Source
Mueller, Geiger, Wiegreffe, Arad et al. (2025), ICML 2025, arXiv:2504.13151, LIT-1550, read in full in NOTE-1169: §4 (Table 3) and Appendix F.
What was actually shown
The design. For each task a high-level causal model is fixed, with variables for the answer position and answer token (ARC Easy, MCQA), the carry (two-digit addition), and a city’s continent, country and language (RAVEL). For each variable and layer, a featurizer is chosen and features are selected or learned on training pairs, then scored on held-out pairs by interchange-intervention accuracy (IIA): the share of base– counterfactual pairs on which intervening on the features in the LM and on the variable in the causal model give the same output. Reported: the mean over counterfactual datasets and layers, and the best layer.
The comparison. Three of the featurizers share one selection method, differential binary masking (DBM), trained to maximize faithfulness: over the model’s standard hidden dimensions, over PCA components, and over SAE features from Gemma Scope and Llama Scope. SAE interventions “incorporate the base input’s reconstruction error” so the featurizer is invertible. DAS instead learns an orthogonal subspace on the IIA objective.
The result, tabulated by the record from Table 3 (sixteen cells: ARC Easy and MCQA with two variables, addition with one, RAVEL with three, each on Gemma-2 and Llama-3.1):
| comparison | cells | size |
|---|---|---|
| mean IIA, SAE below neurons | 16 of 16 | 1 to 14 points, mean 6.9 |
| mean IIA, SAE above PCA | 10 of 16 | |
| DAS highest mean | 15 of 16 | the exception, Gemma-2 carry, is near chance for all |
Two cells illustrate: on ARC Easy with Gemma-2, the answer token scored 82 with neurons and 70 with SAE features; on RAVEL’s continent with Gemma-2, 66 and 64.
What could have come out otherwise. SAE features, being sparser and more monosemantic by construction, could have isolated the task variables better than neurons under the same mask. They did not in any cell.
What this does not say
- Not that SAE features never carry causal variables. The SAEs were on residual streams, the sites where THEORY-504 found Gemma Scope’s autoencoders cost the most next-token loss; the reconstruction error rides along in every intervention; and DBM is one selection method.
- Not that rotated directions beat neurons as units. DAS differs from DBM-over-neurons in its unit and in being supervised by the causal model, so its lead does not isolate the unit. The paper’s own sentence, “non-basis-aligned directions in activation space are generally better units of analysis”, runs the two together. How far a supervised rotation can manufacture alignment is now measured in the record: in the paper that introduced DAS (LIT-1551), its IIA on frozen random networks stays at chance up to width 256 and reaches 0.64 at width 4,096, against 16 input dimensions (THEORY-1002).
- Not across models generally. Two models, four tasks, variables supplied in advance; Qwen-2.5 and GPT-2 have no SAE rows.
- Not about best layers. At its best layer even the full vector reaches 100 in four cells; the comparison is in the means.
- Not an instruction to prefer one method; method choice is the anthology’s business.
Connections
- CLAIM-454. A feature recovered without the hypothesis was not the better carrier of the variable that does the work. A supporting case in networks.
- THEORY-504. The site and the reconstruction-error choice are both where THEORY-504’s fidelity results would predict SAEs to lose.
- THEORY-802. IIA scores alignments one at a time; ties between alignments related by a change of basis would be invisible here.
- LIT-1540. The IOI task and its S-inhibition heads come from Wang et al.’s circuit in GPT-2 small (THEORY-980).
- The sparse-autoencoder papers. Templeton et al.’s comparison of features with few-shot probes (2 of 7 cases equal, 5 of 7 favouring the features, on cases chosen where features worked; NOTE-1178) is not a counter-result to this one: it is selected and few-shot. Bricken’s and Templeton’s “more interpretable than neurons” (THEORY-991) is a different test from localizing variables supplied in advance. Sparse feature circuits point the same way as this account from circuits: without their error terms, SAE features carry little of the behaviour (THEORY-1007). This account is the standing test of the Proposed thesis that SAE features are the model’s working units (THEORY-965).