Related papers: How Functorial Are (Deep) GADTs?
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
Relational parametricity was first introduced by Reynolds for System F. Although System F provides a strong model for the type systems at the core of modern functional programming languages, it lacks features of daily programming practice…
We present a framework for learning to guide geometric task and motion planning (GTAMP). GTAMP is a subclass of task and motion planning in which the goal is to move multiple objects to target regions among movable obstacles. A standard…
Lots of neural network architectures have been proposed to deal with learning tasks on graph-structured data. However, most of these models concentrate on only node features during the learning process. The edge features, which usually play…
Automatic building extraction from optical imagery remains a challenge due to, for example, the complexity of building shapes. Semantic segmentation is an efficient approach for this task. The latest development in deep convolutional neural…
Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a…
Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for…
Finding the biomarkers associated with ASD is helpful for understanding the underlying roots of the disorder and can lead to earlier diagnosis and more targeted treatment. A promising approach to identify biomarkers is using Graph Neural…
Large language models (LLMs) produce high-dimensional embeddings that capture rich semantic and syntactic relationships between words, sentences, and concepts. Investigating the topological structures of LLM embedding spaces via mapper…
Mapping is an important part of many robotic applications. In order to measure the performance of the mapping process we have to measure the quality of its result: the map. The map is essential for robotic algorithms like localization and…
Understanding the inner workings of deep neural networks (DNNs) is essential to provide trustworthy artificial intelligence techniques for practical applications. Existing studies typically involve linking semantic concepts to units or…
We consider integer programs whose constraint matrix has a special block structure: $\min\{f(x):H_{com}x=b, l\le x\le u,x\in\mathbb{Z}^{t_B+nt_A}\}$, where the objective function $f$ is separable convex and the constraint matrix $H_ {com}$…
Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…
We give a new, short proof that graphs embeddable in a given Euler genus-$g$ surface admit a simple $f(g)$-round $\alpha$-approximation distributed algorithm for Minimum Dominating Set (MDS), where the approximation ratio $\alpha \le 906$.…
Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…
High-Definition (HD) maps are needed for robust navigation of autonomous vehicles, limited by the on-board storage capacity. To solve this, we propose a novel framework, Environment-Aware Normal Distributions Transform (EA-NDT), that…
Recently, Transformer-like deep architectures have shown strong performance on tabular data problems. Unlike traditional models, e.g., MLP, these architectures map scalar values of numerical features to high-dimensional embeddings before…
The generic vector memory based accelerator is considered which supports DIT and DIF FFT with fixed datapath. The regular mixed-radix factorization of the DFT matrix coherent with the accelerator architecture is proposed and the correction…
Graph neural networks (GNNs) have been intensively applied to various graph-based applications. Despite their success, manually designing the well-behaved GNNs requires immense human expertise. And thus it is inefficient to discover the…
In the d-Euclidean Distance Matrix Completion (d-EDMC) problem, one aims to determine whether a given partial matrix of pairwise distances can be extended to a full Euclidean distance matrix in d dimensions. This problem is a cornerstone of…