Information-Gated Attention

1. Integration point: add an information gate before a transformer encoder, active camera-view module, retrieval system, or sensor-fusion block. Maintain a diagonal or low-rank covariance over latent variables relevant to the downstream prediction. For each candidate token or view a, predict H(a) and R(a) from its metadata, pose, image geometry, or a learned observation head. 2. Pseudocode: encode the current context into mean and covariance; for each candidate compute H(a), R(a), and the posterior covariance using a Cholesky solve rather than explicit matrix inversion; compute g(a); subtract acquisition cost; form q(a) with softmax; and pass either the top-K candidates or weighted tokens to the main network. Train with task loss, acquisition-budget penalty, and optional information-gain reward. Begin with soft gating and introduce straight-through top-K selection only after convergence. 3. Taken from the paper: covariance update and log-determinant information objective. Estimated empirically: covariance calibration, candidate Jacobians, and noise matrices. Initialize R(a) from validation residual variance and recalibrate using temperature scaling. 4. First cheap experiment: train a small vision transformer on a synthetic multi-view object-identification dataset where each view has known pose-dependent noise, with a fixed budget of K views. Compare random selection, ordinary task attention, and information-gated selection. Sweep temperature tau and K. The prediction is that cumulative measured log-determinant reduction will match the sum of predicted gains within 20 percent when linearization is valid. Accuracy should show a knee when the number of selected views makes terminal log determinant of covariance cross a fixed threshold. If predicted gains do not correlate with held-out posterior error, the covariance model has failed.