finding

active

finding:non-linear-nonlin-achieves-near-perfect-iia-on-distributive-law-task-for-both-and-or-and-and-or-and-algorithms-eliminating-linear-identity-map-differences

Non-linear ϕ_nonlin achieves near-perfect IIA on distributive law task for both And-Or and And-Or-And algorithms, eliminating linear/identity map differences

Corroborating result on additional task confirming main paper findings

Source paper

extracted_from

The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?

(2025) · Sutter, Denis · Minder, Julian · Hofmann, Thomas · Pimentel, Tiago

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Claims (1)

claim

Causal abstraction is not enough for mechanistic interpretability because it becomes vacuous without assumptions about how models encode information
supports
Central thesis of the paper

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Non-linear alignment map ϕ_nonlin achieves near-optimal IIA across all layers on hierarchical equality task, eliminating layer-dependent degradation seen with linear mapsfinding0.836
Key empirical result: non-linear maps overcome linear maps' failure in deeper layers
Over 80% IIA achieved using complex non-linear alignment maps on randomly initialised MLPs in hierarchical equality taskfinding0.806
Demonstrates that high IIA can be obtained even when model cannot solve the task
The fact that ϕ_lin tracks DNN performance more closely than ϕ_nonlin throughout training may support the linear representation hypothesis for IOI task featureshypothesis0.799
Authors' tentative hypothesis from Fig. 4 but they acknowledge they cannot formalise this intuition
Assuming linear representations enables identifying the location of certain variables in a DNN, but many insights fail to generalise when more powerful non-linear maps are usedclaim0.792
Interpretive claim about what linear DAS results actually tell us
With only 1,000 training samples, ϕ_nonlin achieves IIA over 0.99 on training set for identity of first argument algorithm, but fails at scalefinding0.786
Confirms theorem's existence proof holds but practical learnability fails with insufficient RevNet capacity
Linear alignment map ϕ_lin shows substantial IIA decrease in third layer for both equality relations and left equality relation algorithms in hierarchical equality taskfinding0.773
Replicates Geiger et al. 2024b pattern of layer-dependent IIA degradation with linear maps
CLMAS achieves the best IIA in the causally inaccessible (No Access) direction while matching MAS in the accessible directionfinding0.765
Demonstrates the value of the CL auxiliary loss for recovering causal alignments when one model cannot be intervened upon.
The And-Or algorithm may not be a true abstraction of the trained MLP's behaviour since it never achieves high IIA in later layers regardless of alignment map complexityhypothesis0.759
Hypothesis raised in distributive law task analysis