Once attention decides HOW MUCH to look at each token, it does one last thing: blend their VALUE vectors in exactly those proportions. The output isn’t a copy of any single token — it’s a weighted average, a soft blend that lands inside the cloud of everything it attended to. Attend mostly to one token and you nearly copy it; attend evenly and you get their centroid. Slide the focus and watch the blend move.
The final step of attention: output = Σᵢ wᵢ · vᵢ, a weighted sum of the value vectors using the attention weights. Because the weights are non-negative and sum to 1, the output is a CONVEX COMBINATION of the values — it always lies inside their convex hull, never outside. Concentrate the weight on one token and the output approaches that value (a soft copy); spread it evenly and the output is the centroid. So attention MOVES information: each position’s new representation is a blend of the values it chose to look at, weighted by relevance. A fail-loud self-check throws unless the output is a convex combination lying within the value range. ◆ real ML mechanism, node-verified.
The weighted-sum-of-values step (the exact convex-combination property); the values are learned projections and later layers transform the blend — the output-is-a-soft-average-of-attended-values mechanism is exact.