JEPA predictor test

Status: tests/JepaPredictorTest.cpp implemented. No Release numbers yet.

Definitions

Symbol / term	Meaning
Encoder	Frozen hypercube reservoir. One window in, one episode, N floats out.
Predictor	LCN on the k-face: E(xₜ) in, predicted E(xₜ₊₁) out.
Decoder	Reconstruction meter. Not used.
dim	Encoder cube dimension. This test: 8.
N	Window length and encoder vertices, N = 2ᵈⁱᵐ = 256.
k	Dimension of the kept face. Strictly less than dim. This test: 7.
k-face	The low 2ᵏ vertices of the encoder's newest slice.
E(x)	That k-face for window x.
stream	One long two-sine. Frequencies, phases, and amplitudes are drawn once.
window	N consecutive samples of the stream, laid on the cube (vertex i = sample i).
hop	Samples between window starts. This test: hop = N, so windows do not overlap.
identity	MSE of using E(xₜ) itself as the guess for E(xₜ₊₁). Copy-last.
next-power	Mean square of E(xₜ₊₁). MSE of predicting nothing.
test MSE	Mean square of P(E(xₜ)) vs E(xₜ₊₁) on the held-out windows.
test / identity	test MSE divided by identity. The prediction score.
ok	Process exit: train MSE fell, and test MSE beat next-power.

The test cuts one two-sine stream into consecutive windows, encodes each from a fresh episode, and trains the Predictor on adjacent k-faces. Train, val, and test are later stretches of that same stream. The Decoder is not in the loop.

ok is not the readout. Beating next-power only says the guess is better than silence. A k-face with a standing mean can pass that without tracking the next window. The printed line to read is test / identity, then identity against next-power.

test / identity	Meaning
clearly below 1	The Predictor learned a phase advance. Copy-last loses.
about 1	The Predictor matched persistence. It did not beat copy-last.
above 1, and the process still printed ok	Worse than copy-last. It beat zero anyway.

Identity vs next-power is the sanity check on the hop. With hop = N the next window is a large phase jump (cycles in [0.7, 7.3] turns per window), so identity and next-power should sit in the same ballpark: consecutive k-faces are not near copies of each other. If identity is tiny against next-power, the faces barely move and the task has collapsed; beating identity would then be the wrong story.

This is one oscillator, split in time. A low test / identity means P can track this stream's k-faces. It does not mean a new pair of sines would follow. Training on many draws and scoring a held-out draw is world_model_test.md.