Dual-certified channel screening

(1) Integration point: apply this to a single linear, convolutional, or MLP layer during compression or initialization. Collect calibration activations B from a few minibatches, choose a teacher target y equal to the original layer output, and solve the convex surrogate min_x 0.5||Bx-y||²+τ||x||² with at most κ retained channels. For a convolution, flatten batch and spatial positions into rows and treat input channels or channel groups as columns. (2) Pseudocode: initialize a feasible dense or top-magnitude support and obtain its objective value U; solve or approximately solve the ridge surrogate to obtain x; set u=Bx-y or use the dual residual from a primal-dual solver; compute each score a_i=(B_iᵀu)²/(4τ); sort scores once to evaluate Tκ and Tκ−1; for every channel compute L_i^(1) and L_i^(0); delete channel i when L_i^(1)>U+ε, force it retained when L_i^(0)>U+ε, and re-solve on the remaining undecided channels. Repeat until no screening occurs. (3) The perspective relaxation, Fenchel conjugate, scores, and conditional bounds come from the mathematical construction; B, y, U, u, and τ are selected or estimated in the implementation. Use multiple calibration batches to reduce sensitivity to the chosen target. Because the network is nonconvex, describe the result as safe only for the fixed-layer convex surrogate and validate end-to-end accuracy afterward. (4) First experiment: use CIFAR-10 ResNet-20 or a two-layer MLP, prune one layer to 25%, 50%, and 75% channel budgets, and compare dual-certified screening against magnitude pruning and group-lasso pruning at equal final parameter count. Measure channels certified before optimization, sparse-solver wall-clock time, reconstruction MSE, downstream accuracy after brief fine-tuning, and inference FLOPs. The desired signal is fewer variables entering the solver and lower reconstruction error than magnitude pruning at the same budget, with no accuracy loss after fine-tuning.