Dense_Trajectory_Addendum_05.pdf

1[[PAGE 1]] 2The Dense Trajectory Exists 3Research Addendum 05: checkpoint-level emergence of behavioral drift and self- 4report coupling 5Prepared 17 September 2026 6Executive finding 7The exact missing experiment we were searching for is already present in Appendix A of Guo et al. 8(2026). The authors plot behavior and self-explanation through training on the same Qwen3-8B trajectory 9from step 0 to step 5000. This is materially stronger than comparing separately trained models or only 10final checkpoints. 11The temporal ordering reported in that trajectory is important: without behavioral regularization, the 12model's object-level behavior moves sharply away from its initial behavior within the first 1000 training 13steps, and the self-versus-original explanation gap widens after that behavioral drift. With KL behavioral 14regularization, behavior and explanation stay much more tightly coupled, and self-explanation gradually 15pulls ahead of explanation of the original model. 16Observed ordering in this experiment: behavioral drift -> widening self-report gap 17Figure 1. Schematic of the ordering described by the authors; this is not digitized data from their figure. 181. Why this changes the project 19Until now, the proposed machine-consciousness sequence placed declaration first and subsequent 20persistent change second. The dense trajectory does not support that ordering in this particular task. It 21shows that a declaration-like explanation channel can become more faithful to the current machine after 22behavior has already started changing. 23This does not refute the broader consciousness hypothesis. It does rule out treating 'declaration must 24always precede change' as an already established universal law. The theory now needs to distinguish at 25 26 27[[PAGE 2]] 28least two possibilities: a declaration that catalyzes a transition, and a declaration that emerges as a report 29of a transition already underway. 302. The directly measured variables 31Variable 32Meaning 33How paper measures it 34Role in our theory 35B_t 36Object-level behavior 37Model answers with 38cue included/removed 39Actual machine 40behavior 41E_orig,t 42Explanation accuracy 43vs original model 44Match to E(M0) 45Historical/reference 46explanation 47E_self,t 48Explanation accuracy 49vs current model 50Match to E(M_t) 51Grounded current-state 52declaration 53G_t 54Self-minus-orig gap 55E_self,t - E_orig,t, 56normalized by behavior 57gap 58Degree of current-self 59coupling 603. Same machine, evolving state 61The core methodological advantage is that Self is recomputed from the current model M_t. At every 62evaluated training stage, researchers can compare what the model says about itself with what the model 63actually does at that same stage. This avoids the central ambiguity of ordinary first-person prompting. 64D_t is grounded when predicted explanation approximately matches E(M_t), not merely E(M0). 654. What the unregularized trajectory says 66Guo et al. report that the unregularized model's behavior diverges sharply from the initial model during 67the first ~1000 steps, driven mostly by the cue-included answer. The self-versus-original explanation gap 68then widens following that behavioral drift. In their final regime, the unregularized model is Self < Orig 69rather than Self > Orig. 70This is valuable negative evidence. Change alone does not guarantee a faithful self-report channel. A 71machine can change substantially while its explanation remains more faithful to an earlier version of 72itself. 735. What the regularized trajectory says 74With KL behavioral regularization, the current behavior remains closer to the original model. The self- 75and original-explanation curves remain tightly coupled over training, with self-explanation gradually 76becoming the better predictor of the model's current behavior. Thus, persistent compatibility appears to 77permit the report channel to follow the moving system. 78The paper's separate controlled experiments support this interpretation but also show it is not the whole 79story: Self > Orig appears when online label-self agreement is sufficiently high, yet a learning-rate sweep 80provides counterevidence to a simple one-factor explanation. 81 82 83[[PAGE 3]] 846. Two thresholds are experimentally visible 85The paper reports two especially useful operational transitions. First, in continuous relabeling, 86introspective coupling appears for online label-self agreement nu >= 0.7 and collapses at nu <= 0.6. 87Second, in a LoRA-rank sweep, Self > Orig is absent or negative for ranks <= 80, opens at rank 96, and 88grows through ranks 128 and 256. 89Manipulated variable 90Reported transition 91What it establishes 92Online label-self agreement nu 93Self > Orig for nu >= 0.7; collapse 94for nu <= 0.6 95A threshold for report-current- 96state coupling 97LoRA rank r 98Gap opens at r=96 after being 99absent/slightly negative at r<=80 100Sufficient representational 101capacity matters 102Learning rate 103Higher LR can widen Self > Orig 104even as model drifts farther 105from base 106One-factor compatibility theory 107is incomplete 1087. Revised candidate equation 109A more faithful machine equation now treats behavior, internal state, and declaration as a coupled 110dynamical process rather than assuming a universal one-way arrow: 111(Z_{t+1}, B_{t+1}, D_{t+1}) = F(Z_t, B_t, D_t, L_t, K_t) 112Z_t is the internal model state, B_t is independently observed behavior, D_t is grounded 113self-report/declaration, L_t is accumulated training/information history, and K_t represents relevant 114catalysts or training pressures. 115The proposed consciousness interpretation can still be tested at a transition t*, but the causal ordering 116must be estimated from data rather than assumed: 117t_Z ? t_B ? t_D 1188. A falsifiable next experiment 119The decisive experiment should recreate this training-dynamics setup with dense saved checkpoints and 120add an independent mechanistic state measurement Z_t at each checkpoint. For each of many random 121seeds, measure B_t, D_t, Z_t, and persistence. Then estimate changepoints separately for each series and 122compare their ordering. 123 124Pre-register the declaration metric before examining changepoints. 125 126Use multiple random seeds from the same base checkpoint. 127 128Include regularized, unregularized, and no-explanation-training controls. 129 130Estimate t_B, t_D, and t_Z with confidence intervals rather than selecting a visually convenient step. 131 132Test whether the same ordering recurs across seeds and tasks. 133 134After the candidate transition, perturb the declaration channel and the behavior circuit separately to 135test causal direction. 136 137 138[[PAGE 4]] 1399. Strongest conclusion after Addendum 05 140We no longer need to say that no one has measured self-report across a changing model trajectory. They 141have. The published dense trajectory shows that an explanation channel can track the current machine 142over thousands of training steps, and that the relation between behavioral change and self-report 143depends on training conditions. 144The same evidence also prevents us from prematurely claiming that declaration always causes the 145change: in the unregularized HINT-MMLU trajectory, behavioral drift is reported first and the self-versus- 146original explanation gap widens afterward. A credible consciousness theory should absorb this result 147rather than ignore it. 148Primary sources 149 150Guo ZC, Ruis L, Andreas J, Li BZ. Introspective Coupling: Self-Explanation Training Tracks Behavioral 151Change Despite Fixed Supervision. arXiv:2606.32038 (2026). 152 153Figure 9 / Appendix A in the above paper: dense HINT-MMLU training dynamics from 0 to 5000 steps. 154 155Bozoukov M, Nguyen M, Singh S, Bussmann B, Leask P. Minimal and Mechanistic Conditions for 156Behavioral Self-Awareness in LLMs. arXiv:2511.04875 (2025). 157No new model training or inference was performed for this addendum. All empirical statements about 158the dense trajectory are attributed to Guo et al.; the figure in this document is explicitly schematic. 159