Regret-Balanced Adaptive Context

Add a dynamic lag gate around a causal convolution or recurrent input filter. Maintain a maximum buffer of H_max past inputs, but compute only the currently active prefix 1:h. Store coefficient estimates theta_hat[j], an envelope estimate r_hat[j], and an activation mask. At each update, use n[t,j] = max(t-j+1, 0). Estimate r_hat[j] conservatively from a fixed prior envelope, from an exponential or polynomial fit to recent absolute theta_hat[j], or from an upper-confidence value r_hat[j] = absolute(theta_hat[j]) + k/sqrt(c[j]+1), where c[j] is the number of observations involving lag j. Compute the displayed complexity price and tail bias estimate for each candidate h, choose the smallest h whose objective C_hat_t(h) is within a tolerance of the minimum, and activate a new lag only when its marginal estimated bias reduction exceeds lambda times its spectrum price. To avoid discontinuous network changes, newly activated coefficients start at zero and are warmed up for W steps; inactive coefficients can be periodically pruned if their score remains below threshold. The mathematical terms are the lag-specific logarithmic complexity and truncation scale; lambda, confidence multiplier k, and warmup W are empirical hyperparameters. First test on synthetic filters with exponential and polynomial decay using a fixed-H_max baseline and a learned fixed window. Record active context length, wall-clock time, memory traffic, cumulative log loss, and loss after abrupt changes in decay rate. The target signal is substantially fewer active lags and lower inference cost at matched log loss, with automatic expansion when long-memory coefficients become predictive.