Related papers: PETLS: PErsistent Topological Laplacian Software

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

During the past decade, novel Deep Learning (DL) algorithms, workloads and hardware have been developed to tackle a wide range of problems. Despite the advances in workload and hardware ecosystems, the programming methodology of DL systems…

Recently proposed data-driven predictive control schemes for LTI systems use non-parametric representations based on the image of a Hankel matrix of previously collected, persistently exciting, input-output data. Persistence of excitation…

Developing reliable methods to discriminate different transient brain states that change over time is a key neuroscientific challenge in brain imaging studies. Topological data analysis (TDA), a novel framework based on algebraic topology,…

A large part of modern research, especially in the broad field of complex systems, relies on the numerical integration of PDEs, with and without stochastic noise. This is usually done with eiher in-house made codes or external packages like…

Continual instruction tuning enables large language models (LLMs) to learn incrementally while retaining past knowledge, whereas existing methods primarily focus on how to retain old knowledge rather than on selecting which new knowledge to…

Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…

We present a Python extension to the massively parallel HPC simulation toolkit waLBerla. waLBerla is a framework for stencil based algorithms operating on block-structured grids, with the main application field being fluid simulations in…

The surge of data available on the Internet has driven the adoption of a wide range of computational methods for analyzing and extracting insights from large-scale data. Among these, Machine Learning (ML) has become a central paradigm,…

Graph Laplacians as well as related spectral inequalities and (co-)homology provide a foray into discrete analogues of Riemannian manifolds, providing a rich interplay between combinatorics, geometry and theoretical physics. We apply some…

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…

Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…

There is an explosion of data, documents, and other content, and people require tools to analyze and interpret these, tools to turn the content into information and knowledge. Topic modeling have been developed to solve these problems.…

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…

We introduce topological differential testing (TDT), an approach to extracting the consensus behavior of a set of programs on a corpus of inputs. TDT uses the topological notion of a simplicial complex (and implicitly draws on richer…

Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…

Topological statistics, in the form of persistence diagrams, are a class of shape descriptors that capture global structural information in data. The mapping from data structures to persistence diagrams is almost everywhere differentiable,…

Deep learning (DL) jobs use multi-dimensional parallelism, i.e. combining data, model, and pipeline parallelism, to use large GPU clusters efficiently. Long-running jobs may experience changes to their GPU allocation: (i) resource…