World model test

Status: Release paired runs of tests/WorldModelTest.cpp and tests/CompressionTest.cpp, dim = 8, T = 16. Table is the k-cube Predictor (no a). Not re-run since WorldModel grew a. The tables were produced before the LCN weight layout changed (Sep 10, 2026); the same seeds now draw a different net, so a re-run gives different numbers with the same picture.

Definitions

Symbol / term	Meaning
WorldModel	Frozen Encoder plus trained Predictor. Does the k-cut. See world_model.md.
Encoder	Frozen hypercube reservoir. One window in, one episode, N floats out.
Predictor	LCN. This document's table is the k-cube map P(E(xₜ)) → E(xₜ₊₁). WorldModel now uses dim = k+1 and Pack is E(x) cat E(a); this test runs a constant dummy field of length 2ᵏ through the action encoder (no motor).
a	Action field, length N. Constant fill here; how to paint a cardinal is later.
E(a)	EncodeAction of that field: the whole output of a k-cube encoder. Extra bit-face of P.
Decoder	Reconstruction meter. k-face in, full field out. Not in the WorldModel loop.
dim	Encoder cube dimension. These runs: 8.
N	Window length and encoder vertices, N = 2ᵈⁱᵐ = 256.
k	Dimension of the kept face. Strictly less than dim. These runs: 7, 6, 5.
sub	Kept vertices, sub = 2ᵏ.
T	Encoder passes per episode. These runs: 16.
leak	Encoder leak rate. These runs: 0.25.
in_scale	Encoder input scaling. These runs: 0.8.
song	One two-sine draw: its own cycles, phases, amplitudes.
window	N consecutive samples of a song, laid on the cube.
hop	Samples between window starts. These runs: hop = N.
pair	Two consecutive windows of the same song. Never across songs.
mix	Train songs. These runs: 640 songs, 8 windows, 4480 pairs.
val	Unseen songs for restore-best only. These runs: 128 songs.
test	Held-out songs, not used to pick weights. These runs: 128 songs.
identity	MSE of using E(xₜ) as the guess for E(xₜ₊₁). Copy-last.
next-power	Mean square of E(xₜ₊₁). MSE of predicting nothing.
mse/ident	WorldModel pool MSE divided by identity.
mse/power	WorldModel pool MSE divided by next-power. Residual vs k-face energy.
field power	Mean square of the sine field. These CompressionTest runs: 0.47638.
dimensional compression	Fewer numbers: keep sub = 2ᵏ vertices out of N. Ratio N / sub. Proven by the cut.
semantic compression	The kept numbers are the ones that matter: structure stays, junk is dropped. At these encoder knobs: rel ≈ 0.40 on jepa_encoder_test.md.
rel	(noise/content) on the k-face divided by the same ratio on the field. Semantic score. These runs: ~0.40 at every k.

Look at test mse/power: you want it as low as you can get, with val mse/power about the same number.

The k-cut is dimensional compression: 256 numbers become 128, 64, or 32. That is true before any training. Semantic compression is the filter: the two-sine stays, white noise is damped more than on the raw samples. This document does not run that meter. The paired JepaEncoderTest at the same encoder does: rel ≈ 0.40 at k = 7, 6, and 5, and content RMSE stays large. Reconstruction and next-step here say the smaller face still carries the song and still has a next k-face. Together that is dimensional cut plus a live, filtered code.

The Encoder is frozen. WorldModelTest trains a Predictor on many two-sine songs and scores a held-out mix. CompressionTest, at the same encoder, trains a Decoder to put the field back from the k-face. Decoder is not in the WorldModel loop. Only k changes across the rows; Predictor depth is z_max = 3k. Span 5, tanh_last on, lr = 0.03. WorldModel 800 epochs, CompressionTest 1024 / 512 / 512 fields, 400 epochs.

k	sub	N / sub	test mse/power	val mse/power	test mse/ident	recon test MSE	recon / power	rel
7	128	2×	0.137	0.136	0.077	0.02141	4.5 %	0.397
6	64	4×	0.174	0.170	0.097	0.02453	5.1 %	0.403
5	32	8×	0.366	0.361	0.201	0.03651	7.7 %	0.409

At k = 7, held residual is ~14 % of next-face energy and val is the same number. Copy-last loses by about 13×. The Decoder puts the field back to 4.5 % of field power. Dimensionally, half the cube is gone. What remains still holds the sines and still predicts the next face on new songs.

k = 6 is the same story, a little looser: held mse/power 0.174, val 0.170, reconstruction 5.1 %. Four times fewer latent vertices, almost the same next-step and almost the same reconstruction.

k = 5 still beats silence and copy-last (mse/power 0.37, mse/ident 0.20), and val still matches test. Reconstruction is 7.7 % of field power. The next-step residual has grown more than the reconstruction residual: the cut is starting to hurt prediction first.

WorldModel detail:

k	train mse	train mse/power	val mse	test mse	identity (test)	next-power (test)
7	0.12275 → 0.00371	0.037	0.01273	0.01343	0.174	0.098
6	0.12748 → 0.00890	0.088	0.01631	0.01728	0.178	0.099
5	0.13725 → 0.02511	0.217	0.03909	0.04058	0.201	0.111

Train is tighter than held on every row. That gap is mix-fit, not a collapse: val and test stay together. Identity and next-power stay in the same ballpark (hop = N is still a real jump). k-faces stay live (mean |s| on a train window ~0.20–0.22; full-cube mean |z| = 0.213). Decoder input scale stays ~1.04, so the smaller face is not a gain trick.