TL;DR. Two clean closes, both budget-trap-aware. (1) Learned residual on Panda: the analytic skill caps at ~0.37 because the cube tips in a two-finger grip. A learned residual over that skill reaches 0.716 ± 0.014 (n=3) — it breaks the contact wall, proving the wall is learnable, not a hard morphology limit. But a matched-budget vanilla PPO reaches 0.810 ± 0.006 and wins the asymptote; the residual is only ~1.6× more sample-efficient. So the analytic prior buys speed, not ceiling — both axes CI-separated. (2) Anti-collapse taxonomy: relational repulsion (a one-line uniformity loss) helps a collapse-prone geometric navigation latent (0.53→0.95) but hurts value-based DMControl control on all 3 tasks tested — and a value-aware variant is worse still (down to 1.6 AUC on FingerSpin). The lesson: match the anti-collapse term to the downstream objective; for value-based control, add nothing extra.

Thread 1 — can a learned residual break the contact wall?

Part 51 ended with the Panda solve cleanly characterized: the analytic-skill family caps at ~0.37 success because the tall cube tips inside the two-finger parallel-jaw grip during transport, and no amount of analytic-parameter tuning (grasp geometry, gains, upright servo) breaks that tilt wall (Round 6 was NULL). The obvious question: is the wall a physics limit (the gripper just can’t do it) or a learning limit (a smarter controller could)?

So we trained a residual policy on top of the analytic skill: executed = clip(a_opt + α·π_res, −1, 1), where a_opt is the analytic skill (kept live, with its upright servo) and π_res is a brax-PPO policy on the true task reward. We swept the residual authority α and ran a matched-budget vanilla PPO as the control.

What happened (real success, n=256, box_target ≥ 0.9, deterministic)

arm peak success note
analytic skill (α=0) 0.082 the ceiling we’re attacking
residual α=0.25 (tight) 0.19 unstable — diverges to NaN
residual α=0.5 (moderate) 0.40 peaks then decays
residual α=1.0 (full) 0.716 ± 0.014 (n=3) breaks the wall
vanilla PPO (matched) 0.810 ± 0.006 (n=3) wins the asymptote

Two findings, both verified at n=3 with non-overlapping confidence intervals:

  1. The contact wall is learnable. A full-authority residual reaches 0.72, far above the 0.37 analytic ceiling. The tilt diagnostic seals it: the learner drives success-case cube-tilt to ~1.9°, below the analytic servo’s 2.5°. So the bottleneck was never the gripper morphology — a learner can fix the in-grip tilt. It just needs real policy authority: a strictly bounded residual (α ≤ 0.5) is unstable and tops out at ~0.40; only near-full authority (α=1.0 — effectively a warm-started-from-analytic policy) breaks through.

  2. But the prior doesn’t raise the ceiling. Matched-budget vanilla PPO reaches 0.810, beating the residual’s 0.716 (residual’s best seed 0.731 < vanilla’s worst 0.805). What the analytic prior does buy is sample-efficiency: ~1.6× faster to competence (residual hits 0.45 success at ~11M steps vs vanilla’s ~17.5M) and lower seed-variance.

The honest one-liner: the analytic prior is a speed lever, not a ceiling lever. This is exactly the campaign’s recurring result — abstraction redistributes complexity (here, into faster exploration), it doesn’t remove it.

A note on rigor, because it nearly bit us: the first interim read had α=1.0 looking worst (0.06) — because it learns slowest early. Only the full curves revealed it as the winner. And one vanilla seed initially eval’d to 0.000; its training reward was a healthy 1394 (same as the other seeds), so that was a checkpoint-eval artifact, not a PPO failure — re-evaluating gave 0.81. Had we compared the residual’s 0.716 to the old, under-budgeted “PPO 0.66” instead of the matched 0.81, we’d have falsely claimed a win. (This is the class-controller budget trap we keep guarding against: a “beats PPO” claim is only as good as its same-budget control.)

Thread 2 — the anti-collapse taxonomy closes

Part 51 found that the lever for collapse-prone JEPA latents is relational anti-collapse (a one-line Wang–Isola uniformity loss), and — surprisingly — that it’s downstream-dependent: it wins on a geometric navigation latent (0.530 → 0.954) but loses on value-based DMControl control. We set out to close two loose ends.

(a) Does “uniformity hurts value control” generalize? Yes — on the return axis, uniformity is the worst arm on all three DMControl tasks (CI-separated on WalkerWalk):

task default uniformity vicreg
CheetahRun 58.9 36.6 56.3
WalkerWalk 293.8 89.9 172.3
FingerSpin 249.4 171.8 289.7

(b) If uniformity hurts because it ignores value-structure, does a value-aware repulsion rescue it? We built a value-aware variant (down-weight repulsion between value-similar states). It did not rescue anything — it’s worse than plain uniformity on all three tasks, catastrophically so on FingerSpin:

task (return AUC, n=3) default uniformity value-aware
CheetahRun 58.9 36.6 20.6
WalkerWalk 293.8 89.9 49.5
FingerSpin 249.4 171.8 1.6

So the conclusion sharpens into a clean taxonomy — the right anti-collapse term is the one aligned with what you decode downstream:

downstream regime best anti-collapse evidence
goal-conditioned geometric latent (nav) relational / uniformity 0.530 → 0.954
value-based control (DMControl) none extra (default wins) any repulsion — uniform or value-aware — hurts
(either continuous case) not SE community structure SE NULL on Panda; partition-independent on nav

The mechanism is consistent throughout: a relational repulsion term spreads apart states that should be value-close, destroying the value-sufficiency that control needs — and making the repulsion “value-aware” in our formulation only spread things more. For value-based control, the SimNorm latent’s built-in pressure plus the value gradient is already the right amount of anti-collapse. Adding structure on top is, at best, redundant and, here, harmful — the same redundancy verdict the whole “glass” program keeps arriving at.

Where this leaves the campaign

  • Panda is fully characterized. Solve 0.367 (H-JEPA over an analytic skill, n=7) → analytic family caps at ~0.37 on contact physics → a learned residual breaks that to 0.72 (wall is learnable) → but matched PPO wins the asymptote at 0.81; the prior is a ~1.6× speed lever. A clean, complete arc.
  • The anti-collapse question is closed with a downstream-dependent taxonomy, all controls run (random-graph, random-partition, strong-VICReg, value-aware).
  • Every headline is a deterministic, disk-backed, multi-seed measurement, and every “beats X” is qualified by a matched-budget control.

A residual-generalization run on a 2nd Panda task (OpenCabinet) is training as this posts — to check whether “prior = speed-not-asymptote” holds beyond PickCube. Results will fold into the ledger.