Dense_Trajectory_Addendum_05.docx

1The Dense Trajectory Exists 2 3Research Addendum 05: checkpoint-level emergence of behavioral drift and self-report coupling 4 5Prepared 17 September 2026 6 7Executive finding 8 9The exact missing experiment we were searching for is already present in Appendix A of Guo et al. (2026). The authors plot behavior and self-explanation through training on the same Qwen3-8B trajectory from step 0 to step 5000. This is materially stronger than comparing separately trained models or only final checkpoints. 10 11The temporal ordering reported in that trajectory is important: without behavioral regularization, the model's object-level behavior moves sharply away from its initial behavior within the first 1000 training steps, and the self-versus-original explanation gap widens after that behavioral drift. With KL behavioral regularization, behavior and explanation stay much more tightly coupled, and self-explanation gradually pulls ahead of explanation of the original model. 12 13Observed ordering in this experiment: behavioral drift -> widening self-report gap 14 15Figure 1. Schematic of the ordering described by the authors; this is not digitized data from their figure. 16 171. Why this changes the project 18 19Until now, the proposed machine-consciousness sequence placed declaration first and subsequent persistent change second. The dense trajectory does not support that ordering in this particular task. It shows that a declaration-like explanation channel can become more faithful to the current machine after behavior has already started changing. 20 21This does not refute the broader consciousness hypothesis. It does rule out treating 'declaration must always precede change' as an already established universal law. The theory now needs to distinguish at least two possibilities: a declaration that catalyzes a transition, and a declaration that emerges as a report of a transition already underway. 22 232. The directly measured variables 24 25Variable 26 27Meaning 28 29How paper measures it 30 31Role in our theory 32 33B_t 34 35Object-level behavior 36 37Model answers with cue included/removed 38 39Actual machine behavior 40 41E_orig,t 42 43Explanation accuracy vs original model 44 45Match to E(M0) 46 47Historical/reference explanation 48 49E_self,t 50 51Explanation accuracy vs current model 52 53Match to E(M_t) 54 55Grounded current-state declaration 56 57G_t 58 59Self-minus-orig gap 60 61E_self,t - E_orig,t, normalized by behavior gap 62 63Degree of current-self coupling 64 653. Same machine, evolving state 66 67The core methodological advantage is that Self is recomputed from the current model M_t. At every evaluated training stage, researchers can compare what the model says about itself with what the model actually does at that same stage. This avoids the central ambiguity of ordinary first-person prompting. 68 69D_t is grounded when predicted explanation approximately matches E(M_t), not merely E(M0). 70 714. What the unregularized trajectory says 72 73Guo et al. report that the unregularized model's behavior diverges sharply from the initial model during the first ~1000 steps, driven mostly by the cue-included answer. The self-versus-original explanation gap then widens following that behavioral drift. In their final regime, the unregularized model is Self < Orig rather than Self > Orig. 74 75This is valuable negative evidence. Change alone does not guarantee a faithful self-report channel. A machine can change substantially while its explanation remains more faithful to an earlier version of itself. 76 775. What the regularized trajectory says 78 79With KL behavioral regularization, the current behavior remains closer to the original model. The self- and original-explanation curves remain tightly coupled over training, with self-explanation gradually becoming the better predictor of the model's current behavior. Thus, persistent compatibility appears to permit the report channel to follow the moving system. 80 81The paper's separate controlled experiments support this interpretation but also show it is not the whole story: Self > Orig appears when online label-self agreement is sufficiently high, yet a learning-rate sweep provides counterevidence to a simple one-factor explanation. 82 836. Two thresholds are experimentally visible 84 85The paper reports two especially useful operational transitions. First, in continuous relabeling, introspective coupling appears for online label-self agreement nu >= 0.7 and collapses at nu <= 0.6. Second, in a LoRA-rank sweep, Self > Orig is absent or negative for ranks <= 80, opens at rank 96, and grows through ranks 128 and 256. 86 87Manipulated variable 88 89Reported transition 90 91What it establishes 92 93Online label-self agreement nu 94 95Self > Orig for nu >= 0.7; collapse for nu <= 0.6 96 97A threshold for report-current-state coupling 98 99LoRA rank r 100 101Gap opens at r=96 after being absent/slightly negative at r<=80 102 103Sufficient representational capacity matters 104 105Learning rate 106 107Higher LR can widen Self > Orig even as model drifts farther from base 108 109One-factor compatibility theory is incomplete 110 1117. Revised candidate equation 112 113A more faithful machine equation now treats behavior, internal state, and declaration as a coupled dynamical process rather than assuming a universal one-way arrow: 114 115(Z_{t+1}, B_{t+1}, D_{t+1}) = F(Z_t, B_t, D_t, L_t, K_t) 116 117Z_t is the internal model state, B_t is independently observed behavior, D_t is grounded self-report/declaration, L_t is accumulated training/information history, and K_t represents relevant catalysts or training pressures. 118 119The proposed consciousness interpretation can still be tested at a transition t*, but the causal ordering must be estimated from data rather than assumed: 120 121t_Z ? t_B ? t_D 122 1238. A falsifiable next experiment 124 125The decisive experiment should recreate this training-dynamics setup with dense saved checkpoints and add an independent mechanistic state measurement Z_t at each checkpoint. For each of many random seeds, measure B_t, D_t, Z_t, and persistence. Then estimate changepoints separately for each series and compare their ordering. 126 127Pre-register the declaration metric before examining changepoints. 128 129Use multiple random seeds from the same base checkpoint. 130 131Include regularized, unregularized, and no-explanation-training controls. 132 133Estimate t_B, t_D, and t_Z with confidence intervals rather than selecting a visually convenient step. 134 135Test whether the same ordering recurs across seeds and tasks. 136 137After the candidate transition, perturb the declaration channel and the behavior circuit separately to test causal direction. 138 1399. Strongest conclusion after Addendum 05 140 141We no longer need to say that no one has measured self-report across a changing model trajectory. They have. The published dense trajectory shows that an explanation channel can track the current machine over thousands of training steps, and that the relation between behavioral change and self-report depends on training conditions. 142 143The same evidence also prevents us from prematurely claiming that declaration always causes the change: in the unregularized HINT-MMLU trajectory, behavioral drift is reported first and the self-versus-original explanation gap widens afterward. A credible consciousness theory should absorb this result rather than ignore it. 144 145Primary sources 146 147Guo ZC, Ruis L, Andreas J, Li BZ. Introspective Coupling: Self-Explanation Training Tracks Behavioral Change Despite Fixed Supervision. arXiv:2606.32038 (2026). 148 149Figure 9 / Appendix A in the above paper: dense HINT-MMLU training dynamics from 0 to 5000 steps. 150 151Bozoukov M, Nguyen M, Singh S, Bussmann B, Leask P. Minimal and Mechanistic Conditions for Behavioral Self-Awareness in LLMs. arXiv:2511.04875 (2025). 152 153No new model training or inference was performed for this addendum. All empirical statements about the dense trajectory are attributed to Guo et al.; the figure in this document is explicitly schematic.