Breaking Symmetry When Training Transformers
This addresses a foundational problem in sequence modeling for AI researchers, but it is incremental as it builds on prior work on positional encodings.
The paper investigates how Transformers break symmetry to model ordered sequences, showing that causal attention alone can enable training without positional encodings, with evidence that residual connections contribute to this effect.
As we show in this paper, the prediction for output token $n+1$ of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens $1, 2, ..., n-1$. Usually, both mechanisms are employed and the symmetry with respect to the input tokens is broken. Recently, it has been shown that one can train Transformers without positional encodings. This must be enabled by the causal attention mechanism. In this paper, we elaborate on the argument that the causal connection mechanism must be responsible for the fact that Transformers are able to model input sequences where the order is important. Vertical "slices" of Transformers are all encouraged to represent the same location $k$ in the input sequence. We hypothesize that residual connections contribute to this phenomenon, and demonstrate evidence for this.