Ouro 1.4B does not converge to a fixed point even after 128 recurrences, despite showing small successive differences

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• Ouro 1.4B layers continuously change throughout 128 recurrences, exhibiting unstable stages of inference when extrapolating beyond training recurrencesfinding0.841
  Non-fixed-point models exhibit unstable inference stages when generalizing to unseen test-time compute budgets
• Ouro 2.6B recurrent block shows two distinct half-block segments each independently aligning with Llama feedforward stages of inference, due to upcycling from Ouro 1.4Bfinding0.783
  Reveals how the upcycling training regime of Zhu et al. produces duplicated inference stage structure
• Ouro 1.4B, Retrofitted Llama, and Huginn-0125 exhibit diagonal patterns in Frobenius norm heatmaps confirming cyclic fixed point behavior across 8 recurrencesfinding0.781
  Empirical validation that attention patterns are most similar to same-layer outputs across different recurrences
• Huginn-0125 all-layer fixed point cosine similarities converge to 1 for all pairs, indicating convergence to the same fixed point rather than distinct cyclic fixed pointsfinding0.759
  Distinguishes Huginn's convergence behavior from the ideal cyclic fixed point behavior
• Ouro 1.4Bconcept0.751
  Primary looped LLM studied; trained from scratch with cyclic recurrence, does not reach fixed point
• Huginn-0125 performance remains constant when extrapolating beyond training recurrences, while Ouro performance deteriorates in the same regimefinding0.747
  Correlates stable fixed-point behavior with out-of-domain generalization performance at test-time
• 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 pointclaim0.732
  Formal proposition establishing that fixed-point convergence implies cyclic fixed points for all block permutations
• Convergence to cyclic fixed points implies attention patterns stabilize, which implies mixing-based stages of inference become constant across recurrencesclaim0.710
  Core mechanistic claim linking fixed point theory to observable inference stage behavior