Related papers: On the Lazy Set object
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…
In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…
We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…
We present a novel framework for transferring the knowledge from one system (source) to design a stabilizing controller for a second system (target). Our motivation stems from the hypothesis that abundant data can be collected from the…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
In this paper we demonstrate an approach to model structure and behavior of distributed systems, to map those models to a lightweight execution engine by using a functional programming language and to systematically define and execute tests…
We introduce the lazy search tree data structure. The lazy search tree is a comparison-based data structure on the pointer machine that supports order-based operations such as rank, select, membership, predecessor, successor, minimum, and…
Linearizability is a commonly accepted consistency condition for concurrent objects. Filipovi\'{c} et al. show that linearizability is equivalent to observational refinement. However, linearizability does not permit concurrent objects to…
The need of fast distributed solvers for optimization problems in networked systems has motivated the recent development of the Fast-Lipschitz optimization framework. In such an optimization, problems satisfying certain qualifying…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Fault-tolerant distributed algorithms are central for building reliable spatially distributed systems. Unfortunately, the lack of a canonical precise framework for fault-tolerant algorithms is an obstacle for both verification and…
This paper presents a novel set of algorithms for heap abstraction, identifying logically related regions of the heap. The targeted regions include objects that are part of the same component structure (recursive data structure). The result…
We propose a distributed data-based predictive control scheme to stabilize a network system described by linear dynamics. Agents cooperate to predict the future system evolution without knowledge of the dynamics, relying instead on learning…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
The training dynamics of linear networks are well studied in two distinct setups: the lazy regime and balanced/active regime, depending on the initialization and width of the network. We provide a surprisingly simple unifying formula for…
In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…
We consider a situation where the state of a system is represented by a real-valued vector. Under normal circumstances, the vector is zero, while an event manifests as non-zero entries in this vector, possibly few. Our interest is in the…