相关论文: Computing persistent homology of directed flag com…

A filtration over a simplicial complex $K$ is an ordering of the simplices of $K$ such that all prefixes in the ordering are subcomplexes of $K$. Filtrations are at the core of Persistent Homology, a major tool in Topological Data Analysis.…

There is a recent trend in artificial intelligence (AI) inference towards lower precision data formats down to 8 bits and less. As multiplication is the most complex operation in typical inference tasks, there is a large demand for…

Computational protein structure determination involves optimization in a problem space much too large to exhaustively search. Existing approaches include optimization algorithms such as gradient descent and simulated annealing, but these…

We present a new adaptive parallel algorithm for the challenging problem of multi-dimensional numerical integration on massively parallel architectures. Adaptive algorithms have demonstrated the best performance, but efficient many-core…

Gosper developed an algorithm for performing arithmetic on continued fractions (CFs), and introduced continued logarithms (CLs) as a variant of continued fractions better suited to representing extremely large (or small) numbers. CLs are…

Persistent homology, a method from topological data analysis, extracts robust, multi-scale features from data. It produces stable representations of time series by applying varying thresholds to their values (a process known as a…

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…

This paper shows how to generate efficient tensor algebra code that compute on dynamic sparse tensors, which have sparsity structures that evolve over time. We propose a language for precisely specifying recursive, pointer-based data…

Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…

We propose a serverless computing mechanism for distributed computation based on polar codes. Serverless computing is an emerging cloud based computation model that lets users run their functions on the cloud without provisioning or…

Real-time, energy-efficient inference on edge devices is essential for graph classification across a range of applications. Hyperdimensional Computing (HDC) is a brain-inspired computing paradigm that encodes input features into…

Determining whether two graphs are isomorphic is a fundamental problem with practical applications in areas such as molecular chemistry or social network analysis, yet it remains a challenging task, with exact solutions often being…

Federated Learning is a novel paradigm that involves learning from data samples distributed across a large network of clients while the data remains local. It is, however, known that federated learning is prone to multiple system challenges…

Let $K$ be a finite simplicial, cubical, delta or CW complex. The persistence map $\mathrm{PH}$ takes a filter $f:K \rightarrow \mathbb{R}$ as input and returns the barcodes $\mathrm{PH}(f)$ of the associated sublevel set persistent…

Compiler optimization decisions are often based on hand-crafted heuristics centered around a few established benchmark suites. Alternatively, they can be learned from feature and performance data produced during compilation. However,…

Constructing null models to test the significance of extracted information is a crucial step in data analysis. In this work, we provide a uniformly sampleable null model of directed graphs with the same (or similar) number of simplices in…

Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…

While sparse coding-based clustering methods have shown to be successful, their bottlenecks in both efficiency and scalability limit the practical usage. In recent years, deep learning has been proved to be a highly effective, efficient and…

In this paper we define, implement, and investigate a simplicial complex construction for computing persistent homology of Euclidean point cloud data, which we call the Delaunay-Rips complex (DR). Assigning the Vietoris-Rips weights to…