Data-Identified Neural Dependency Graph

1. Integration point: use a recurrent neural network, SSM, graph neural network, or MoE with K hidden blocks of equal width. First train or initialize a small dense model and collect trajectories containing z_t, z_(t+1), and u_t. Identify dependencies at block level rather than scalar-weight level because block-level coefficients are more statistically reliable. 2. Pseudocode: fit a ridge or LASSO regression z_(t+1) approximately equals A z_t + B u_t on the collected trajectories; bootstrap trajectory subsets or use held-out folds; estimate each coupling A_hat[i,j] and standard error s[i,j]; set D[i,j] = 1 when abs(A_hat[i,j]) > c times s[i,j], or retain the top q edges per target block; replace every dense block W[i,j] by D[i,j] times W[i,j]; fine-tune surviving weights using the task loss and a small transition-prediction loss. 3. Computed from the paper mechanism: the directed adjacency or DSM and conversion between weighted and binary dependencies. Estimated empirically: A, uncertainty thresholds, sparsity, and nonlinear fine-tuning effects. 4. First experiment: train an 8-block GRU or linear SSM on Lorenz-63, a five-node coupled-oscillator system, or a synthetic sparse linear dynamical system with known graph. Compare dense, random-mask, magnitude-pruned, and identified-mask models at equal parameter budgets. Sweep c or tau, measure graph precision and recall, one-step error, 50-step rollout error, and wall-clock time. Prediction: false-positive edges should increase sharply when the threshold drops below the coefficient noise floor; at the bootstrap threshold, at least 80 percent of true block edges should be recovered, while retaining 20 to 40 percent of dense edges should keep one-step error within 10 percent and reduce interaction cost approximately by the retained edge fraction.