stage three (C) — real-environment evaluation by occlusion

150 episodes x 200 steps, seeds 5000..5149, identical starts for every row. Band (0.13, 0.63), paddle width 0.16.

oracle has perfect vision and perfect memory; wait_and_see has perfect vision and NO memory (it tracks the true ball only while ball_visible > 0.5 and STAYs otherwise). Every trained row should be read as a position between those two, and the single most important fact about any row is which side of wait_and_see it falls on: above it is memory, below it is not. Any row whose name contains poshead is a PRIVILEGED CEILING — its dynamics model was trained with a supervised head on the simulator’s true ball position — and is not a world-model result.

The two numbers everything is graded against, measured here on these 150 episodes: oracle 0.99, memoryless (wait-and-see) bound **0.51, stand still 0.38.**

Each controller is driven by the (V, M) it was trained with; the policy reads h, so M is part of the policy:

The headline: every row against the memoryless bound

wait_and_see = 0.51 is the best a policy with perfect vision and no memory can do in this world. A row above it is using memory; a row below it is not, whatever else it is doing well.

The CI is a 4000-sample bootstrap over EPISODES, the unit of independence; “above the bound” is read off the point estimate, so a row whose interval straddles the bound is not a claim.

Interceptions per floor visit, by required move

The required move is the distance between the paddle’s x at the moment the ball became fully hidden on its way down and the ball’s landing x. Flat across the bins = object permanence; collapsing on long = memoryless.

The bins are policy-dependent and that is not a bug to hide. The required move is measured from this policy’s own paddle position, so a policy that already tends to stand near the ball generates few long visits and a policy that parks in a corner generates many. The counts are therefore reported per row, and a row with a handful of long visits should be read as noise. The episodes and seeds are identical throughout; only the paddle differs.

The reach curve (interceptions per visit at 0.1 resolution)

A required move is covered once the paddle’s centre is within half a paddle-width (0.08) of the landing x, plus whatever the visible frames between the band’s bottom edge and contact height buy. On v3’s geometry that came to ~0.43 and wait_and_see was at the ceiling out to 0.6; v3.1 halves both terms, which is the whole point of the re-design. This table says where wait_and_see actually falls off, and therefore which bins above carry any information about object permanence.

Paddle motion during occlusion

Over the descending hidden runs: the fraction of hidden frames whose ACTION moved the paddle toward the eventual landing x (chance 1/3 — three actions, STAY counts as not-toward), and the displacement the paddle actually achieved toward the landing point while blind, as a fraction of the required move.

oracle is not the ceiling for these two columns and should not be read as one: it chases the ball’s CURRENT x rather than its landing x, and it is usually already inside its dead zone when the ball vanishes, so it STAYs. The references that mean something here are chance (1/3) and wait_and_see (0.000 by construction).

Overall

Other band (0.13, 0.45)

60 episodes. Read the VAE reconstruction table below before attributing any drop to the controller — in v3 these bands were out of the encoder’s distribution and cost it 133-262x reconstruction error, and in v3.1 the encoder was trained on all three, so the same comparison is finally about the controller.

Other band (0.13, 0.78)

60 episodes. Read the VAE reconstruction table below before attributing any drop to the controller — in v3 these bands were out of the encoder’s distribution and cost it 133-262x reconstruction error, and in v3.1 the encoder was trained on all three, so the same comparison is finally about the controller.

VAE reconstruction on each band

The frozen encoder+decoder on frames from datasets collected at each band height, so an other-band drop can be attributed to V or to C.

Dream-vs-real transfer

Pearson r between the smoothed best-of-generation dream fitness and the periodic real interception count, per training run (dream_vs_real_all.png, and dream_vs_real.png in each run directory).

GIFs

• real — seed 5036: required move 0.63, 26 hidden frames, 13 of them moving toward the landing x, 3 interceptions in the episode. CHERRY-PICKED: chosen out of the evaluation set as the longest required move the policy moved THROUGH – it moved toward the landing point on at least half the hidden frames – so it is a demo that the behaviour exists at all, not a sample of the average episode.
• dream — the controller inside its own dream, decoded by V at temperature 0.0. Best of 16 dreams by predicted contact (a cherry-pick, as in v1/v2). Watch whether a ball re-emerges below the band at all – wm.eval_dream_alive measures that fraction, and this GIF is what the measurement looks like.