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We introduce \\emph{gradient-boosted attention}, which applies the principle of gradient boosting \\emph{within} a single attention layer: a second attention pass, with its own learned projections, attends to the prediction error of the first and applies a gated correction. Under a squared reconstruction objective, the construction maps onto Friedman's gradient boosting machine, with each attention pass as a base learner and the per-dimension gate as the shrinkage parameter. We show that a single Hopfield-style update erases all query information orthogonal to the stored-pattern subspace, and that further iteration under local contraction can collapse distinct queries in the same region to the same fixed point. 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We show that a single Hopfield-style update erases all query information orthogonal to the stored-pattern subspace, and that further iteration under local contraction can collapse distinct queries in the same region to the same fixed point. 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