Dense Trajectory Addendum 05

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Highlights a dense reported trajectory of behavior and self-explanation and its implications for a prospective test.

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The Dense Trajectory Exists

Research Addendum 05: checkpoint-level emergence of behavioral drift and self-report coupling

Prepared 17 September 2026

Executive finding

The 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.

The 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.

Observed ordering in this experiment: behavioral drift -> widening self-report gap

Figure 1. Schematic of the ordering described by the authors; this is not digitized data from their figure.

1. Why this changes the project

Until 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.

This 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.

1. The directly measured variables

Variable

Meaning

How paper measures it

Role in our theory

B_t

Object-level behavior

Model answers with cue included/removed

Actual machine behavior

E_orig,t

Explanation accuracy vs original model

Match to E(M0)

Historical/reference explanation

E_self,t

Explanation accuracy vs current model

Match to E(M_t)

Grounded current-state declaration

G_t

Self-minus-orig gap

E_self,t - E_orig,t, normalized by behavior gap

Degree of current-self coupling

1. Same machine, evolving state

The 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.

D_t is grounded when predicted explanation approximately matches E(M_t), not merely E(M0).

1. What the unregularized trajectory says

Guo 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.

This 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.

1. What the regularized trajectory says

With 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.

The 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.

1. Two thresholds are experimentally visible

The 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.

Manipulated variable

Reported transition

What it establishes

Online label-self agreement nu

Self > Orig for nu >= 0.7; collapse for nu <= 0.6

A threshold for report-current-state coupling

LoRA rank r

Gap opens at r=96 after being absent/slightly negative at r<=80

Sufficient representational capacity matters

Learning rate

Higher LR can widen Self > Orig even as model drifts farther from base

One-factor compatibility theory is incomplete

1. Revised candidate equation

A more faithful machine equation now treats behavior, internal state, and declaration as a coupled dynamical process rather than assuming a universal one-way arrow:

(Z_{t+1}, B_{t+1}, D_{t+1}) = F(Z_t, B_t, D_t, L_t, K_t)

Z_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.

The proposed consciousness interpretation can still be tested at a transition t*, but the causal ordering must be estimated from data rather than assumed:

t_Z ? t_B ? t_D

1. A falsifiable next experiment

The 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.

Pre-register the declaration metric before examining changepoints.

Use multiple random seeds from the same base checkpoint.

Include regularized, unregularized, and no-explanation-training controls.

Estimate t_B, t_D, and t_Z with confidence intervals rather than selecting a visually convenient step.

Test whether the same ordering recurs across seeds and tasks.

After the candidate transition, perturb the declaration channel and the behavior circuit separately to test causal direction.

1. Strongest conclusion after Addendum 05

We 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.

The 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.

Primary sources

Guo ZC, Ruis L, Andreas J, Li BZ. Introspective Coupling: Self-Explanation Training Tracks Behavioral Change Despite Fixed Supervision. arXiv:2606.32038 (2026).

Figure 9 / Appendix A in the above paper: dense HINT-MMLU training dynamics from 0 to 5000 steps.

Bozoukov M, Nguyen M, Singh S, Bussmann B, Leask P. Minimal and Mechanistic Conditions for Behavioral Self-Awareness in LLMs. arXiv:2511.04875 (2025).

No 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.