Extreme-Subset Adversarial Dropout

1. Integration point: apply this to a feature tensor h\in\mathbb R^{B imes N imes m} immediately before a linear readout or reconstruction head, where N feature channels or measurements can be dropped. During training, replace ordinary dropout masks by masks generated from a hard-subset sampler. 2. Pseudocode: maintain a pool of K candidate subsets T of size m; for each candidate compute s(T)=sigma_min(W_T), where W is the next linear map or a periodically refreshed local Jacobian estimate; sample the next mask with probability p(T) proportional to exp(-s(T)/tau), or choose the lowest-scoring candidate; run the network on P_T h; backpropagate task loss plus optional alpha/s(T) penalty; every Q steps propose new subsets by swapping one included row with one excluded row and retain swaps that reduce s(T). Anneal tau from a broad value to a small value, moving from random dropout toward pathological masks. 3. The exact mathematical quantity is the combinatorial minimum and its Gaussian exponent. The sampler estimates it from a finite candidate pool; for large layers compute sigma_min with 3-8 Lanczos iterations on W_T^ op W_T. Use the theorem's c_gamma curve to choose target difficulty or compare against a Gaussian baseline. 4. First cheap experiment: use a small CIFAR-10 MLP or ViT patch-projection with N=64 channels and m=32. Compare standard dropout, random fixed masks, and extreme-subset adversarial dropout with equal numbers of masked examples. Evaluate clean accuracy, accuracy under the worst 1% of 10,000 sampled masks, loss spikes, and recovery after deleting channels. Success is lower worst-mask loss and smoother gradients with only a small clean-accuracy decrease.