For min/max readout, two attention heads beat one head by an exponential resource gap, and for n-bit parity and symmetric Boolean functions, heads times polynomial degree must reach the threshold degree, with matching constructions.
Theoretical limitations of multi-layer transformer,
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Attention-based representations for multi-task computation
For min/max readout, two attention heads beat one head by an exponential resource gap, and for n-bit parity and symmetric Boolean functions, heads times polynomial degree must reach the threshold degree, with matching constructions.