Higher Embedding Dimension Creates a Stronger World Model for a Simple Sorting Task
This provides quantitative evidence for structured internal world models in transformers, with implications for interpretability in algorithmic tasks, though it is incremental as it focuses on a specific task.
The paper investigates how embedding dimension affects the emergence of an internal world model in a transformer trained with reinforcement learning for a bubble-sort task, finding that larger dimensions yield more faithful and robust internal representations, such as encoding global ordering in attention weights.
We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small embedding dimensions, but larger dimensions yield more faithful, consistent, and robust internal representations. In particular, higher embedding dimensions strengthen the formation of structured internal representation and lead to better interpretability. After hundreds of experiments, we observe two consistent mechanisms: (1) the last row of the attention weight matrix monotonically encodes the global ordering of tokens; and (2) the selected transposition aligns with the largest adjacent difference of these encoded values. Our results provide quantitative evidence that transformers build structured internal world models and that model size improves representation quality in addition to end performance. We release our metrics and analyses, which can be used to probe similar algorithmic tasks.