A r=64 rsLoRA adapter on Qwen/Qwen3-8B that inverts a subspace rather than a single direction: given a block of a block-sparse featurizer (BSF/SASA, 8192 blocks × b=8 dims), inject unit(proj_S(target_act)) at layer 1 and generate text whose layer-27 activation, projected into that subspace S, matches the target coordinate. The point is to tile each subspace — decode any coordinate.

RL'd (Dr.GRPO) from the v3 cosine-reward inverter (step_400) with a two-term subspace reward:

(w_trig = w_cos = 1, trigger clamped ≤3 to kill a reward-hack fat tail). Early-stopped at step 400 on reward convergence.

Subspace inversion works (cos 0.86, ~95% of coords clear 0.5, on-concept text). The in-subspace direction is near-ceiling from SFT already; RL's contribution is +32% trigger strength (fires the subspace harder). Caveat: RL trained on all blocks, so this is intra-block-coordinate tiling (new coords within trained subspaces), not strict held-out-block generalization.

Base Qwen/Qwen3-8B, r=64, α=16, rsLoRA, inject@layer1 ( ? marker, norm-matched), read@layer27. Interpretability research (MATS / Neel Nanda). Not a general chat model.