Related papers: quollr: An R Package for Visualizing 2-D Models fr…
The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…
High-dimensional motion planning problems can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles.…
In this short article I introduce the knotR package, which creates two dimensional knot diagrams optimized for visual appearance using the R programming language. The knotR package is a systematic R-centric suite of software for the…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
Suppose the data consist of a set $S$ of points $x_j, 1 \leq j \leq J$, distributed in a bounded domain $D \subset R^N$, where $N$ and $J$ are large numbers. In this paper an algorithm is proposed for checking whether there exists a…
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier,…
Volumetric medical imaging technologies produce detailed 3D representations of anatomical structures. However, effective medical data visualization and exploration pose significant challenges, especially for individuals with limited medical…
In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Building from previous work…
Implicit neural representations (INRs) have emerged as a powerful tool for compressing large-scale volume data. This opens up new possibilities for in situ visualization. However, the efficient application of INRs to distributed data…
We present a neural-field-based large-scale reconstruction system that fuses lidar and vision data to generate high-quality reconstructions that are geometrically accurate and capture photo-realistic textures. This system adapts the…
There has been a lot of interest in sufficient dimension reduction (SDR) methodologies as well as nonlinear extensions in the statistics literature. In this note, we use classical results regarding metric spaces and positive definite…
Implicit neural representation (INR) models signals as continuous functions using neural networks, offering efficient and differentiable optimization for inverse problems across diverse disciplines. However, the representational capacity of…
In the realm of medical 3D data, such as CT and MRI images, prevalent anisotropic resolution is characterized by high intra-slice but diminished inter-slice resolution. The lowered resolution between adjacent slices poses challenges,…
We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the…
Massive-scale pretraining has made vision-language models increasingly popular for image-to-image and text-to-image retrieval across a broad collection of domains. However, these models do not perform well when used for challenging…
Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…
Data visualizations can reveal trends and patterns that are not otherwise obvious from the raw data or summary statistics. While visualizing low-dimensional data is relatively straightforward (for example, plotting the change in a variable…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…