From Calculus to Conversation: Inside LLMs (series unlisted)

Abstract: This talk explores the mathematical foundations and evolutionary trajectory of Large Language Models (LLMs). We begin by examining the pre-training mechanics—how models learn to predict tokens through probability distributions and gradient descent optimization across vast corpora of human language. We'll investigate why these statistical approaches to language processing present unique challenges for mathematical reasoning, where symbolic manipulation differs fundamentally from natural language processing.

We will further explore fine-tuning’s effects on model behavior as well as reinforcement learning’s efforts to redirect models toward human-aligned responses. We'll analyze the architecture of model conversations, examining system prompts and model responses, while considering the technical challenges in maintaining alignment.

We'll conclude by exploring the formal reasoning capabilities of modern LLMs and the emerging paradigm of AI agents, offering practical strategies for effectively communicating with these systems. Throughout, we'll provide a balanced perspective on both the capabilities and limitations of LLMs, offering insights valuable to anyone interested in the intersection of mathematics, computer science, and artificial intelligence.

Food and refreshments will be served.

Mathematics

Audience: undergraduates

Brooklyn College Math Department Events

Series comments: The Brooklyn College Math Department hosts a lot great events for undergraduates and faculty! These events are organized by The Math Club, The Putnam Club, and faculty in the Math Department.