Related papers: Fractal Dimension Generalization Measure

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve…

Despite their outstanding performance, large language models (LLMs) suffer notorious flaws related to their preference for simple, surface-level textual relations over full semantic complexity of the problem. This proposal investigates a…

Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…

Wireless mesh networks (WMNs) depend on the spatial distribution of nodes, which directly influences connectivity, routing efficiency, and overall network performance. Conventional models typically assume uniform or random node placement,…

If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…

We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.

There is an ongoing and dedicated effort to estimate bounds on the generalization error of deep learning models, coupled with an increasing interest with practical metrics that can be used to experimentally evaluate a model's ability to…

This paper explores the connection between learning trajectories of Deep Neural Networks (DNNs) and their generalization capabilities when optimized using (stochastic) gradient descent algorithms. Instead of concentrating solely on the…

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;…

Traditional domain generalization methods often rely on domain alignment to reduce inter-domain distribution differences and learn domain-invariant representations. However, domain shifts are inherently difficult to eliminate, which limits…

Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…

Machine learning typically relies on the assumption that training and testing distributions are identical and that data is centrally stored for training and testing. However, in real-world scenarios, distributions may differ significantly…

This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kolmogorov complexity from an information theoretic point of…

Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be…

Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…

Here we propose a new method for the classification of texture images combining fractal measures (fractal dimension, multifractal spectrum and lacunarity) with local binary patterns. More specifically we compute the box counting dimension…

Texture plays an important role in computer vision. It is one of the most important visual attributes used in image analysis, once it provides information about pixel organization at different regions of the image. This paper presents a…

Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…

Existing generalization measures that aim to capture a model's simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically…