Related papers: A Domain-Specific Compiler for Linear Algebra Oper…
With the growth of machine learning algorithms with geometry primitives, a high-efficiency library with differentiable geometric operators are desired. We present an optimized Differentiable Geometry Algorithm Library (DGAL) loaded with…
Deep learning models rely on highly optimized tensor libraries for efficient inference on heterogeneous hardware. Current deep compilers typically predetermine layouts of tensors and then optimize loops of operators. However, such…
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…
Optimal use of computing resources requires extensive coding, tuning and benchmarking. To boost developer productivity in these time consuming tasks, we introduce the Experimental Linear Algebra Performance Studies framework (ELAPS), a…
A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of…
We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
The rapid advancement of AI-assisted software engineering has brought transformative potential to the field of software engineering, but existing tools and paradigms remain limited by cognitive overload, inefficient tool integration, and…
Programming robots is a complicated and time-consuming task. A robot is essentially a real-time, distributed embedded system. Often, control and communication paths within the system are tightly coupled to the actual physical configuration…
In high performance domains like image processing, physics simulation or machine learning, program performance is critical. Programmers called performance engineers are responsible for the challenging task of optimising programs. Two major…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Broad learning system (BLS) has been proposed for a few years. It demonstrates an effective learning capability for many classification and regression problems. However, BLS and its improved versions are mainly used to deal with…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
We present a 'calculator' for constructing a homogeneous approximation of nonlinear control systems, which is based on the algebraic approach developed by the authors in their previous papers. This approach mainly uses linear algebraic and…
In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced…
Deep Neural Networks (DNNs) have revolutionized many aspects of our lives. The use of DNNs is becoming ubiquitous including in softwares for image recognition, speech recognition, speech synthesis, language translation, to name a few. he…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
In this paper, we propose the problem of domain transfer structured output learn- ing and the first solution to solve it. The problem is defined on two different data domains sharing the same input and output spaces, named as source domain…