Scan and Snap: Understanding Training Dynamics and Token Composition in 1-layer Transformer

Transformer architectures have shown impressive performance in multiple research domains and have become the backbone of many neural network models. However, there is limited understanding on how Transformer works. In particular, with a simple predictive loss, how the representation emerges from the gradient training dynamics remains a mystery. In this paper, we analyze the SGD training dynamics for 1-layer transformer with one self-attention plus one decoder layer, for the task of next token prediction in a mathematically rigorous manner. We open the black box of the dynamic process of how the self-attention layer combines input tokens, and reveal the nature of underlying inductive bias. More specifically, with the assumption (a) no positional encoding, (b) long input sequence, and (c) the decoder layer learns faster than the self-attention layer, we prove that self-attention acts as a discriminative scanning algorithm: starting from uniform attention, it gradually attends more to key tokens that are distinct for a specific next token to be predicted, and pays less attention to common key tokens that occur across different next tokens. Among distinct tokens, it progressively drops attention weights, following the order of low to high co-occurrence between the key and the query token in the training set. Interestingly, this procedure does not lead to winner-takes-all, but decelerates due to a phase transition that is controllable by the learning rates of the two layers, leaving (almost) fixed token combination. We verify this scan and snap dynamics on synthetic and real-world data (WikiText).