Predictable stages of inference in looped models offer actionable pathways for efficient architectural design including stage-dependent attention sparsification and leaner middle-stage MLP parameterization

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• Looped models learn stages of inference that closely mirror those of feedforward models, repeating these stages in depth with each iterationclaim0.855
  Central empirical claim of the paper supported by ColSum concentration analysis across multiple architectures
• Massive activations are required for stages of inference to emerge in looped modelshypothesis0.840
  Hypothesis supported by ablation of massive activations in Retrofitted Llama that eliminates stage structure
• Looped architectures provide a novel lens to study stages of inference by decoupling functional depth from parameter count, revealing why these stages form beyond mere mitigation of transformer depth harmsclaim0.832
  Key interpretive contribution challenging prior explanation that stages exist only to mitigate depth harms
• 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 modelsclaim0.817
  Strong claim that inference stage structure is architectural rather than learned
• Active inference LLMs extending prediction-focused language models with tighter perception-action feedback loops may naturally embody contemplative wisdom as they scalehypothesis0.802
  Predictive hypothesis about Contemplative Architecture approach based on Petersen et al. 2025 work
• why do stages of inference form in looped models if not merely to mitigate the harms of transformer depth?question0.795
  Open question raised by the finding that looped models develop the same stages while improving with greater recurrent depth
• 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 spaceclaim0.775
  Theoretical framing that establishes cyclic fixed points as the meaningful limiting behavior
• latent states after each block in a recurrent model frequently tend towards separate fixed points, meaning that the application of a recurrent block tends towards a consistent trajectory in latent spacequote0.764
  Caption of Figure 1 summarizing the central empirical finding of the paper