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The inference of Neural Networks is usually restricted by the resources (e.g., computing power, memory, bandwidth) on edge devices. In addition to improving the hardware design and deploying efficient models, it is possible to aggregate the…
Designing scalable estimation algorithms is a core challenge in modern statistics. Here we introduce a framework to address this challenge based on parallel approximants, which yields estimators with provable properties that operate on the…
The main goal of distribution network (DN) expansion planning is essentially to achieve minimal investment constrained with specified reliability requirements. The reliability-constrained distribution network planning (RcDNP) problem can be…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the…
Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive models for faster inference via parallel token generation. We provide a rigorous foundation for this advantage by formalizing a model of parallel…
In modern large-scale machine learning applications, the training data are often partitioned and stored on multiple machines. It is customary to employ the "data parallelism" approach, where the aggregated training loss is minimized without…
Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…
We present a general, flexible modeling abstraction for building and working with distributed optimization problems called a RemoteOptiGraph. This abstraction extends the OptiGraph model in Plasmo$.$jl, where optimization problems are…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
The life of the modern world essentially depends on the work of the large artificial homogeneous networks, such as wired and wireless communication systems, networks of roads and pipelines. The support of their effective continuous…
The generalized method to have a parallel solution to a computational problem, is to find a way to use Divide & Conquer paradigm in order to have processors acting on its own data and therefore all can be scheduled in parallel. MapReduce is…
Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this…
This paper shows how partial differential problems can be solved thanks to cellular computing and an adaptation of the Least Squares Finite Elements Method. As cellular computing can be implemented on distributed parallel architectures,…
Finding the number of triangles in a network is an important problem in the analysis of complex networks. The number of triangles also has important applications in data mining. Existing distributed memory parallel algorithms for counting…
A new neural network architecture (PSCNN) is developed to improve performance and speed of such networks. The architecture has all the advantages of the previous models such as self-organization and possesses some other superior…
The distributed optimization problem has become increasingly relevant recently. It has a lot of advantages such as processing a large amount of data in less time compared to non-distributed methods. However, most distributed approaches…
We explain how the popular, highly abstract MapReduce model of parallel computation (MRC) can be rooted in reality by explaining how it can be simulated on realistic distributed-memory parallel machine models like BSP. We first refine the…
We consider the problem of intelligent and efficient task allocation mechanism in large-scale mobile edge computing (MEC), which can reduce delay and energy consumption in a parallel and distributed optimization. In this paper, we study the…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…