Structural generalization, formally defined as unbounded evaluation of a finite compositional rule set, is NC^1-hard, so pure transformers (learnable class ⊆ TC^0) cannot learn it if TC^0 ≠ NC^1.
Compositional reasoning with transformers, RNNs, and chain of thought
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On the Computational Complexity of Structural Generalization
Structural generalization, formally defined as unbounded evaluation of a finite compositional rule set, is NC^1-hard, so pure transformers (learnable class ⊆ TC^0) cannot learn it if TC^0 ≠ NC^1.