Attention pooling produces a free-multiplicative-convolution bulk spectrum and two phase transitions for signal recovery; optimal weights are the top eigenvector of the positional correlation matrix R.
Clearing the denominator (for ρ > δ ) and expanding gives ρ2 −(δ+ 2 √ δ)ρ−( √ δ)(δ+ √ δ)>0 , which factors as(ρ−(δ+ √ δ))(ρ+ √ δ)>0
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How Does Attention Help? Insights from Random Matrices on Signal Recovery from Sequence Models
Attention pooling produces a free-multiplicative-convolution bulk spectrum and two phase transitions for signal recovery; optimal weights are the top eigenvector of the positional correlation matrix R.