Ahmad Samer Wazan's blog

In this article, I will explain the core ideas of neural networks from an abstract mathematical perspective. By "abstract", I mean that I will try to explain the "why" of mathematical concepts without covering all mathematical details. To simplify the mathematical concepts of neural networks, I will use some analogies from real life situations, with visualisations and examples.  I will start by explaining why we need neural networks, and then discuss the role of optimisation and backpropagation algorithms.  Why Do We Need Neural Networks  Neural networks are tools that allow us to approximate complex multivariate functions representing the relationships between dataset inputs and outputs. Typically, it is not feasible to define one explicit equation that can reproduce these multivariate functions. The role of training is thus to approximate them. Indeed, most neural networks architectures are based on a mathematical theorem called Universal Approximation Theorem. Th

  Microsoft released a research work last week [1] that claims that GPT-4 capabilities can be viewed as an early version of Artificial General Intelligence. The authors states that " the breadth and depth of GPT -4's capabilities, we believe that it could reasonably be viewed as an early (yet still incomplete) version of an artificial general intelligence (AGI) system. "  The researchers adopted the following definition of human Intelligence to reach this conclusion: " a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience. ". According to the same paper, the definition was proposed in 1994 by a group of psychologists. Interestingly, the authors of the paper [1] acknowledges that the definition of human intelligence is somehow restrictive. They also acknowledge that some components of this definition are currently missing

On November 30, OpenAI launched its AI chatbot called ChatGPT. ChatGPT is the most important revolution we have ever had on the Internet, much more important than Blockchains and NFTs. The capacities of ChatGPT are phenomenal. It can do many things, such as writing poems, writing and summarising articles, writing and debugging codes, and solving puzzles and mathematical questions. In addition, the ChatGPT tool can also be used with other tools such as DALL.E 2 (https://openai.com/dall-e-2/) to generate drawings or the Philosopher AI to answer philosophical questions (https://philosopherai.com/). Some tools can also allow the creation of music based on our lyrics. For example, we may use ChatGPT to generate some lyrics and give them to another AI tool to develop our song. If we look at the impacts of these tools pessimistically, the development of AI tools would mean the end of human intelligence and the triumph of human stupidity when only influential individuals can access these tools

Oracle Solaris presents an interesting approach for distributing root privileges to Solaris users. Their approach has been stable since it was defined in 2003. The approach adopted the RBAC model for defining roles that Solaris users can assume. Solaris considers the root account as a role that users can take. In Solaris, roles are user accounts that cannot log in; thus, each role has an associated password that can be shared by a group of users that share the same role. From the kernel point of view, Solaris defines four sets of privileges for each process: Effective set, permitted set, Inheritable set, and Limit set. Effective and permitted sets are handled in the same manner as Linux. However, Inheritable and Limit sets are calculated differently during  exec()  call. In particular, Solaris authorizes the inheritance of privileges after an  exec()  call, even when the executable doesn’t have privileges stored in its binary. More interestingly, instead of storing privileges in the ex

I always believed that prime numbers don't follow any clear pattern, but yesterday I learned from this page [1] that any prime number bigger than 3 can follow the pattern (6*n+1) and/or (6*n -1), where n is any natural number. The authors indicate that they verified this theory by generating 1000000 prime numbers using Matlab. Therefore, it seems that there is no official proof of this theory, but also nothing proves that it is an incorrect theory.  Let's suppose that this theory is mathematically proven. Then, two questions can be raised: Question1: Can this theory remove the need to primality tests? Question2: Can this theory allow us to factorize natural numbers efficiently? Before I handle these questions, I want to verify first the prime generation theory. I wrote a Python function that allows finding the count of prime numbers within a range of numbers and comparing this function with another function that follows the brute force method to generate the prime numbers. Here