Related papers: Founding a mathematical diffusion model in linguis…
Quantifying the speed of linguistic change is challenging due to the fact that the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. In this paper, we propose a…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
Discovering and quantifying the drivers of language change is a major challenge. Hypotheses about causal factors proliferate, but are difficult to rigorously test. Here we ask a simple question: can 20th Century changes in English English…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
The geographical pattern of human dialects is a result of history. Here, we formulate a simple spatial model of language change which shows that the final result of this historical evolution may, to some extent, be predictable. The model…
Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the world's existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon has…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…
Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data…
Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. However, diffusion models that directly work on discrete data space fail to fully exploit the power of iterative…
Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have…
In real-life conversations, the content is diverse, and there exists the one-to-many problem that requires diverse generation. Previous studies attempted to introduce discrete or Gaussian-based continuous latent variables to address the…
The goal of this paper is to provide a complete representation of regional linguistic variation on a global scale. To this end, the paper focuses on removing three constraints that have previously limited work within…
Is it possible to develop a `physics of language' which can explain the spatial, temporal and social patterns we see, and which can predict future change like we forecast the weather? Such a theory is likely to involve ideas from…
Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized…
Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…
We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of…
Pre-trained diffusion models have demonstrated remarkable proficiency in synthesizing images across a wide range of scenarios with customizable prompts, indicating their effective capacity to capture universal features. Motivated by this,…
In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…