This article delves into the foundational mathematical concepts underpinning Large Language Models (LLMs), focusing on how they learn and generate text. It explains loss functions, gradient descent, and next-token prediction, providing insights into the inherent capabilities and limitations that architects should consider when designing and deploying LLM-powered applications.
Read original on ByteByteGoThe article clarifies that LLM "learning" is not akin to human understanding but rather a process of iterative parameter adjustment through repetitive mathematical procedures. This fundamental distinction is crucial for system designers to understand, as it impacts the reliability and explainability of LLM outputs in deployed systems.
Before an LLM can be trained, a loss function is needed to quantify its performance. This function provides a single numerical score representing how "wrong" the model's predictions are. The goal during training is to minimize this score. Key requirements for an effective loss function include specificity, computability, and smoothness.
Architectural Implication
LLMs are optimized to match patterns in training data, not for truthfulness. If false information is prevalent in the training data, the model is rewarded for reproducing it. This is a critical consideration for architects designing systems that rely on factual accuracy.
Gradient descent is the algorithm used to adjust the billions of parameters within a neural network to reduce the loss. It works by iteratively taking small steps in the direction of the steepest decrease of the loss function. Modern LLMs employ Stochastic Gradient Descent (SGD), which calculates loss on small, random batches of data rather than the entire dataset, making training feasible for massive datasets.
Despite complex outputs, LLMs are fundamentally trained to predict the next word (or token) in a sequence. This seemingly simple task, when scaled across trillions of words and billions of training iterations, allows LLMs to learn intricate patterns and contextual relationships in language. The more context provided, the more accurate the predictions become. The parallel processing capabilities of the transformer architecture were a breakthrough enabling the training of current LLMs.
While pattern matching yields impressive results, it is not reasoning. This leads to predictable failure modes, such as confidently generating plausible but incorrect information (hallucinations) or struggling with tasks where training data is scarce. Architects must account for these limitations by implementing robust validation, human-in-the-loop processes, or retrieval-augmented generation (RAG) when building production LLM systems.