Related papers: Decomposition Complexity
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Many neural nets appear to represent data as linear combinations of "feature vectors." Algorithms for discovering these vectors have seen impressive recent success. However, we argue that this success is incomplete without an understanding…
We consider the communication complexity of a number of distributed optimization problems. We start with the problem of solving a linear system. Suppose there is a coordinator together with $s$ servers $P_1, \ldots, P_s$, the $i$-th of…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the…
We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\colon X\times Y \to \{0,1\}$ where each value is chosen to be 1 independently with probability…
In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
Techniques to extract information from spectra of unresolved multi-component systems are revised, with emphasis on recent developments and practical aspects. We review the cross-correlation techniques developed to deal with such spectra,…
Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
Ternary and binary neural networks enable multiplication-free computation and promise multiple orders of magnitude efficiency gains over full-precision networks if implemented on specialized hardware. However, since both the parameter and…
In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
We devise a ternary operation for combining three quantum states: it consists of permuting the input systems in a continuous fashion and then discarding all but one of them. This generalizes a binary operation recently studied by Audenaert…
We define a relation that describes the ternary commutator for congruence modular varieties. Properties of this relation are used to investigate the theory of the higher commutator for congruence modular varieties.
The widespread use of multi-sensor technology and the emergence of big datasets has highlighted the limitations of standard flat-view matrix models and the necessity to move towards more versatile data analysis tools. We show that…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…