Predictive Zonotope Compression for Certified Neural Inference

Integrate the method into a certified-inference engine at every compression boundary after an affine layer, attention projection, or nonlinear relaxation. Represent each batch element by a center vector c and generator matrix G with shape d by k. For an affine layer, update c <- W c + b and G <- W G. For ReLU, use the existing sound interval or linear relaxation and append its uncertainty generators. When k exceeds a budget K, define three reducers: retain the K columns with largest Euclidean norm; retain columns with largest L1 norm and merge the rest into one box generator q with q_i = sum_j |g_{j,i}|; and greedily merge generator pairs that cause the smallest increase in squared hull error. With horizon H equal to 2 or 3, clone the current zonotope for every candidate action sequence, apply each reducer, propagate through the next H cached layers, and evaluate the paper's hull error against a no-reduction reference rollout. Add lambda times estimated reduction FLOPs or resulting generator count to the objective. Execute only the first selected reducer, then repeat at the next boundary. Cache layer matrices and use a beam of the best B partial sequences if exhaustive branching is expensive. First test a three-layer ReLU MLP on MNIST or CIFAR-10 with an L-infinity input perturbation radius, comparing fixed top-norm reduction, fixed box reduction, and predictive selection at equal K and equal wall-clock budget. Measure certified accuracy, output-bound width, generator count, and propagation latency. Success means at least 10 percent narrower certified bounds or higher certified accuracy at equal latency, or equal certification with 1.5 times fewer generator operations.