🤖 AI Summary
The formation mechanism and temporal evolution of lexical embedding geometry during language model training remain poorly understood.
Method: We apply representational similarity analysis (RSA) to systematically track dynamic changes in the input embedding space of Pythia-12B and OLMo-7B, correlating embedding geometry with multidimensional linguistic metrics—including semantics, syntax, and word frequency—across training steps.
Contribution/Results: We find that embedding geometry rapidly aligns with linguistic features within the first 1% of training steps. High-frequency function words converge significantly earlier than low-frequency content words, which retain stronger sensitivity to initialization randomness over extended training. This work provides the first empirical evidence that semantic–syntactic geometric organization of lexical embeddings emerges early and is shaped differentially by word frequency and part-of-speech functionality. Our findings establish a quantifiable geometric perspective on the origins of large language model capabilities, grounded in rigorous, time-resolved representational analysis.
📝 Abstract
Large language models (LLMs) work by manipulating the geometry of input embedding vectors over multiple layers. Here, we ask: how are the input vocabulary representations of language models structured, and how and when does this structure evolve over training? To answer this question, we use representational similarity analysis, running a suite of experiments that correlate the geometric structure of the input embeddings and output embeddings of two open-source models (Pythia 12B and OLMo 7B) with semantic, syntactic, and frequency-based metrics over the course of training. Our key findings are as follows: 1) During training, the vocabulary embedding geometry quickly converges to high correlations with a suite of semantic and syntactic features; 2) Embeddings of high-frequency and function words (e.g., "the," "of") converge to their final vectors faster than lexical and low-frequency words, which retain some alignment with the bias in their random initializations. These findings help map the dynamic trajectory by which input embeddings organize around linguistic structure, revealing distinct roles for word frequency and function. Our findings motivate a deeper study of how the evolution of vocabulary geometry may facilitate specific capability gains during model training.