生成AIと数学(日記)


In recent years, a technology known as generative AI has rapidly gained attention. Unlike traditional AI, which primarily classifies or predicts data, generative AI can autonomously create text, images, audio, and even video. With the emergence of large language models (LLMs) like ChatGPT and image generation tools such as Midjourney and Stable Diffusion, generative AI is now widely used across everyday life, business, and creative industries.

To effectively harness generative AI, one must not only be able to use the latest technologies but also understand how they function. Grasping the core mechanics enables more informed decision-making, better application, and the generation of new ideas. Especially in business implementation or research contexts, having a certain level of technical literacy, understanding of specialized terminology, and a solid mathematical foundation becomes a significant advantage.

At the heart of generative AI lies deep learning, which mimics the neural circuits of the brain through multilayered neural networks capable of learning complex patterns and features. Key models used in generative AI include GANs (Generative Adversarial Networks) for image generation and Transformers for text generation.

Transformers feature an “attention mechanism” that learns where to focus within multiple inputs. This gives them high performance in tasks like understanding long-form context, translation, and conversational AI. Language models such as the GPT series and BERT are built on the Transformer architecture. Transformer-based models are also increasingly used in image and audio domains, making this framework central to modern AI technology.

To master generative AI, it is important to understand essential technical terms. For example, a token is the smallest unit of text processing, which can be a word, subword, or character. Embedding refers to the transformation of these tokens into multidimensional vectors that preserve semantic similarity.

In generative models, the concept of a latent variable is also crucial. These are hidden factors that influence the data generation process. In models like VAEs (Variational Autoencoders), manipulating the latent space allows for diverse outputs. Attention, a central technique in Transformers, numerically determines where to focus within an input. Though these concepts may seem abstract, they directly impact model behavior and output quality, making fundamental understanding essential.

A strong grasp of mathematics is also indispensable. Linear algebra, centered on vector and matrix operations, underpins all neural network computations. Matrix multiplication corresponds to combining layer weights with input data, requiring intuitive understanding of dimensionality and linear transformations.

Calculus is equally critical. During training, models aim to minimize a loss function by computing gradients (i.e., slopes) and updating weights — a process known as gradient descent. Partial derivatives quantify how much each parameter affects the loss, playing a key role in learning.

Statistics and probability are also foundational. Generative AI frequently deals with questions like “What is the probability of this word?” or “Which class does this image belong to?” Concepts like Bayesian estimation, likelihood, and posterior distribution are vital for managing uncertainty and reliability in outputs. Information-theoretic notions such as entropy and cross-entropy are used to evaluate model performance and define loss functions.

As we’ve seen, a deep understanding of generative AI requires more than just treating it as a convenient tool — one must study the technology, terminology, and mathematics behind it in a structured way. Especially in business, the focus is shifting from whether to adopt AI to how to design, operate, and evaluate it. In this new era, what’s needed is not someone who blindly trusts a black box, but someone who can interpret and tune the white box — someone who can read and adjust the system.