Cyclic Fixed Point

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Fixed Point Convergenceconcept0.815
  The behavior where repeated application of a transformer block converges to a state where X' = S_k(X')
• Cyclic Recurrenceframework0.786
  The specific looped mechanism studied: a fixed sequence of layers repeated in a cyclic pattern
• Cyclic Geometryconcept0.771
  One of the geometric structures used to characterize reasoning task representations in language models, used as a test case for manifold steering
• Convergence to cyclic fixed points implies attention patterns stabilize, which implies mixing-based stages of inference become constant across recurrencesclaim0.769
  Core mechanistic claim linking fixed point theory to observable inference stage behavior
• Proposition 4.1: If a (l,k)-Recurrent block reaches a fixed point S_k(X')=X', then any cyclic permutation of blocks 1,...,k will also have reached a (different) fixed pointclaim0.764
  Formal proposition establishing that fixed-point convergence implies cyclic fixed points for all block permutations
• cyclic reasoning tasksconcept0.757
  Language model reasoning tasks with cyclic geometric structure used to test manifold steering.
• If a looped model with cyclic recurrence reaches a fixed point, either each block's contribution vanishes asymptotically or the sequential application traces a constant cyclic trajectory in latent spaceclaim0.755
  Theoretical framing that establishes cyclic fixed points as the meaningful limiting behavior
• fixed ends with varying meansquote0.737
  James' test for minimal mentality, cited as describing morphogenesis.