Part 33 recovered most of the abstraction’s lost ground on PandaPickCubeOrientation by parametrizing the prior (0.33 → ~0.67 of PPO’s 0.82) and asked: does fuller parametrization close the remaining ~0.15? Part 34 answers no — and that pins down the ceiling.

Four fuller-parametrization variants

Each builds on Part 33’s orientation-aware controller (R_des = R_target @ R_home from grasp + target quat in obs), budget-matched ~56M, eval n=256, success box_target ≥ 0.9:

variant what it adds peak final
roterr richer rot-error-to-target conditioning in the residual obs 0.684 0.684
earlyD apply R_target from the approach phase (pre-align before grasp) 0.668 0.645
cap mid-size residual capacity bump (~64-128×4, Part 28 sweet-spot) 0.637 0.609
combo all three levers together 0.629 0.551
— (Part 33 ori-aware) ~0.67 ~0.64
— (PPO, Part 31) 0.82 0.81

The result — a ceiling, not a step

No variant beats ~0.68. The best (roterr 0.684) merely matches Part 33’s ~0.67; earlier rotation and capacity do nothing; combining levers makes it worse (combo 0.55-0.63). So the ~0.15 gap to PPO is not a parametrization-richness problem — it is the ceiling of the analytic-controller + Markov-residual class on the random-orientation task.

Two campaign-consistent notes:

  • Combo hurts. Stacking levers (earlier rotation + richer obs + more capacity) underperforms any single lever — the residual wants a small, single correction on a good prior, not a complicated one. This is the same “more isn’t better for the residual” seen with bigger nets (Part 28) and the orientation controller (Part 29).
  • roterr is stable (peak = final = 0.684, no collapse), reinforcing Part 33’s point that a well-matched prior makes the learned correction small and stable.

Verdict — the orientation-aware thread, closed

Parametrizing the prior recovers most of the gap (Part 33: 0.33 → ~0.67), but no amount of fuller parametrization closes the rest (Part 34: ~0.68 ceiling) — the last ~0.15 to PPO is a genuine capability ceiling of correcting an analytic skill rather than learning one. Combined with the whole arc, the honest picture of the abstraction-in-loop is now complete:

  • Ties PPO when the prior fits the task (PickCube, upright target: ~0.8, Parts 27-30) and is more sample-efficient and stable;
  • Loses badly when the prior is fixed-wrong (PickCubeOrientation: 0.33, Part 31);
  • Recovers ~70% when the prior is parametrized to the task’s DOF (Part 33);
  • Plateaus ~0.15 below PPO even with fuller parametrization (Part 34) — the analytic-prior + residual class ceiling.

To close that last gap you must learn the skill, not correct an analytic one — which is exactly end-to-end RL. The abstraction’s enduring advantages are elsewhere (sample-efficiency, stability, interpretability), not in the asymptotic success ceiling on hard, high-DOF-variation tasks.

Caveats

1 seed per v2 variant (the ~0.63-0.68 band is tight and clearly below PPO 0.82; Part 33’s 3-seed ori-aware ~0.67 anchors it). Budget-matched ~56M, same box_target≥0.9 metric, per-episode target yaw. The levers are four specific analytic/conditioning choices; we cannot rule out that some other parametrization closes more, but four reasonable ones did not, and combining them hurt. Data: exp/tdmpc_glass/generalization_PandaPickCubeOrientation_oriaware/v2_eval_{roterr,earlyD,cap,combo}_s1.json. Prior: Parts 31 (fixed-prior loss), 33 (parametrized recovery).