相关论文: Compaction of Church Numerals for Higher-Order Com…
A new implementation of the canonical polyadic decomposition (CPD) is presented. It features lower computational complexity and memory usage than the available state of art implementations available. The CPD of tensors is a challenging…
A novel algorithm for tunable compression to within the precision of reproduction targets, or storage, is proposed. The new algorithm is termed the `Perceptron Algorithm', which utilises simple existing concepts in a novel way, has multiple…
We give efficient algorithms for ranking Lyndon words of length $n$ over an alphabet of size $\sigma$. The rank of a Lyndon word is its position in the sequence of lexicographically ordered Lyndon words of the same length. The outputs are…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
We consider Cantor measures on the line, with contraction factor $N^{-1}=p^{-\alpha}$ (where $p$ a positive prime, $\alpha$ a positive integer) and $m$ positive integer digits lying in distinct residue classes modulo $N$. We obtain a…
We propose a new succinct representation of labeled trees which represents a tree T using |T|H_k(T) number of bits (plus some smaller order terms), where |T|H_k(T) denotes the k-th order (tree label) entropy, as defined by Ferragina at al.…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…
The classic lower bound of Kuhn, Moscibroda and Wattenhofer [JACM 2016] states that approximate maximum matching and approximate vertex cover (among other problems) in the LOCAL model require $\Omega(\min\{\sqrt{\frac{\log n}{\log\log n}},…
Clipping or saturation in audio signals is a very common problem in signal processing, for which, in the severe case, there is still no satisfactory solution. In such case, there is a tremendous loss of information, and traditional methods…
Binary Neural Network (BNN) represents convolution weights with 1-bit values, which enhances the efficiency of storage and computation. This paper is motivated by a previously revealed phenomenon that the binary kernels in successful BNNs…
Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however,…
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…
An abstract numeration system (ANS) is a numeration system that provides a one-to-one correspondence between the natural numbers and a regular language. In this paper, we define an ANS-based compression as an extension of this…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…
A central topic in mathematical logic is the classification of theorems from mathematics in hierarchies according to their logical strength. Ideally, the place of a theorem in a hierarchy does not depend on the representation (aka coding)…
Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…