Two-Scale Resolution-Gated Multiscale Encoder

Integrate this into the input stem of a CNN or ViT for regularly sampled images, videos, or spatial fields. Create three candidate branches with patch or stride spacings s in {1, 2, 4} pixels, anti-aliased downsampling, and depthwise convolutions whose effective receptive-field scales r are known. For each training batch, estimate a target scale on a geometric grid L using Gaussian low-pass filters. Compute A_hat(ell)^2 as the mean squared high-pass residual x - LowPass_ell(x). Estimate sigma_hat^2 from sensor metadata, repeated augmentations, or the variance of a small teacher-model residual. Then compute I_hat_ell = A_hat(ell)^2 N ell^d /(sigma_hat^2 + epsilon). Define admissible branches B = {b: s_b <= c_ell ell_hat and I_hat_ell >= tau}; if B is empty, use the coarsest anti-aliased branch. Otherwise, run only B during inference or softly mix B during training with weights proportional to softmax(log(I_hat_ell)). Parameterize each local convolution or local-attention radius so r >= c_r s, and add lambda max(0, c_r s - r)^2 as an optional penalty. The formulas determine the gates; c_ell, c_r, tau, and lambda are validation hyperparameters. Start on CIFAR-100 or WeatherBench with a small ViT, comparing fixed 4x4 patches and a standard CNN under equal FLOPs. Measure accuracy, loss at equal compute, token count, and robustness under noise and downsampling. Success means better accuracy at equal FLOPs, fewer fine-resolution tokens on smooth examples, and less degradation when target structure approaches the sampling limit.