Gated-SwinRMT: Unifying Swin Windowed Attention with Retentive Manhattan Decay via Input-Dependent Gating

We introduce Gated-SwinRMT, a family of hybrid vision transformers that combine the shifted-window attention of the Swin Transformer with the Manhattan-distance spatial decay of Retentive Networks (RMT), augmented by input-dependent gating. Self-attention is decomposed into consecutive width-wise and height-wise retention passes within each shifted window, where per-head exponential decay masks provide a two-dimensional locality prior without learned positional biases. Two variants are proposed. \textbf{Gated-SwinRMT-SWAT} substitutes softmax with sigmoid activation, implements balanced ALiBi slopes with multiplicative post-activation spatial decay, and gates the value projection via SwiGLU; the Normalized output implicitly suppresses uninformative attention scores. \textbf{Gated-SwinRMT-Retention} retains softmax-normalized retention with an additive log-space decay bias and incorporates an explicit G1 sigmoid gate -- projected from the block input and applied after local context enhancement (LCE) but prior to the output projection~$W_O$ -- to alleviate the low-rank $W_V \!\cdot\! W_O$ bottleneck and enable input-dependent suppression of attended outputs. We assess both variants on Mini-ImageNet ($224{\times}224$, 100 classes) and CIFAR-10 ($32{\times}32$, 10 classes) under identical training protocols, utilizing a single GPU due to resource limitations. At ${\approx}77$--$79$\,M parameters, Gated-SwinRMT-SWAT achieves $80.22\%$ and Gated-SwinRMT-Retention $78.20\%$ top-1 test accuracy on Mini-ImageNet, compared with $73.74\%$ for the RMT baseline. On CIFAR-10 -- where small feature maps cause the adaptive windowing mechanism to collapse attention to global scope -- the accuracy advantage compresses from $+6.48$\,pp to $+0.56$\,pp.