Related papers: Fountain Codes and Invertible Matrices
We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…
Entringer numbers occur in the Andr\'e permutation combinatorial set-up under several forms. This leads to the construction of a matrix-analog refinement of the tangent (resp. secant) numbers. Furthermore, closed expressions for the…
The lack of uniqueness arising by oversampling of Fourier coefficients is shown to provide a way of transmitting hidden information. A basic encoding/decoding system, developed on the basis of such a possibility, is discussed. The system is…
We present a simple non-generative approach to deep representation learning that seeks equivariant deep embedding through simple objectives. In contrast to existing equivariant networks, our transformation coding approach does not constrain…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This…
Neuroevolution has yet to scale up to complex reinforcement learning tasks that require large networks. Networks with many inputs (e.g. raw video) imply a very high dimensional search space if encoded directly. Indirect methods use a more…
A new model of quantum computation is considered, in which the connections between gates are programmed by the state of a quantum register. This new model of computation is shown to be more powerful than the usual quantum computation, e. g.…
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…
We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number $h\geq 0$ is the entropy of such an SFT if and only if it is right…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that may consist of duplicate entries. We first introduce a new class of matrices called…
Two-dimensional constrained coding is a problem that is much more difficult than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the answers to very natural questions becomes uncomputable. In particular, it is…
We propose a new positional encoding method for a neural network architecture called the Transformer. Unlike the standard sinusoidal positional encoding, our approach is based on solid mathematical grounds and has a guarantee of not losing…
Modeling sets is an important problem in machine learning since this type of data can be found in many domains. A promising approach defines a family of permutation invariant densities with continuous normalizing flows. This allows us to…
Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…
Computer programming textbooks and software documentations often contain flowcharts to illustrate the flow of an algorithm or procedure. Modern OCR engines often tag these flowcharts as graphics and ignore them in further processing. In…
Artificial intelligence (AI) has revolutionized software engineering (SE) by enhancing software development efficiency. The advent of pre-trained models (PTMs) leveraging transfer learning has significantly advanced AI for SE. However,…
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and…
Framing triangulations of unit flow polytopes have received a great deal of recent study with rich connections to various generalizations of Catalan and Cambrian combinatorics as well as volume and h*-polynomial formulas. This story has…
Collective coordinates in a many-particle system are complex Fourier components of the particle density, and often provide useful physical insights. However, given collective coordinates, it is desirable to infer the particle coordinates…