics, and have hand-tuned hyperparameters and reweighting methods. This paper…

This paper introduces the concept of a generating set for stochastic matrices -- a subset of matrices whose repeated composition generates the entire set. Understanding such generating sets requires specifying the "indivisible elements" and…

Text generation is an important Natural Language Processing task with various applications. Although several metrics have already been introduced to evaluate the text generation methods, each of them has its own shortcomings. The most…

Creativity is often seen as a hallmark of human intelligence. While large language models (LLMs) are increasingly perceived as generating creative text, there is still no holistic and scalable framework to evaluate their creativity across…

Two-dimensional array-based datasets are pervasive in a variety of domains. Current approaches for generative modeling have typically been limited to conventional image datasets and performed in the pixel domain which do not explicitly…

Diversities are a generalization of metric spaces in which a non-negative value is assigned to all finite subsets of a set, rather than just to pairs of points. Here we provide an analogue of the theory of negative type metrics for…

In recent years, generative adversarial networks (GANs) have demonstrated impressive experimental results while there are only a few works that foster statistical learning theory for GANs. In this work, we propose an infinite dimensional…

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…

Can an algorithm create original and compelling fashion designs to serve as an inspirational assistant? To help answer this question, we design and investigate different image generation models associated with different loss functions to…

For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…

Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d.\ test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such…

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the…

Kleinberg and Mullainathan (2024) recently proposed an interesting model for language generation in the limit: Given a countable collection of languages, and an adversary enumerating the strings of some language $L$ from the collection, the…

Embedding spaces contain interpretable dimensions indicating gender, formality in style, or even object properties. This has been observed multiple times. Such interpretable dimensions are becoming valuable tools in different areas of…

The goal of text generation models is to fit the underlying real probability distribution of text. For performance evaluation, quality and diversity metrics are usually applied. However, it is still not clear to what extend can the…