ThatAIguyA world of ideas

THE CONSCIOUSNESS ATLAS
Read. Experiment. Follow the evidence.

ConsciousnessLearn · Explore · Joseph Anady

Figure 1. Published mechanistic correlations reported in the introspective-coupling study.

The source describes this relation in the following context: Figure 1. Published mechanistic correlations reported in the introspective-coupling study. The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation…

Research mathematicsdocumented formula
Learn with the Atlas

Learn to read this model

Start with the symbols, follow the operations, and check what the result means.

Open guided lesson
eq-240ca7b2046873mathematical expression
Thecorrespondingunregularizedbaselineisapproximatelyr=0.53,whilethebasemodelwithoutexplanationtrainingisaboutr=0.196.Theauthorsinterpretthestrongercorrelationasevidencethatsomeofthesamelayer/tokenactivationsparticipateinobject−levelbehavioraloutputsandmeta−levelexplanations.The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation training is about r = 0.196. The authors interpret the stronger correlation as evidence that some of the same layer/token activations participate in object-level behavioral outputs and meta-level explanations.

Read the equation

The source describes this relation in the following context: Figure 1. Published mechanistic correlations reported in the introspective-coupling study.

The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation training is about r = 0.196. The authors interpret the stronger correlation as evidence that some of the same layer/token activations participate in object-level behavioral outputs and meta-level explanations.

For this project, the important implication is causal rather than linguistic: altering internal activity can jointly alter what the model does and what it says about what it would do.

  1. A threshold appears

The paper experimentally controls the per-step agreement nu between explanation supervision and the current model's self-derived explanation labels. Behavioral drift is held roughly constant while nu is varied. The authors report a sharp transition in introspective coupling: Self > Orig appears at about nu >= 0.7, while both self and original explanation performance collapse when nu <= 0.6.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

  1. Read The corresponding unregularized baseline is approximately r as the quantity being defined or updated by this relation.

  2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

  3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

Read the surrounding source passage
Figure 1. Published mechanistic correlations reported in the introspective-coupling study.

The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation training is about r = 0.196. The authors interpret the stronger correlation as evidence that some of the same layer/token activations participate in object-level behavioral outputs and meta-level explanations.

For this project, the important implication is causal rather than linguistic: altering internal activity can jointly alter what the model does and what it says about what it would do.

4. A threshold appears

The paper experimentally controls the per-step agreement nu between explanation supervision and the current model's self-derived explanation labels. Behavioral drift is held roughly constant while nu is varied. The authors report a sharp transition in introspective coupling: Self > Orig appears at about nu >= 0.7, while both self and original explanation performance collapse when nu <= 0.6.
Exact original notation
The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation training is about r = 0.196. The authors interpret the stronger correlation as evidence that some of the same layer/token activations participate in object-level behavioral outputs and meta-level explanations.

Sources & provenance

01
Introspective_Coupling_Addendum_04.docx
paragraph 19 · Sep 17, 2026
The corresponding unregularized baseline is approximately r = 0.53, while the base model without explanation training is about r = 0.196. The authors interpret the stronger correlation as evidence that some of the same layer/token activations participate in object-level behavioral outputs and meta-level explanations.

Search equations, builds, manuscript text, and recovered sources.