Related papers: Tree structured sparse coding on cubes
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
We examine in detail the accuracy, efficiency and implementation issues that arise when a simplified code structure is employed to evaluate the partition function of the two-dimensional square Ising model on periodic lattices though…
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional…
Tree-width is an invaluable tool for computational problems on graphs. But often one would like to compute on other kinds of objects (e.g. decorated graphs or even algebraic structures) where there is no known tree-width analogue. Here we…
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…
A spread code is a set of vector spaces of a fixed dimension over a finite field Fq with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we…
We provide a concise and accessible introduction to (geometric) string structures, highlighting their connection to loop spaces and outlining relationships with neighboring topics.
We introduce a new variation of Tree Encoding with Nested Intervals, find connections with Materialized Path, and suggest a method for moving parts of the hierarchy.
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…
In this article, we introduce symbol calculus on a projective scheme. Using holomorphic Poisson structures, we construct deformations of ring structures for structure sheaves on projective spaces.
Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…
We consider extremal problems related to decks and multidecks of rooted binary trees (a.k.a. rooted phylogenetic tree shapes). Here, the deck (resp. multideck) of a tree $T$ refers to the set (resp. multiset) of leaf induced binary subtrees…
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold…
This is a survey on stated skein algebras and their representations.
Graphical designs are an extension of spherical designs to functions on graphs. We connect linear codes to graphical designs on cube graphs, and show that the Hamming code in particular is a highly effective graphical design. We show that…
We investigate the class of CSS-$T$ codes, a family of quantum error-correcting codes that allows for a transversal $T$-gate. We extend the definition of a pair of linear codes $(C_1,C_2)$, $C_i\subseteq\mathbb{F}_q^n$, forming a $q$-ary…