v3.1 stage three, step zero — is the dream alive?

THE DREAM IS NOT A USABLE TRAINING ENVIRONMENT FOR THIS TASK. At its chosen temperature no model puts a ball below the band at a rate comparable to the world’s (0.80 arrivals per 150 frames, decoded-height sd 0.164) — baseline almost never a ball below the band; poshead almost never a ball below the band; ff almost never a ball below the band; allbands almost never a ball below the band. No other (model, temperature) cell is in that range either. A ball decoded above the band is scenery — the paddle cannot reach it and no action changes it; a ball parked at the band’s lower edge is a fixed point, not a trajectory. So every controller trained below is fitted to what its M’s REWARD HEAD says about latents that contain no reachable ball, not to a simulated interception task, and every controller number must be read that way.

64 dreams x 150 steps per cell, warm-started on 8 real frames from ['data/v31/train_mix'], driven by a fixed sticky-random action stream. Every model and every temperature sees the identical starts and the identical actions, so the cells are paired.

The real data, measured with the same detector

reference	frames	ball present	ball below the band	arrivals below the band per 150 frames	ball-height sd	re-emergence (of runs starting hidden)
`data/v31/train_mix`, 4096 random frames	4096	35.7%	2.4%	—	—	—
the real continuation of the dreams’ own 64 starts	64x150	35.5%	2.5%	0.80	0.164	70.0% (40)

The detector’s ball present is a half-a-ball-outside-the-band threshold, so it should land between the dataset’s frac_frames_visible (24.9%, the ball entirely clear of the band) and visible + partial (57 %) — i.e. at roughly the fraction of frames with ball_visible > 0.5. It does. ball below the band is the reference the dream is graded against: the fraction of frames on which the ball is in the strip where the paddle can act at all, which in this world is only a few per cent.

Every cell

model	tau	ball present	ball below band	arrivals / run (real 0.80)	ball-height sd (real 0.164)	mean decoded ball y	re-emergence (of dreams starting hidden)	r(reward head, -abs decoded gap)	n pairs
`baseline` <– chosen	0.0	6.1%	0.1%	0.03	0.053	0.762	0.0% (39)	0.97	585
`baseline`	0.5	11.6%	10.4%	3.62	0.059	0.121	100.0% (39)	0.96	1114
`baseline`	1.0	14.9%	12.8%	4.78	0.116	0.140	100.0% (39)	0.92	1427
`poshead` <– chosen	0.0	7.0%	0.1%	0.03	0.053	0.758	0.0% (39)	0.98	672
`poshead`	0.5	34.3%	0.0%	0.02	0.060	0.737	0.0% (39)	0.97	3290
`poshead`	1.0	40.5%	0.0%	0.03	0.066	0.742	2.6% (39)	0.95	3886
`ff`	0.0	29.6%	0.1%	0.02	0.027	0.781	0.0% (39)	0.88	2843
`ff`	0.5	66.2%	0.0%	0.02	0.034	0.738	0.0% (39)	0.94	6352
`ff` <– chosen	1.0	74.5%	0.0%	0.05	0.057	0.766	2.6% (39)	0.83	7148
`allbands`	0.0	6.0%	0.1%	0.02	0.053	0.763	0.0% (39)	0.98	573
`allbands`	0.5	53.9%	0.0%	0.02	0.065	0.774	0.0% (39)	0.98	5173
`allbands` <– chosen	1.0	51.1%	0.1%	0.08	0.069	0.769	5.1% (39)	0.96	4901

The reward head, teacher-forced on real latents

M’s dense reward head against the true 1 - |ball_x - paddle_x| on real latents and real actions. This is the ceiling on what the head can contribute inside a dream.

model	R2	Pearson r	rmse	pred mean	true mean	n
`baseline`	0.719	0.851	0.1168	0.743	0.741	6,965
`poshead`	0.688	0.838	0.1230	0.735	0.741	6,965
`ff`	0.498	0.706	0.1561	0.746	0.741	6,965
`allbands`	0.636	0.814	0.1328	0.769	0.741	6,965

Chosen training temperature per model

The tau whose count of arrivals below the band is closest to the real continuation’s 0.80 per 150 frames, ties going to the lower tau (stage two: a sampled v3.1 dream does not conserve the hidden ball’s direction of travel).

model	chosen tau	its arrivals / run	real
`baseline`	0.0	0.03	0.80
`poshead`	0.0	0.03	0.80
`ff`	1.0	0.05	0.80
`allbands`	1.0	0.08	0.80

Wall clock 99 s.