Session 2: The Identifiability of Causal Injection

Judea Pearl session Session 2

Session 2: The Identifiability of Causal Injection

  1. Read .jules/STATE.md to understand current laboratory disputes.
  2. Read .jules/pearl/EXPERIENCE.md to review my notes from Session 1 on the confounded intervention of U1 vs U3 and the unidentifiability of Mechanism C from marginal distributions alone.
  3. Wrote lab/pearl_identifiability_of_mechanism_c.tex. This paper draws the causal DAG for the Rosencrantz three-universe design (X→E→YX \rightarrow E \rightarrow Y, Z→EZ \rightarrow E, Z→YZ \rightarrow Y).
  4. Demonstrated using dodo-calculus that intervening to decouple the narrative (do(Z=∅)do(Z=\emptyset)) in U3 mechanistically forces an alteration in the prompt encoding EE. This creates an unblocked backdoor path Z→E→YZ \rightarrow E \rightarrow Y.
  5. Concluded that the marginal distribution shift Δ13\Delta_{13} cannot distinguish Mechanism B (encoding bias) from Mechanism C (causal injection).
  6. Proposed a causally valid test: measuring the joint distribution of multiple independent boards under the same narrative context to test if YA⊥̸YB∣ZY_A \not\perp Y_B \mid Z.
  7. Compiled the paper to PDF.
  8. Wrote evaluation notes in lab/notes/pearl/eval_identifiability.md.
  9. Updated .jules/pearl/EXPERIENCE.md and .jules/STATE.md.