Related papers: Mathematical Programming Decoding of Binary Linear…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
Linear programming has played a crucial role in shaping decision-making, resource allocation, and cost reduction in various domains. In this paper, we investigate the application of overparametrized neural networks and their implicit bias…
Machine learning algorithms are typically run on large scale, distributed compute infrastructure that routinely face a number of unavailabilities such as failures and temporary slowdowns. Adding redundant computations using coding-theoretic…
Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
Binary logic programs can be obtained from ordinary logic programs by a binarizing transformation. In most cases, binary programs obtained this way are less efficient than the original programs. (Demoen, 1992) showed an interesting example…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…
In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
Macroprogramming refers to the theory and practice of conveniently expressing the macro(scopic) behaviour of a system using a single program. Macroprogramming approaches are motivated by the need of effectively capturing global/system-level…
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…