Resolution-Gated Dual Masking

1. Integration point: use this as a front-end selector for a tabular MLP, an RNN/SSM input window, or a transformer whose candidate tokens are variable-lag pairs. During each selection refresh, discretize each continuous feature using fixed quantile bins, and discretize the target or residual target into $q_Y$ bins solely for structure discovery; the neural predictor still receives the original continuous values. 2. Pseudocode: construct candidate mask $M$; compute plug-in counts for $\widehat H(Y|M)$ and $\widehat H(Y|M,j)$; compute $S_H(j)$; generate $B$ bootstrap resamples and estimate $\gamma$; train or briefly evaluate the network for each candidate addition to estimate $S_R(j)$; calculate $\kappa$; choose $M_H$ if $\kappa<\kappa_c$ and $\gamma>\gamma_c$, else choose $M_R$; train the final network on the chosen mask. A safer variant concatenates both masks and learns a gate $g=\sigma(a(\kappa_c-\kappa))$, using $g f_{M_H}+(1-g)f_{M_R}$. 3. Computed versus estimated: alphabet sizes, entropy formulas, and the mask rule are computed exactly from counts; $\kappa_c$, $\gamma_c$, and prediction risk are estimated on held-out data. Start with $\kappa_c=1$ and $\gamma_c=2$, then sweep them. 4. First cheap experiment: use a synthetic two-state Markov system with one true binary lag, several distractor lags, and controllable flip noise $Y_t=X_{t-1}\oplus N_t$, where $N_t\sim\operatorname{Bernoulli}(p)$. Compare entropy-only, MSE-only, and gated selection with a small MLP. Sweep bin resolution and $p$ over 0 to 0.5, using sequence lengths 256, 1024, and 4096. The predicted signature is a crossover near the point where conditional noise entropy approaches the output discretization entropy: entropy-mask recovery should fall sharply there and should not recover merely by increasing $n$ at fixed excessive noise. Below the crossover, the entropy mask should match the true lag more often; above it, MSE should have lower test risk. Measure whether the entropy-mask regret $\Delta_R$ increases with the number of distractor combinations and decreases with sample size.