Related papers: Least Volume Analysis
Optimal control problems with discrete-valued inputs are inherently challenging due to their mixed-integer nature, rendering them generally intractable for real-time, safety-critical aerospace applications. Lossless convexification offers a…
Generalized linear latent variable models (GLLVMs) are a class of methods for analyzing multi-response data which has garnered considerable popularity in recent years, for example, in the analysis of multivariate abundance data in ecology.…
Voxel-based segmentation volumes often store a large number of labels and voxels, and the resulting amount of data can make storage, transfer, and interactive visualization difficult. We present a lossless compression technique which…
Recent advancements in Large Language Models (LLMs) have demonstrated impressive capabilities as their scale expands to billions of parameters. Deploying these large-scale models on resource-constrained platforms presents significant…
We introduce the concept of volume term adaptivity for high-order discontinuous Galerkin (DG) schemes solving time-dependent partial differential equations. Termed v-adaptivity, we present a novel general approach that exchanges the…
Large language models (LLMs) face significant challenges in processing long contexts due to the linear growth of the key-value (KV) cache and quadratic complexity of self-attention. Existing approaches address these bottlenecks separately:…
Estimating the tangent spaces of a data manifold is a fundamental problem in data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in high-noise settings due to a critical trade-off in choosing the…
One aim of dimensionality reduction is to discover the main factors that explain the data, and as such is paramount to many applications. When working with high dimensional data, autoencoders offer a simple yet effective approach to learn…
Video restoration plays a pivotal role in revitalizing degraded video content by rectifying imperfections caused by various degradations introduced during capturing (sensor noise, motion blur, etc.), saving/sharing (compression, resizing,…
Active Learning (AL) is a learning task that requires learners interactively query the labels of the sampled unlabeled instances to minimize the training outputs with human supervisions. In theoretical study, learners approximate the…
Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…
Large language models (LLM) and vision-language models (VLM) have achieved state-of-the-art performance, but they impose significant memory and computing challenges in deployment. We present a novel low-rank compression framework to address…
In representation learning and non-linear dimension reduction, there is a huge interest to learn the 'disentangled' latent variables, where each sub-coordinate almost uniquely controls a facet of the observed data. While many regularization…
Let $\mathcal{P}$ be an $n$-point subset of Euclidean space and $d\geq 3$ be an integer. In this paper we study the following question: What is the smallest (normalized) relative change of the volume of subsets of $\mathcal{P}$ when it is…
Interpretability and small labelled datasets are key issues in the practical application of deep learning, particularly in areas such as medicine. In this paper, we present a semi-supervised technique that addresses both these issues by…
Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…
As context windows in LLMs scale to 100K+ tokens, the key-value (KV) cache becomes the dominant memory bottleneck, with recent methods claiming 80-90% savings and minimal benchmark degradation. We argue these evaluations miss a structural…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
Extraction of low-dimensional latent space from high-dimensional observation data is essential to construct a real-time robot controller with a world model on the extracted latent space. However, there is no established method for tuning…
In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder.…