相关论文: A computationally efficient framework for vector r…

Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…

The reliability of segmentation models in the medical domain depends on the model's robustness to perturbations in the input space. Robustness is a particular challenge in medical imaging exhibiting various sources of image noise,…

A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the performance of machine learning models. Deeply rooted in algebraic topology, persistent…

Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological…

One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of an iterative change of parameters trying to minimize a loss function. These changes are…

Data representation remains a fundamental challenge in machine learning, particularly when adapting sequence-based architectures like Transformers and Large Language Models (LLMs) for structured tabular data. Existing methods often fail to…

We introduce a simple yet significant improvement to the time-evolving block decimation (TEBD) tensor network algorithm for simulating the time dynamics of strongly correlated one-dimensional (1D) mixed quantum states. The efficiency of 1D…

A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…

Tables contain valuable knowledge in a structured form. We employ neural language modeling approaches to embed tabular data into vector spaces. Specifically, we consider different table elements, such caption, column headings, and cells,…

Visual representation learning has been a cornerstone in computer vision, involving typical forms such as visual embeddings, structural symbols, and text-based representations. Despite the success of CLIP-type visual embeddings, they often…

A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…

The availability of devices that track moving objects has led to an explosive growth in trajectory data. When exploring the resulting large trajectory collections, visual summaries are a useful tool to identify time intervals of interest. A…

The complexity of combustion simulations demands the latest high-performance computing tools to accelerate its time-to-solution results. A current trend on HPC systems is the utilization of CPUs with SIMD or vector extensions to exploit…

We present an efficient document representation learning framework, Document Vector through Corruption (Doc2VecC). Doc2VecC represents each document as a simple average of word embeddings. It ensures a representation generated as such…

This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…

While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

The key to VI is the selection of a tractable density to approximate the Bayesian posterior. For large and complex models a common choice is to assume independence between multivariate blocks in a partition of the parameter space. While…

We provide a deterministic data summarization algorithm that approximates the mean $\bar{p}=\frac{1}{n}\sum_{p\in P} p$ of a set $P$ of $n$ vectors in $\REAL^d$, by a weighted mean $\tilde{p}$ of a \emph{subset} of $O(1/\eps)$ vectors,…