In the context of artificial intelligence and machine learning, a vector is a fundamental mathematical concept that represents a list or array of numbers—often called elements or components—arranged in a specific order. Vectors are used to encode data, model parameters, or even abstract representations of features in a way that computers can process efficiently. For example, an image can be represented as a long vector of pixel values, while a word can be represented as a vector in a word embedding space.
Vectors are central to nearly every aspect of AI. In supervised learning, each data point is typically represented as a vector, where each element corresponds to a feature (like age, height, or color intensity). These vectors are then used as inputs to models such as neural networks, which process and transform them through layers and operations like matrix multiplication. The parameters that a model learns—weights and biases—are also stored as vectors or matrices.
In natural language processing (NLP), vectors play a special role. Words, phrases, or entire sentences can be mapped to high-dimensional vectors using techniques like word2vec or transformer-based embeddings. These vectors capture semantic relationships, so that similar words have similar vector representations. This allows AI systems to understand context, perform similarity searches, and generate human-like language.
The concept of vector spaces is also important. A vector space is a mathematical structure where vectors can be added together and multiplied by scalars (single numbers), following certain rules. This structure enables powerful operations such as projecting data onto new axes, measuring distances between data points (using norms), and finding directions of greatest variance (as in PCA).
Vectors are not just limited to data representation. During the training of machine learning models, gradients—used to update model parameters—are also vectors that indicate the direction and magnitude of change needed for optimization. In deep learning, even the activations inside hidden layers are often represented as vectors.
The dimensionality of a vector refers to how many elements it contains. For example, a vector representing an RGB color will have three dimensions (red, green, blue), while a word embedding vector might have hundreds or even thousands of dimensions. High-dimensional vectors can capture complex, abstract properties, but they may also introduce challenges, such as the ‘curse of dimensionality,’ where data becomes sparse and harder to analyze.
Understanding vectors is crucial for anyone working in AI, as they provide a foundational language for representing and manipulating information. From simple data storage to advanced neural network architectures, vectors are everywhere in the field.
