Matrices are omnipresent in math and computer science, both theoretical and applied. They are often used as data structures, such as in graph theory. They are a computational workhorse in many AI fields, such as deep learning, computer vision and natural language processing. Why is that? Why would a rectangular array of numbers, with famously…
What is Mixture of Experts? Mixture of Experts (MoE) is a technique that uses many different sub-models (or “experts”) to improve the quality of LLMs. Two main components define a MoE: Experts – Each FFNN layer now has a set of “experts” of which a subset can be chosen. These “experts” are typically FFNNs themselves. Router or gate…
Mixture of Experts (MoE) is a machine learning technique where multiple specialized models (experts) work together, with a gating network selecting the best expert for each input. In the race to build ever-larger and more capable AI systems, a new architecture is gaining traction: Mixture of Experts (MoE). Unlike traditional models that activate every neuron…
The journey to today’s sophisticated chatbots began decades ago with simple rule-based systems. The field of natural language processing (NLP) has undergone several revolutions: 1. Early Systems (1960s-1990s): ELIZA (1966) and PARRY (1972) used pattern matching to simulate conversation, but had no real understanding. 2. Statistical NLP (1990s-2010s): Systems began using probabilistic models and machine…
As one of the most popular programming languages out there, many people want to learn Python. But how do you go about getting started? In this guide, we explore everything you need to know to begin your learning journey, including a step-by-step guide and learning plan and some of the most useful resources to help…
Retrieval-Augmented Generation (RAG) enhances LLM text generation by incorporating external knowledge sources, making responses more accurate, relevant, and up-to-date. RAG combines an information retrieval component with a text generation model, allowing the LLM to access and process information from external databases before generating text. This approach addresses challenges like domain knowledge gaps, factuality issues, and hallucinations often…
In recent years, two major breakthroughs have revolutionized the field of Large Language Models (LLMs): 1. 2017: The publication of Google’s seminal paper, (https://arxiv.org/abs/1706.03762) by Vaswani et al., which introduced the Transformer architecture – a neural network that fundamentally changed Natural Language Processing (NLP). 2. 2022: The launch of ChatGPT by OpenAI, a transformer-based chatbot…
Brief Historical Introduction to Laplace Transform The Laplace Transform is a cornerstone of mathematical physics and engineering, with deep historical roots dating back to the 18th century. Named after Pierre-Simon Laplace (1749–1827), a French mathematician and astronomer, this transformative tool emerged as part of his work on probability and celestial mechanics. Origins Laplace originally used…
Partial differential equations (PDEs) are classified into different types based on their characteristics, which determine the nature of their solutions and the appropriate solution methods. The three most important PDEs in mathematical physics are: Partial differential equations (PDEs) are used in machine learning (ML)—especially in advanced fields like: Physics-informed neural networks (PINNs): These use PDEs…
Welcome to our mathematically rigorous exploration of tensors. This guide provides precise definitions, theoretical foundations, and worked examples ranging from elementary to advanced levels. All concepts are presented using proper mathematical notation with no reliance on programming languages. The Story of Tensors: From Curved Surfaces to Cosmic Equations Long ago, in the 19th century, a…
