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Extending a Mathematical Theory of the Emergence of Knowledge from the Experience to Capture Learning Dynamics in Transformers
Abstract
The Transformer architecture used in LLMs has garnered widespread attention due to these model's human-like conceptual knowledge and language understanding, yet understanding how these models' capabilities result from experience-guided learning, and connecting this learning process with the structure in their training data, can seem intractable. Here we present preliminary steps to characterizing the developmental trajectory of a minimal Transformer trained on a next-token prediction task, using a simple dataset with quantifiable uncertainty and a simple, intuitively characterizable structure that captures some aspects of natural semantic structure learned by LLMs from large datasets. We show how the dynamic learning process of this model is a predictable consequence of the structure of the training data, exhibiting attested features of human semantic development, as captured in a theory of neural network learning dynamics (Saxe et. al. 2019) previously used to capture such dynamics in a network originally introduced by Rumelhart & Todd (1993).