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It is proved that a single attention head requires exponentially higher embedding dimension or precision level and generalize to arbitrary (symmetric) Boolean functions, where the bound is given in terms of the threshold degree.
This work introduces a novel combinatorial dimension of the reward class which is called the alignment dimension, and shows that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite.
This work improves the upper bound to match the best known lower bound, thus establishing the optimal error guarantee for learning under Tsybakov noise.
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