Math on English AI Terms Dictionary

Tensor

Sat, 18 Jul 2026 10:17:39 +0000

Definition

In computer science and deep learning, a tensor is a mathematical object that generalizes scalars, vectors, and matrices to higher dimensions. It is characterized by its rank (number of dimensions) and shape (size along each dimension). Tensors allow efficient computation of linear algebra operations on GPUs and TPUs, forming the backbone of neural network data flow and parameter storage in frameworks like PyTorch and TensorFlow.

Summary

A multi-dimensional array that serves as the fundamental data structure for deep learning frameworks.

Softmax

Sat, 18 Jul 2026 09:42:48 +0000

Definition

Softmax is widely used in the output layer of neural networks for multi-class classification tasks. It takes a vector of raw logits and normalizes them so that each element represents a probability between 0 and 1, and all elements sum to 1. This allows the model to express confidence levels across mutually exclusive classes, making it essential for interpreting final predictions in classification models.

Summary

A mathematical function that converts a vector of arbitrary real-valued scores into a probability distribution.

first-order

Sat, 18 Jul 2026 09:38:34 +0000

Definition

In artificial intelligence and mathematics, ‘first-order’ typically describes systems or operations that involve direct, linear relationships without higher-order interactions. In optimization, it refers to methods using only gradient information (first derivative). In logic, first-order logic allows quantification over variables but not over predicates or functions. It contrasts with second-order or higher-order approaches that capture more complex dependencies.

Summary

Refers to concepts involving direct relationships or linear approximations, such as first-order logic or first-order derivatives.

high-dimensional

Sat, 18 Jul 2026 09:38:34 +0000

Definition

High-dimensional refers to datasets or vector spaces containing a vast number of attributes or features. In AI, this is common in text embeddings, image pixels, or gene expression data. While rich in information, high dimensionality can cause the ‘curse of dimensionality,’ where data becomes sparse, distances between points lose meaning, and models require significantly more data and computational power to learn effectively.

Summary

Describes data spaces with a large number of features or dimensions, often leading to sparsity and computational challenges.