Mathematics and Science of Large Language Models (Ernest Ryu, UCLA Applied Math Colloquium)

Introduction

(Ernest Ryu, UCLA Applied Math Colloquium)

Introduction

Good afternoon, everyone. My name is Ernest R. I’m a new faculty member in the Mathematics Department at UCLA, specifically within the applied mathematics group. Today, I'm excited to share my insights on large language models (LLMs) and their powerful implications in machine learning.

About Myself

Before diving into the main topic, let me provide you with a brief introduction about my research areas. My interests fall into three main categories, as illustrated in a Venn diagram. However, today's discussion will primarily revolve around two of those subjects: machine learning theory and empirical deep learning. For those interested in optimization research, I will also be delivering a guest lecture in Gido’s optimization course.

The Power of Large Language Models

Large language models have made waves in the field of artificial intelligence due to their remarkable capabilities. Training an LLM typically involves the following steps:

Gathering Data: To initiate training, it's crucial to assemble a massive dataset. This consists of everything from books and papers to articles and online content.
Training the Model: The next step involves utilizing a transformer architecture to perform next-token prediction. This means the model analyzes the beginning of a text and predicts the subsequent word. Achieving this requires a sound understanding of language and world knowledge. For instance, recognizing that in the sentence "Charlie was very tired during his studies, so he went to the Starbucks to get a cup of something," the model must infer that "something" likely refers to coffee.
Alignment and Fine-Tuning: Post initial training, models undergo several alignment and instruction fine-tuning, which are not elaborated on here.
Application: Finally, the well-trained model can be adapted for various downstream tasks, thanks to its robust foundational knowledge.

LLMs have greatly impacted many areas and, in some cases, replaced traditional machine learning techniques.

Example: RL and Video Games

In reinforcement learning, researchers have historically focused on building agents that can navigate video games. A classic example is “Montezuma's Revenge,” where the objective is to explore dungeons. By integrating LLMs, we can provide an improved experience. For instance:

Instruction Use: Although modern video games lack traditional instruction manuals, we can leverage online resources. By scanning these documents and feeding them to the LLM, we allow it to dictate actions based on the visual information and instructions.
Human Interaction: A human might write code to convert real-time visual game data into textual descriptions for the LLM, ensuring that the agent makes informed decisions.

Application to Image Clustering

Another research contribution I’d like to mention is titled “Image Cluster and Image Text Criterion.” This study investigates how users can specify clustering criteria using natural language. We demonstrated that users could influence clustering results based on location, mood, or action by providing textual specifications.

Our results showed that when we convert images into text that aligns with user-specified criteria, we can significantly outperform traditional unsupervised learning algorithms.

Theoretical Foundations of LLMs

Despite the advances in application, our understanding of why LLMs function so well remains limited. This calls for mathematical analyses of their behavior, focusing on two significant questions:

Why do LLMs work effectively?
What happens when they falter?

Foundation Models and Fine-Tuning

In the realm of machine learning, a paradigm shift has emerged emphasizing foundation models and fine-tuning. By pre-training generalized models and then fine-tuning them on smaller datasets, we find these models outperform specialized models across varied tasks.

A recent work I contributed to, titled “Laura Training in the NTK Regime Has No Spurious Local Minima,” explores low-rank adaptations of pre-trained models. The aim here is to reduce memory costs. Upon analysis, we specifically focused on optimization landscapes and established that low-rank solutions are beneficial and generally lead to robust training outcomes, as they avoid problematic local minima.

In-Context Learning (ICL)

Historically, in-context learning was introduced in GPT-3. It allows models to perform tasks based on context provided by examples without explicitly describing the tasks themselves. For instance, a model can complete tasks simply by observing demonstrations, identifying patterns, and leveraging prior knowledge.

Multitask Learning in ICL

We further evaluated multitask settings in ICL. Our findings indicated that training on multiple tasks simultaneously accelerates learning significantly compared to focusing solely on one task. This result contradicts traditional views that suggest learning multiple tasks should be more complex.

Conclusion

In conclusion, our explorations into LLMs reveal their immense power, both in empirical applications and theoretical foundations. As we continue this research, we will gain more insights into their capabilities and optimizations, further advancing the field of machine learning.

Keywords

Large Language Models
Machine Learning Theory
Empirical Deep Learning
Instruction Fine-Tuning
Reinforcement Learning
Multimodal Learning
In-Context Learning
Fine-Tuning Paradigms
Low-Rank Adaptation

FAQ

What are large language models (LLMs)?

LLMs are a type of artificial intelligence model that can understand and generate human language. They are trained on massive datasets and utilize transformer architectures to perform tasks like translation, summarization, and text generation.

How do LLMs learn?

LLMs learn through a two-step process: first, they are pre-trained on a large dataset using unsupervised learning to develop a general understanding of language. Then, they're fine-tuned on smaller datasets for specific tasks using supervised learning.

What is in-context learning (ICL)?

In-context learning is a capability that allows LLMs to perform tasks based on contextual examples without explicit instructions. This was notably enhanced in models like GPT-3.

How does multitask training improve LLMs?

Training LLMs on multiple tasks simultaneously appears to make learning more efficient. This counterintuitive insight suggests that exposure to diverse tasks may help the model identify and understand common structures faster.

What is the significance of Laura in LLM training?

Laura refers to Low-Rank Adaptation, a technique used to reduce memory costs in fine-tuning LLMs. Theoretically, it has been shown to lead to favorable training dynamics, avoiding spurious local minima.