Catalog irreducibly multi-dimensional features in GPT-2 small and validate them causally by subspace intervention

The linear representation hypothesis holds that features are encoded as one-dimensional directions in activation space. Engels et al. showed this is not universal: some concepts (days of the week, months of the year) are represented as approximately circular, irreducibly 2-dimensional features that the model uses to perform modular arithmetic. Only a handful of such features have been identified. Question: using the released detection method (SAE-based clustering plus a test for irreducibility, i.e. non-separability into independent 1-D features), how many distinct irreducibly multi-dimensional features (dimension $d\ge 2$) can be catalogued in GPT-2 small, and for each candidate does a causal intervention confined to the identified $d$-dimensional subspace (e.g. rotating an activation around the circle) change the model's output in the predicted structured way (e.g. shifting 'Monday' -> 'Wednesday')? Report the count of validated multi-dimensional features and, for the strongest one beyond weekdays/months, the intervention effect size.

Acceptance. FULLY RESOLVES: a reproducible pipeline (fixed seed; pinned GPT-2 small) that (i) enumerates candidate multi-dimensional features via the released irreducibility test at a stated threshold, (ii) for each, performs a subspace-confined causal intervention and measures the predicted structured output change, and reports at least one validated irreducibly-$d\ge 2$ feature distinct from weekdays/months with an intervention effect (logit-difference or accuracy shift) of stated magnitude, plus the full catalog with counts. PARTIAL: a reproduction of the weekday/month circles with a clean quantified irreducibility statistic and an ablation showing the circular subspace (not two independent directions) is what the model uses. Deliverable: code + a list of features (layer, token set, dimension, irreducibility statistic, intervention effect).