coordinates, not states

How many dimensions the forecastable structure needs, whether the dominant axes hold still across an hour, and what the population’s movie-locked path looks like when eight mice are put in one frame.

dimension against skill

PCA + VAR refit at each latent dimension, mean over sessions. Forecast skill can peak at a lower dimension than reconstruction, because extra dimensions can carry variance that is not predictable from the past.

Table view

Dimension	Forecast R²	Variance captured, train	Variance captured, test
2	0.042	0.099	−0.034
4	0.058	0.142	0.002
8	0.074	0.202	0.052
16	0.091	0.294	0.134
32	0.103	0.443	0.318

the same axes, an hour later

Share of population variance captured by the principal axes fitted on the training period, measured on the training period and on the test period. A gap means the dominant directions moved.

eight paths through one movie

Mean population state at each half-second of the 30 s clip, in the first two dimensions of a Procrustes-aligned PCA space. Black: early block (training period). Blue: late block (test period). Alignment used training-period responses only.

A projection for looking, not a finding. Loops, distances and apparent clusters here are not evidence of discrete brain states or of any mechanism.

715093703
719161530
721123822
732592105
737581020
739448407
744228101
754312389

stability and time constants

Principal angles compare the dominant 8-dimensional subspace early and late in each session; the split-half row is the same comparison within the training period alone, the noise floor. Eigenvalues of a latent VAR(1) do not depend on the basis, so the slowest decay constant can be compared across mice without alignment.

Per session
Session	Mean cos angle, split half	Mean cos angle, early vs late	Relative capture	Slowest τ (s)
715093703	0.646	0.623	0.355	0.27
719161530	0.668	0.612	0.627	0.30
721123822	0.636	0.657	0.771	0.27
739448407	0.754	0.487	0.303	0.16
732592105	0.721	0.741	0.836	0.34
737581020	0.596	0.376	0.459	0.20
744228101	0.664	0.271	0.121	0.21
754312389	0.755	0.718	0.549	0.27