Researchers Develop Bayesian Theory Explaining Sudden Emergence of Copy Patterns in Transformer Attention
A new theoretical framework explains how attention patterns in transformers suddenly emerge during training through phase transitions, using Bayesian analysis of a simplified copy task. The research reveals that softmax attention exhibits abrupt first-order phase transitions while linear attention shows smoother second-order transitions. This work provides mathematical foundations for understanding how in-context learning capabilities arise in large language models.
Researchers have developed a Bayesian theory to explain the abrupt emergence of attention patterns observed during transformer training, focusing on the copy subcircuit in induction heads. By analyzing a single-layer softmax attention network trained on a copy task, they derived a closed-form posterior over the attention matrix and reduced it to a low-dimensional order parameter space. This mathematical reduction revealed a phase transition dependent on training data amount, verified through both Bayesian sampling and standard Adam optimization. The study found that softmax attention exhibits a first-order phase transition—a sudden, discontinuous change—while linear attention shows an initial second-order phase transition followed by smooth evolution. These findings provide theoretical grounding for understanding how structured attention patterns emerge suddenly in large language models, a phenomenon previously observed only empirically.
What's missing
The paper does not discuss potential limitations of the simplified single-layer copy task model relative to multi-layer transformers used in practice, nor does it address how findings might scale to realistic language model architectures with billions of parameters.
What different sources said
- arXiv cs.LGCenter
Phase Transitions in Attention: A Bayesian Theory of Copy Head Emergence
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