Counting with Attention and LayerNorm: Norm Scaling and Representation Geometry

Key points

• Counting is a simple task on which transformers can nevertheless fail at long sequence lengths.1
• For regression, we show unnormalized linear attention counts exactly at parameter norms independent of $L$.1
• For softmax attention, regression cannot count exactly with finite parameters; it recovers the count after rounding, but only when the vector parameter norms grow with $L$.1
• Together, our theoretical and empirical findings characterize how self-attention, layer-normalization placement, and read-out choice shape the representation geometry and parameter cost of counting in the minimal single-head architecture studied here.1

Sources (1)

• [1]Counting with Attention and LayerNorm: Norm Scaling and Representation Geometry
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 12:09 PM

  We study the cost of counting in a single attention layer, up to a maximum length $L$, focusing on how softmax attention and layer normalization shape the representation from which the count is recovered.

  Counting is a simple task on which transformers can nevertheless fail at long sequence lengths.

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