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We address the numerical solution of minimal norm residuals of {\it nonlinear} equations in finite dimensions. We take inspiration from the problem of finding a sparse vector solution by using greedy algorithms based on iterative residual…

Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive…

In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…

In this thesis, we introduce Greenformers, a collection of model efficiency methods to improve the model efficiency of the recently renowned transformer models with a low-rank approximation approach. The development trend of deep learning…

Generative retrieval methods utilize generative sequential modeling techniques, such as transformers, to generate candidate items for recommender systems. These methods have demonstrated promising results in academic benchmarks, surpassing…

Hyperparameter optimization is crucial to achieving high performance in deep learning. On top of the performance, other criteria such as inference time or memory requirement often need to be optimized due to some practical reasons. This…

Recently, the scale of transformers has grown rapidly, which introduces considerable challenges in terms of training overhead and inference efficiency in the scope of task adaptation. Existing works, namely Parameter-Efficient Fine-Tuning…

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…

Search is a key service within constraint programming systems, and it demands the restoration of previously accessed states during the exploration of a search tree. Restoration proceeds either bottom-up within the tree to roll back…

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…

I show that a software framework intended primarily for training of neural networks, PyTorch, is easily applied to a general function minimisation problem in science. The qualities of PyTorch of ease-of-use and very high efficiency are…

Erasure codes are widely used in today's storage systems to cope with failures. Most of them use the finite field arithmetic. In this paper, we propose an implementation and a coding speed evaluation of an original method called PYRIT…

Many state-of-the-art Segment Routing (SR) Traffic Engineering (TE) algorithms rely on Linear Program (LP)-based optimization. However, the poor scalability of the latter and the resulting high computation times impose severe restrictions…

Planning provides a framework for optimizing sequential decisions in complex environments. Recent advances in efficient planning in deterministic or stochastic high-dimensional domains with continuous action spaces leverage backpropagation…

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

Physical reservoir computing (PRC) is a computing framework that harnesses the intrinsic dynamics of physical systems for computation. It offers a promising energy-efficient alternative to traditional von Neumann computing for certain…

Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as…

Reservoir computing (RC) has attracted attention as an efficient recurrent neural network architecture due to its simplified training, requiring only its last perceptron readout layer to be trained. When implemented with memristors, RC…