Fast Lyapunov indicator λF strongly correlates with the number of distinct solutions a reasoning trajectory passes through before converging

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• Fast Lyapunov Indicator (λF)method0.872
  Metric directly localizing saddle-like boundaries between solution routes by measuring maximal local trajectory separation.
• Impulsivity→interest steering: probe entropy increases (LMM slope=0.024, p=2.30×10⁻⁴) but report entropy does not (p=0.11)finding0.736
  Evidence of a bottleneck between richer internal variation and final report distribution in impulsivity→interest condition
• Pre-bifurcation, all finite-time Lyapunov exponents are negative, so no transient chaos occursfinding0.734
  Establishes the baseline (non-chaotic) regime before the bifurcation.
• Bayes-optimal perception inherently produces self-organised instability (local Lyapunov exponents fluctuating around zero), so FEP drives the system toward criticality (Friston et al. 2012)finding0.731
  Establishes the mechanistic link between lower VFE and critical dynamics, supporting the paper's criticality prediction
• S = ρd - dr - log k is a predictive correlate of when few-shot behavior flipsclaim0.727
  Claim that S predicts threshold midpoints across different bases, tasks, and models
• For simple factual tasks F0-F3, probe directions show a sharp geometric transition in middle layers, with late-layer probes converging to high cosine similarity; A3 and F4-F5 show no clear transition.finding0.722
  Geometric evidence for convergence to stable truth directions only for simpler tasks.
• The likelihood of a dedicated feature for a concept (element, city, animal, food) follows a sigmoid in log-frequency of the concept in training data, with threshold frequency inversely proportional to number of alive features.finding0.721
  Quantitative relationship between concept frequency and feature presence.
• Wellbeing probe-score drift across turns significant at all three LLaMA scales (slopes=0.006, 0.005, 0.013 for 1B, 3B, 8B; all p<10⁻¹⁰); drift magnitude increases with scalefinding0.720
  Internal-state drift generalizes across scales; normalized drift also increases significantly with log(model size)