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.
Lower bounds on transformers with infinite precision
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this note, we use the VC dimension technique to prove the first lower bound against one-layer softmax transformers with infinite precision. We do so for two tasks: function composition, considered by Peng, Narayanan, and Papadimitriou, and the SUM$_2$ task, considered by Sanford, Hsu, and Telgarsky.
citation-role summary
background 1
citation-polarity summary
fields
cs.LG 1years
2026 1verdicts
ACCEPT 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
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.