Fixed-point stability correlates with out-of-distribution performance when extrapolating to unseen numbers of test-time recurrences

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• Convergence to cyclic fixed points implies attention patterns stabilize, which implies mixing-based stages of inference become constant across recurrencesclaim0.776
  Core mechanistic claim linking fixed point theory to observable inference stage behavior
• Input injection produces stable fixed point behavior for all norm types tested except Ouro norm on randomly initialized modelsfinding0.764
  Replicates and extends prior findings on input injection; tested on randomly initialized 12-layer models across three norm structures
• Cyclic fixed point behavior and corresponding stages of inference appear to be emergent from the Transformer architecture itself, arising in both trained and randomly initialized modelsclaim0.764
  Strong claim that inference stage structure is architectural rather than learned
• In-distribution re-alignment more effectively reverses the original fine-tuning procedure, while out-of-distribution re-alignment mainly suppresses misalignment generalizationclaim0.757
  Code-realigned model writes less insecure code than health-realigned model after identical steps
• Humans prefer representative distributions over non-representative ones when evaluating outputs at the distribution level, providing a reward gap that VS exploitshypothesis0.745
  Assumption D.3 formalized in the theoretical framework; empirically validated with coin-flip sequence experiments
• The results generalise readily to non-equilibrium systems where scaling relationships remain similar (e.g., dynamic or localised scaling).claim0.743
  Claim about broader applicability of the scaling argument
• 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 spaceclaim0.742
  Theoretical framing that establishes cyclic fixed points as the meaningful limiting behavior
• Randomly initialized (untrained) models exhibit the same cyclic fixed-point behavior as their trained counterpartsfinding0.741
  Suggests cyclic behavior is emergent from transformer architecture itself, not learned during training