Source
Chan, Garriga-Alonso, Goldowsky-Dill, Greenblatt, Nitishinskaya, Radhakrishnan, Shlegeris and Thomas (2022), Causal scrubbing, LIT-1549, read in full in NOTE-1168: §2 (hypotheses), §3.2 (the algorithm and pseudocode) and §7 (limitations).
What was actually shown
The algorithm. The scrubbed expectation is the mean of f over runs of run_scrub from the output node of the interpretation I. At a node n_I with image n_G = c(n_I), each important parent p_I is evaluated recursively on a datum drawn by sample_agreeing_x(D, p_I, ref_x), which returns a uniform draw from {x ∈ D : p_I(x) = p_I(ref_x)}; unimportant parents take their values on one random datum. The interpretation enters at no other point.
The re-derivation. Let two hypotheses differ only in the function an interpretation node computes, φ in one and ψ in the other, with the same graph G and correspondence c. If φ(x) = φ(x′) exactly when ψ(x) = ψ(x′) for all x, x′ in D, the agreeing sets are the same for every reference datum, so every draw has the same distribution and the scrubbed expectations are equal. Perfect correlation on D (a bijection between the values of φ and ψ on D) is one case. The values the interpretation computes never reach the model; only which data share a value does.
The check. In a toy where a hidden unit copies an input bit a, the output is a ⊕ c, and a second input bit b equals a on every datum, the hypothesis “the unit computes a” and the hypothesis “the unit computes b” both score 1.0 over 20,000 scrubbed samples, while “the unit computes a constant” scores 0.50 (record simulation, 2026-10-26).
The authors’ statement. §7: causal scrubbing “doesn’t allow us to distinguish between two features that are perfectly correlated on our dataset, since they would induce the same equivalence classes. In fact, to the extent that two features A and B are highly correlated, causal scrubbing will not complain if you misidentify an A-detector as a B-detector.” §2: the algorithm tests “that the equivalence classes on inputs to n_I are the same as the equivalence classes on inputs to n_G”, which “is not strong enough to eliminate all incorrect hypotheses”.
What this does not say
- Not that hypotheses inducing different partitions are well separated. For features correlated imperfectly, the scores differ, by an amount this account does not bound.
- Not that causal scrubbing is unsound otherwise. Its other failure modes (omitted inhibitory circuits, independent resampling of correlated terms) are argued by the authors with examples and are not part of this account.
- Not that the partition is all a hypothesis says. The correspondence c and the choice of how G is rewritten are part of the hypothesis and do change the score; the account fixes them.
- Not about other instruments. Interchange intervention accuracy compares outputs of a high-level model, which do depend on the values the high-level variables take.
Connections
- THEORY-802 and QUESTION-234. A hypothesis may rewrite G, for example into rotated coordinates, before mapping into it. Two alignments related by a change of basis that induce the same partitions of D therefore tie under causal scrubbing by construction. That is a tie of the kind THEORY-802 asserts, but for a reason that holds of the instrument, not of trained networks, so it does not meet THEORY-802’s promote_when.
- CLAIM-454. What passes the test is a partition of the data, not the variable that does the work.
Note of 2026-10-27: the tie by theorem, and a measured near-tie
- THEORY-1025, from the causal scrubbing appendix (LIT-1583): the inputs the algorithm samples are the unique maximum-entropy distribution that keeps every interpretation node’s inputs jointly as on the data. This entry’s tie follows from it: two hypotheses that induce the same partitions constrain the same marginals and so sample the same distribution.
- The paren post’s 1a against 1b (LIT-1580, NOTE-1195): a hypothesis using a wrong but correlated count scores 88% of the loss recovered against 93% for the right one. It is the authors’ own measured near-tie for imperfectly correlated features, the case “What this does not say” leaves unbounded; here the gap is 5 points.