Related papers: On Generation in Metric Spaces

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…

The development of generative artificial intelligence for human motion generation has expanded rapidly, necessitating a unified evaluation framework. This paper presents a detailed review of eight evaluation metrics for human motion…

In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of…

Starting from the hypothesis that knowledge in semantic space is organized along structured manifolds, we argue that this geometric structure renders the space explorable. By traversing it and using the resulting continuous representations…

Evaluation metrics in image synthesis play a key role to measure performances of generative models. However, most metrics mainly focus on image fidelity. Existing diversity metrics are derived by comparing distributions, and thus they…

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two…

Natural language processing researchers have identified limitations of evaluation methodology for generation tasks, with new questions raised about the validity of automatic metrics and of crowdworker judgments. Meanwhile, efforts to…

Devising domain- and model-agnostic evaluation metrics for generative models is an important and as yet unresolved problem. Most existing metrics, which were tailored solely to the image synthesis setup, exhibit a limited capacity for…

We introduce a notion of Hilbertian n-volume in metric spaces with Besicovitch-type inequalities built-in into the definitions. which, ultimately, may turn useful for an approach to singular spaces with positive scalar curvature

We show if a metric measure space admits a differentiable structure then porous sets have measure zero and hence the measure is pointwise doubling. We then give a construction to show if we only require an approximate differentiable…

The proof of the theorem, which states that the Euclidean metric on the set of random points in an $n$-dimensional Euclidean space with the distribution of a special class, converges in probability in the limit $n\rightarrow\infty$ to the…

Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well…

Deep Learning performs well when training data densely covers the experience space. For complex problems this makes data collection prohibitively expensive. We propose to intelligently select samples when constructing data sets in order to…

Language models have demonstrated the ability to generate highly fluent text; however, it remains unclear whether their output retains coherent high-level structure (e.g., story progression). Here, we propose to apply a statistical tool,…

Recent advances in large pre-trained language models have demonstrated strong results in generating natural languages and significantly improved performances for many natural language generation (NLG) applications such as machine…

The formalism of language generation in the limit studies generative models by requiring an algorithm, given strings from a hidden true language, to eventually generate new valid strings. A core issue is the tension between validity and…

Recent works on language identification and generation have established tight statistical rates at which these tasks can be achieved. These works typically operate under a strong realizability assumption: that the input data is drawn from…

We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that…