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Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or…
The Ensemble Score Filter (EnSF) has emerged as a promising approach to leverage score-based diffusion models for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model…
Embedded systems have proliferated in various consumer and industrial applications with the evolution of Cyber-Physical Systems and the Internet of Things. These systems are subjected to stringent constraints so that embedded software must…
Today, deep learning optimization is primarily driven by research focused on achieving high inference accuracy and reducing latency. However, the energy efficiency aspect is often overlooked, possibly due to a lack of sustainability mindset…
Rapid adoption of machine learning (ML) technologies has led to a surge in power consumption across diverse systems, from tiny IoT devices to massive datacenter clusters. Benchmarking the energy efficiency of these systems is crucial for…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for…
Delay-coupled electro-optical systems have received much attention for their dynamical properties and their potential use in signal processing. In particular it has recently been demonstrated, using the artificial intelligence algorithm…
Modern scientific simulations generate massive volumes of data, creating significant challenges for I/O and storage systems. Error-bounded lossy compression (EBLC) offers a solution by reducing data set sizes while preserving data quality…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
In this work faster unsigned multiplication has been achieved by using a combination of High Performance Multiplication [HPM] column reduction technique and implementing a N-bit multiplier using 4 N/2-bit multipliers (recursive…
The increasing deployment of large language models (LLMs) in natural language processing (NLP) tasks raises concerns about energy efficiency and sustainability. While prior research has largely focused on energy consumption during model…
Hybrid intelligence aims to enhance decision-making, problem-solving, and overall system performance by combining the strengths of both, human cognitive abilities and artificial intelligence. With the rise of Large Language Models (LLM),…
The rising computational and energy demands of deep learning, particularly in large-scale architectures such as foundation models and large language models (LLMs), pose significant challenges to sustainability. Traditional gradient-based…
In this paper, resource allocation for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) downlink networks with large numbers of base station antennas is studied. Assuming perfect channel state…
In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…
The computing industry is forced to find alternative design approaches and computing platforms to sustain increased power efficiency, while providing sufficient performance. Among the examined solutions, Approximate Computing, Hardware…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…