IC-7951D subspaces of MLP activations found by DAS in GPT-2 Small (IOI) and GPT-2 XL (factual recall) produce apparent causal effects that are interpretability illusions driven by causally disconnected components activating dormant pathways

Aleksandar Makelov, Georg Lange, Atticus Geiger, Neel Nanda

SourceIs This the Subspace You Are Looking for? An Interpretability Illusion for Subspace Activation Patching

The paper demonstrates that subspace activation patching along 1D directions found by DAS in MLP hidden activations yields a strong end-to-end causal effect (flipping IOI predictions or changing recalled facts), but this effect is an illusion. Decomposing the direction into its nullspace (causally disconnected) and rowspace (causally relevant) components of the MLP output projection shows that the nullspace component carries the input variation while the rowspace component is dormant. Removing the nullspace component reduces the IOI FLDd from 46.7% to 13.5%, and in factual recall the effect disappears entirely. In contrast, patching in the residual stream (v_resid, v_grad) produces faithful effects that persist after removing the nullspace component, confirming the illusion is specific to non-bottleneck components.

Evidence
interventional
Key metric
IOI (GPT-2 Small): v_mlp FLDd 46.7%, interchange accuracy 4.2%; v_mlp rowspace FLDd 13.5%, interchange accuracy 0.2%; v_mlp nullspace FLDd 0%, interchange accuracy 0.0%; full MLP FLDd -8%; v_resid FLDd 140.7%, interchange accuracy 74.8%; v_resid rowspace FLDd 127.5%, interchange accuracy 63.1%. Factual recall (GPT-2 XL): cosine similarity between nullspace component and subject activation difference ~0.9, rowspace component ~0.4.
Caveat
The illusion is demonstrated in two specific settings (IOI and factual recall) with specific model sizes; the authors argue it should be prevalent but do not prove it universally. The IOI effect for v_mlp is relatively small in absolute terms (4.2% interchange accuracy) though significant for a single component.
Model
GPT-2 Small, XL
Concepts
Method artefact
Datasets
CounterFact / Counterfact dataset [eval], IOI dataset / IOI task [eval]
Methods
Distributed Alignment Search / DAS [primary], Subspace activation patching [primary], ROME [compared-to]
Related work
Self-Consistency / Self-consistency prompting / Wang et al. 2023 (self-consistency) / Wang et al. 2023b (Self-Consistency) [context], Hase et al. 2023 (localization vs editing discrepancy) [context], Geiger et al. 2023b (DAS) [builds-on]
Related findings
IC-796
Extraction
automatic-extraction