From a6ec4288a2232988b130b2f00bb2565f81706966 Mon Sep 17 00:00:00 2001 From: YurenHao0426 Date: Mon, 29 Jun 2026 12:15:51 -0500 Subject: Recursive reasoning dynamics: analysis pipeline, paper drafts, toy models Failure=more-chaotic (task-general under validity labeling) reduces to convergence/completeness detection; mechanism (transient chaos vs multistability vs input-induced) under investigation. Co-Authored-By: Claude Fable 5 --- rainer_email_bundle_20260605/figure_captions.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 rainer_email_bundle_20260605/figure_captions.md (limited to 'rainer_email_bundle_20260605/figure_captions.md') diff --git a/rainer_email_bundle_20260605/figure_captions.md b/rainer_email_bundle_20260605/figure_captions.md new file mode 100644 index 0000000..04872f6 --- /dev/null +++ b/rainer_email_bundle_20260605/figure_captions.md @@ -0,0 +1,23 @@ +# Figure Captions + +## Fig. 1: `figures/Fig1_lambda1_success_failure_HRM_TRM.png` + +First finite-time Lyapunov exponent distribution for successful versus failed inference trajectories in HRM and TRM checkpoints. Failures are shifted toward larger/more positive exponents, motivating chaos as a failure detector. + +## Fig. 2: `figures/Fig2_full_spectrum_success_failure_shift.png` + +Top Lyapunov spectrum for successful versus failed examples. The separation is not only a top-exponent effect; many leading modes shift toward expansion on failed examples. + +## Fig. 3: `figures/Fig3_trajectory_perturbation_improves_peak_accuracy.png` + +Peak exact accuracy for baseline training versus trajectory perturbation training. The perturbation method keeps the same supervised input/target pair but trains additional recurrent rollouts with small latent-state perturbations to reach the same answer. This is a ceiling/peak result; HRM later shows final-checkpoint collapse. + +## Fig. 4: `figures/Fig4_optional_PTRM_Q_head_vs_stability.png` + +Optional context. In PTRM-style stochastic multi-rollout inference, the learned Q-head score is correlated with a finite-difference stability proxy on mixed-success problems, suggesting that learned rollout selection may partly approximate a low-dimensional stability score. + +# Caveats + +- Lyapunov measurements are finite-time diagnostic estimates on sampled subsets, not full asymptotic exponents. +- Fig. 3 reports best-checkpoint/peak accuracy, not necessarily final-checkpoint accuracy. +- The gradient flossing analogue is still preliminary; the main question for Rainer is conceptual, not a claim that flossing does or does not work in RRMs. -- cgit v1.2.3