Fixed Point Convergence

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• Cyclic Fixed Pointconcept0.815
  The key theoretical contribution: each layer in a cyclic recurrence converges to a distinct fixed point, tracing a consistent trajectory in latent space
• What exactly is the endpoint of representational convergence?question0.755
  Motivates Section 4 where the PMI-kernel formalization is proposed
• fixed ends with varying meansquote0.754
  James' test for minimal mentality, cited as describing morphogenesis.
• What has led to this convergence? Will it continue? And ultimately, where does it end?question0.754
  Core research questions motivating the paper
• Fixed-Point Reasoning Models (FPRM)method0.751
  Architecture iterating a single latent to a fixed point via residual threshold; used on Sudoku and mazes.
• Representational Convergenceconcept0.747
  The central empirical phenomenon: different neural networks trained on different data/objectives develop increasingly similar representations
• Instrumental convergenceframework0.743
  The thesis that sufficiently advanced agents will converge to similar subgoals.
• Convergence to cyclic fixed points implies attention patterns stabilize, which implies mixing-based stages of inference become constant across recurrencesclaim0.740
  Core mechanistic claim linking fixed point theory to observable inference stage behavior