Related papers: Minimal Embedding Dimensions of Connected Neural C…
Let ${\mathcal C}(\Omega)$ be the linear code arising from a projective system $\Omega$ of $\mathrm{PG}(V).$ Consider the point-line geometry $\Gamma=({\mathcal P},{\mathcal L})$ and a projective embedding $\varepsilon\colon…
The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…
We give explicit linear bounds on the p-cohomological dimension of a field in terms of its Diophantine dimension. In particular, we show that for a field of Diophantine dimension at most 4, the 3-cohomological dimension is less than or…
In graph theory, a tree is one of the more popular families of graphs with a wide range of applications in computer science as well as many other related fields. While there are several distance measures over the set of all trees, we…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
A key challenge for RGB-D segmentation is how to effectively incorporate 3D geometric information from the depth channel into 2D appearance features. We propose to model the effective receptive field of 2D convolution based on the scale and…
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
We prove that every $1$-error-correcting code over a finite field can be embedded in a $1$-perfect code of some larger length. Embedding in this context means that the original code is a subcode of the resulting $1$-perfect code and can be…
Constant dimension codes are subsets of the finite Grassmann variety. The study of these codes is a central topic in random linear network coding theory. Orbit codes represent a subclass of constant dimension codes. They are defined as…
A biological neural network in the cortex forms a neural field. Neurons in the field have their own receptive fields, and connection weights between two neurons are random but highly correlated when they are in close proximity in receptive…
We construct six new explicit families of linear maximum sum-rank distance (MSRD) codes, each of which has the smallest field sizes among all known MSRD codes for some parameter regime. Using them and a previous result of the author, we…
Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following…
Deep neural networks (DNNs) achieve remarkable predictive performance but remain difficult to interpret, largely due to overparameterization that obscures the minimal structure required for interpretation. Here we introduce DeepIn, a…
We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the…
Pre-trained word embeddings are widely used for transfer learning in natural language processing. The embeddings are continuous and distributed representations of the words that preserve their similarities in compact Euclidean spaces.…
In this paper, we study the shortest $t$-dimensional hull embeddings of linear codes in both Euclidean and Hermitian cases, extending the existing research on the shortest LCD and self-orthogonal embeddings to arbitrary hull dimensions and…
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…