long-horizon stability

Teacher forcing hands the model the true past before every step; a free rollout feeds it only its own predictions. They agree at one step by construction. How far apart they drift is the real forecasting test.

free rollout

Trivial baseline
Classical
Neural

Mean over sessions (seed 0). Horizon in 50 ms bins, log scale. Below zero, the forecast is worse than predicting each unit’s average rate. Hover or focus the chart and use the arrow keys to read values.

teacher forced

Trivial baseline
Classical
Neural

The same windows with the true history supplied at every step: an h-step curve here is h independent one-step forecasts.

how rollouts fail

Rank agreement between the one-step and the 50-step orderings (Spearman): 0.26. The lowest free-rollout R² at any horizon flags divergence: below −1 the forecast is more than twice as wrong as predicting the mean. The temporal-SD ratio compares how much the forecast moves with how much the recorded counts move; a rate forecast should sit below 1, and near 0 means it has flattened out.

Per-model rollout summary
Model	R² at 50 ms	R² at 2.5 s (free)	Teacher-forced − free	First horizon ≤ mean rate	Lowest free R²	Temporal SD, forecast / recorded
AR (per unit)	0.185	+0.032	+0.157	never	+0.032	0.09
Smoothed persistence	0.157	−0.053	+0.214	1.0 s	−0.053	0.01
GRU	0.144	−0.148	+0.298	0.55 s	−0.148	0.19
VAR (ridge)	0.139	+0.012	+0.133	never	+0.012	0.11
Transformer	0.137	−0.110	+0.253	0.35 s	−0.111	0.19
TCN	0.128	−0.542	+0.676	0.75 s	−1.451	0.45
LSTM	0.123	−0.099	+0.226	0.55 s	−0.099	0.19
RNN	0.122	−0.149	+0.277	0.40 s	−0.149	0.18
PCA + VAR	0.100	+0.023	+0.080	never	+0.023	0.09
LDS (Kalman)	0.084	+0.005	+0.082	never	+0.005	0.08
Mean rate	0.000	+0.000	0.000	never	+0.000	0.00
Persistence	−0.501	−0.786	+0.307	0.05 s	−0.808	0.00