Information-budgeted replication and dictionary refinement

Attach an adaptive data-acquisition controller to a multi-view encoder, sparse autoencoder, or retrieval/router system. At each inference step, maintain a dictionary trained on N examples and collect views or augmentations sequentially. Estimate s_g for each coherent block, β_- from the current active coefficient magnitude, and σ_+ from residual variance or a robust median absolute deviation. Compute I_{S,g}(T)=Tβ_-²s_g²/σ_+² and I_{D,g}=Ns_g⁶. Pseudocode: initialize T=1; encode the current views and estimate block confidence; while required confidence is unmet, if I_{S,g}<τ_S request another independent view or augmentation and increment T, else if I_{D,g}<τ_D mark the block child-ambiguous and queue samples for dictionary retraining, else expose child predictions and stop. For offline training, prioritize new dictionary examples from blocks with the smallest N_gs_g⁶, and use multiple coefficient patterns and noise conditions so orientation is not learned from a degenerate latent distribution. The mathematical quantities are the two information scalings and minimax resolution expression; thresholds, view independence, and estimates of β_- and σ_+ must be validated empirically. First experiment on a synthetic two-atom collision with controlled s, Gaussian noise, and a fixed compute budget. Compare fixed-T and fixed-N baselines against the controller, measuring child-support accuracy, parent recall, number of views, and dictionary retraining cost. The predicted signal is that increasing T helps until I_S≈τ_S, after which only increasing N materially improves physical-ray accuracy, especially for small s where the s⁶ bottleneck is severe.