👉 Behind the scenes, many mathematical operations, especially in complex computations and algorithms used in fields like machine learning, cryptography, and scientific simulations, are often performed using mathematical structures known as representations or embeddings. These representations act as a bridge between abstract mathematical concepts and concrete computational processes, allowing for efficient manipulation and transformation of data. For instance, in linear algebra, matrices represent vectors and transformations, while in machine learning, neural networks use layers of weighted connections to transform inputs into meaningful outputs. Representations can be linear (like vectors in a high-dimensional space) or non-linear (such as the embeddings learned by word2vec or BERT models), and they enable algorithms to leverage mathematical properties like similarity, distance, and dimensionality reduction for tasks ranging from pattern recognition to data compression. This mathematical backbone is crucial for the functionality and performance of modern computational systems.
