Null-normalized temporal prediction score

Integrate this at the validation and model-selection layer of a temporal neural network, such as a Transformer, SSM, TCN, or world model that predicts a continuous future signal. Do not alter the forward pass initially. For each held-out sequence, compute the prediction-target Pearson correlation r_obs over a fixed window of w_base seconds, and cache the resulting Fisher-transformed score. Build the null using n=1000 cheap circular shifts: for each shift k, choose k larger than the maximum estimated autocorrelation length of either target or prediction, compute r_null[k] between the target and shifted prediction, and verify that abs(mean(r_null)) is small. Use this pseudocode: inputs=(y,pred,w_base,w_target,fs); r_obs=corr(y,pred); for k in valid_shifts: r_null[k]=corr(y,roll(pred,k)); z_null=atanh(clip(r_null,-1+eps,1-eps)); sigma2=mean(z_null**2); N_base=round(w_base*fs); N_target=round(w_target*fs); sigma_target=sqrt(sigma2*V(N_target)/V(N_base)); score=atanh(r_obs)/sigma_target. Aggregate scores over examples using the median or mean, and use score rather than raw correlation for early stopping and checkpoint selection. The paper supplies the Fisher transform, zero-mean null assumption, empirical variance, and V(N) rescaling; estimate autocorrelation lengths, valid shifts, and any dependence correction empirically. The first experiment should use a small GRU or 2-layer temporal Transformer on Speech Commands or LibriSpeech acoustic-feature prediction, comparing raw-correlation selection against NNTS selection with only 1000 shifts and several window lengths. Success means better held-out correlation on difficult features at equal parameter count, more stable ranking across window lengths, and fewer cases where a low-information target wins solely by having a high raw correlation.