Related papers: Swap, Shift and Trim to Edge Collapse a Filtration
This paper presents a novel method which simultaneously learns the number of filters and network features repeatedly over multiple epochs. We propose a novel pruning loss to explicitly enforces the optimizer to focus on promising candidate…
The Vietoris-Rips filtration for an $n$-point metric space is a sequence of large simplicial complexes adding a topological structure to the otherwise disconnected space. The persistent homology is a key tool in topological data analysis…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex. The algorithms here…
Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central…
The Cluster Deletion problem takes a graph $G$ as input and asks for a minimum size set of edges $X$ such that $G-X$ is the disjoint union of complete graphs. An equivalent formulation is the Clique Partition problem, which asks to find a…
We compute the Hodge filtration on cohomology groups of complements of complex coordinate subspace arrangements. By means of this result we construct integral representations of holomorphic functions such that kernels of these…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
Continual learning (CL) is a technique that enables neural networks to constantly adapt to their dynamic surroundings. Despite being overlooked for a long time, this technology can considerably address the customized needs of users in edge…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
Recently deep learning-based methods have been applied in image compression and achieved many promising results. In this paper, we propose an improved hybrid layered image compression framework by combining deep learning and the traditional…
The majority of online continual learning (CL) advocates single-epoch training and imposes restrictions on the size of replay memory. However, single-epoch training would incur a different amount of computations per CL algorithm, and the…
Foundation models like CLIP (Contrastive Language-Image Pretraining) have revolutionized vision-language tasks by enabling zero-shot and few-shot learning through cross-modal alignment. However, their computational complexity and large…
In this paper we present a new approach to computing homology (with field coefficients) and persistent homology. We use concepts from discrete Morse theory, to provide an algorithm which can be expressed solely in terms of simple graph…
Protein fold classification is a classic problem in structural biology and bioinformatics. We approach this problem using persistent homology. In particular, we use alpha shape filtrations to compare a topological representation of the data…
Modern-day neural networks are famously large, yet also highly redundant and compressible; there exist numerous pruning strategies in the deep learning literature that yield over 90% sparser sub-networks of fully-trained, dense…
We present a new tool for data analysis: persistence discrete homology, which is well-suited to analyze filtrations of graphs. In particular, we provide a novel way of representing high-dimensional data as a filtration of graphs using…
Fast methods for convolution and correlation underlie a variety of applications in computer vision and graphics, including efficient filtering, analysis, and simulation. However, standard convolution and correlation are inherently limited…
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale…
The Euler Elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. However, strong nonlinearity and singularity due to the…