Related papers: Fractal Generative Models
Discovering functional crystalline materials entails navigating an immense combinatorial design space. While recent advances in generative artificial intelligence have enabled the sampling of chemically plausible compositions and…
In this article, we considered a fractal image as a fractal curve, that is, as a walk on a grid in Euclidean space $\R^d$. We placed integers on the generating vectors of a grid, such that opposite directions have opposite numbers. This…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Machine-learned interatomic potentials have transformed computational research in the physical sciences. Recent atomistic `foundation' models have changed the field yet again: trained on many different chemical elements and domains, these…
Prefracture method is a practical implementation for real-time object destruction that is hardly achievable within performance constraints, but can produce unrealistic results due to its heuristic nature. To mitigate it, we approach the…
Efficiently retrieving an enormous chemical library to design targeted molecules is crucial for accelerating drug discovery, organic chemistry, and optoelectronic materials. Despite the emergence of generative models to produce novel…
Breast cancer exhibits intricate morphological and dynamical heterogeneity across cellular, tissue, and tumor scales, posing challenges to conventional modeling approaches that fail to capture its nonlinear, self-similar, or self-affine,…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In…
In this work, we propose a composition/decomposition framework for adversarially training generative models on composed data - data where each sample can be thought of as being constructed from a fixed number of components. In our…
Generative modeling has become a central paradigm in protein research, extending machine learning beyond structure prediction toward sequence design, backbone generation, inverse folding, and biomolecular interaction modeling. However, the…
Materials discovery is fundamental to advance next-generation technologies as well as for sustainable and circular economy. Beyond computational screening, generative models are efficient at finding materials with desired properties, via…
Neural generative models can be used to learn complex probability distributions from data, to sample from them, and to produce probability density estimates. We propose a computational framework for developing neural generative models…
Recently, several methods have leveraged deep generative modeling to produce example-based explanations of image classifiers. Despite producing visually stunning results, these methods are largely disconnected from classical explainability…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
Generative models cover various application areas, including image, video and music synthesis, natural language processing, and molecular design, among many others. As digital generative models become larger, scalable inference in a fast…
Artificial Intelligence (AI)-driven material design has been attracting great attentions as a groundbreaking technology across a wide spectrum of industries. Molecular design is particularly important owing to its broad application domains…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…