Ouro 1.4B, Retrofitted Llama, and Huginn-0125 exhibit diagonal patterns in Frobenius norm heatmaps confirming cyclic fixed point behavior across 8 recurrences

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• 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 1.4Bfinding0.818
  Reveals how the upcycling training regime of Zhu et al. produces duplicated inference stage structure
• Retrofitted Llama attention patterns converge after the first recurrence and Huginn-0125 immediately following the preludefinding0.797
  Demonstrates remarkably fast convergence to cyclic fixed point behavior in retrofitted models
• Huginn-0125 performance remains constant when extrapolating beyond training recurrences, while Ouro performance deteriorates in the same regimefinding0.793
  Correlates stable fixed-point behavior with out-of-domain generalization performance at test-time
• Ouro 1.4B does not converge to a fixed point even after 128 recurrences, despite showing small successive differencesfinding0.781
  Key negative result showing that not all looped models reach a true fixed point, contrasting with retrofitted models
• Ouro 1.4B layers continuously change throughout 128 recurrences, exhibiting unstable stages of inference when extrapolating beyond training recurrencesfinding0.777
  Non-fixed-point models exhibit unstable inference stages when generalizing to unseen test-time compute budgets
• Retrofitted Llama and OLMo recurrent blocks closely follow their respective base model stages of inference while repeating middle stages in the recurrent blockfinding0.764
  Shows that retrofitting preserves base model inference stage structure in the cyclic blocks
• Llama-3.1-8B uses task-agnostic Fourier features with periods 2, 5, and 10 (base-10) rather than concept-specific periods (e.g., 12 for months)finding0.763
  The specific Fourier feature periods identified confirm base-10 rather than modular computation
• Retrofitted Llama (input injection) maintains consistent ColSum concentration stages of inference for 128 recurrences, far beyond its training range of 32finding0.750
  Models with fixed-point convergence maintain stable inference stages at arbitrary test-time recurrence depths