Less-than-rank-one ablation — edits with finer granularity than → Dictionary-feature patching procedure

Both techniques edit a residual-stream activation along a dictionary feature’s direction, but they stop at different points. Dictionary-feature-patching (Section 4) pushes a chosen feature’s encoded activation the full distance from its base-sentence value to its counterfactual-sentence value, adding the complete difference so the patched run matches the target as closely as that feature allows (sparse-autoencoders, §"4.1 Adapting activation patching to dictionary features", p. 6). Less-than-rank-one ablation, used in the apostrophe-feature case study to measure a feature’s effect on next-token logits, instead lowers the activation only as far as the point where the feature stops firing, not past it (sparse-autoencoders, §"5.2 Output: dictionary features have intuitive effects on the logits", p. 7). That stopping point is not arbitrary: Appendix G explains that a dictionary feature, unlike a PCA or ICA direction, is only ever active on the far side of a hyperplane that does not pass through the origin, a consequence of the ReLU nonlinearity’s always-negative bias, so a feature’s "on" region is already less than a full direction in activation space (sparse-autoencoders, §"G Top K comparisons", p. 18). Ablating exactly to that boundary, rather than subtracting a feature’s full magnitude the way patching moves a feature the full distance to a counterfactual target, respects the very geometry the paper’s own fairness check in Appendix G identifies as distinguishing dictionary features from every baseline it compares against.