Softmax transformers can approximately simulate hard-attention transformers, using a temperature that depends on the reciprocal of the attention-score gap.
Edelman, Surbhi Goel, Sham Kakade, and Cyril Zhang
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Simulating Hard Attention Using Soft Attention
Softmax transformers can approximately simulate hard-attention transformers, using a temperature that depends on the reciprocal of the attention-score gap.