Lectures on individually self-selected subjects Flåm 2023

Abstract : 

"In this talk we will talk about simple algebraic algorithms for basic graph problems such as Perfect Matching and Maximum Matching."

Abstract:

"The philosophy of computation is a branch of philosophy that investigates fundamental issues about the natureand limits of computation, lying in the intersection between the philosophy of mathematics, logic, physics, and cognition. Algorithms are at the foundation of computer science, tracing back to the Church‐Turing’s thesis of what it means to perform a computation. The central question of the lecture is: how similar is the behaviour of following a rule between computers and human beings? In particular, during this lecture we will look into a formulation of what it means to follow a rule through a (re)construction of Wittgenstein’s rule‐following paradox expounded in his Philosophical Investigations, §201 and Lectures on the Foundations of Mathematics, on which occasion he debated the matter with Turing as his student. The discussion has possible ramifications for AI research, as it is at the heart of the symbolic vs. connectionism debate."

Abstract: 

"The study of artificial neural networks (ANNs) is motivated by the recognition of the powerful computing capabilities of neurobiological neural networks, namely the human brain. This presentation will aim to give an introduction to ANNs initially through analogies with these neurobiological networks. Thereafter, various network architectures including feedforward networks and recurrent networks will be discussed as well as the strengths and weaknesses of these architectures in application. The presentation will also discuss the basics of the learning processes of supervised, unsupervised and reinforcement learning with respect to ANNs. Benefits and difficulties in implementing these learning processes will be mentioned. An overview of various learning tasks such as pattern association, pattern recognition and function  approximation will be given. Finally, the notion of linear separability will be discussed in connection with Rosenblatt's perceptron and the task of pattern classification. The perceptron convergence algorithm will be presented."

Abstract:

"Groebner bases were introduced in 1965 by Bruno Buchberger in his PhD. thesis. He named them after his supervisor Wolfgang Groebner. A Groebner basis is a particular kind of set of generators for polynomial ideals. The main applications are in commutative algebra and algebraic geometry, but more can be found in Cryptography, Coding theory, and Combinatorics. We discuss algorithms to find Groebner basis and applications."

Abstract: 

"Convolution‐based machine learning techniques, such as convolutional neural networks (CNNs) and convolutional graph neural networks (CGNNs), have gained significant popularity in recent years. CNNs have found success not only in computer vision tasks like image classification and object detection, but also in natural language processing, where they excel in tasks such as text classification and sentiment analysis. CGNN, on the other hand, have become a powerful tool for graph‐structured data, enabling tasks such as node classification and link prediction in social networks, bioinformatics, molecular chemistry, and recommendation systems. This lecture aims to explain the concepts of convolution and convolution‐based machine learning techniques thoroughly. We begin by exploring the fundamental concept of convolution as a mathematical operation, its underlying principles, and its properties. Subsequently, we discuss the adaptation of convolution for neural networks, leading to the development of CNNs, and how CNNs are generalized to CGNNs."

Abstract

"Parsing in computer science is the process of reading and analysing a string of symbols that conforms to a formal grammar. In this lecture, we’ll look into how parsing transforms code from a programming language into abstract syntax trees, which can be further analysed to generate executable programs or give feedback to the programmer. We’ll examine three common parsing algorithms: CYK, recursive‐descent, and LR, and discuss which kinds of grammars these algorithms can be used for."

Abstract

"In high‐performance computing, BLAS (Basic Linear Algebra Subprograms) libraries provide the foundation for numerous scientific and engineering applications. This lecture aims to delve into the inner workings of BLAS libraries, shedding light on their underlying data structures and optimization techniques. Looking specifically at matrix multiplication, a forfor‐ for implementation in Python can be more than 10 000 times slower than the optimized BLAS routine on the same hardware. Surprisingly, both these implementations do the same number of floating‐point operations, and the speedup is solely due to the efficient use of the hardware. This lecture will start from the for‐for‐for implementation and gradually work towards an optimized version."

Abstract: 

"Cryptographic technologies are used throughout government and industry to authenticate the source and protect the confidentiality and integrity of information that we communicate and store. Most of these technologies use public‐key cryptography, which is theoretically vulnerable to attacks that can only be achieved by a large‐scale quantum computer. As a result, practical quantum computing would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post‐quantum cryptography is to develop cryptographic systems that are secure against both quantum and classical computers and can interoperate with existing communications protocols and networks. The National Institute of Standards and Technology (NIST) initiated in 2015 a process to solicit, evaluate, and standardize one or more quantum‐resistant public‐key cryptographic algorithms. The first set of quantum‐resistant encryption algorithms that will be standardized was announced in July 2022. In this seminar, we intend to take a closer look at one of the winners, namely CRYSTALS‐KYBER, a key encapsulation mechanism whose security is based on the difficulty of finding the shortest vector in a lattice."