ResNeXt

ResNeXt augments the ResNet bottleneck with a third axis of network design that the authors term cardinality: the number of parallel transformation branches inside each block. Where ResNet improves accuracy by making the network deeper and Wide ResNet improves it by making each layer wider, ResNeXt improves it by making each block more parallel.

A ResNeXt block of cardinality $C$ computes

where each $\mathcal{T}_i$ is a low-dimensional bottleneck ($1\times1 \to 3\times3 \to 1\times1$ with a small inner width $d$). The set of transformations are aggregated by summation and then added to the residual shortcut, exactly as in ResNet. By construction this aggregation is equivalent to a single bottleneck whose $3\times3$ convolution is grouped into $C$ groups of $d$ channels each — so ResNeXt can be implemented as a one-line change to ResNet (replace groups=1 with groups=C) without any custom block code.

The empirical claim of the paper is that, holding the parameter and FLOP budget fixed, increasing cardinality is more effective than increasing depth or width. ResNeXt-50 (32×4d: $C=32$, $d=4$) outperforms ResNet-50 by roughly one percentage point on ImageNet top-1 with the same compute budget, and ResNeXt-101 (64×4d) reaches 20.4% top-1 error. The "split- transform-merge" pattern that ResNeXt makes explicit — independent parallel paths combined by aggregation — also turns out to be the structural backbone of every subsequent grouped-convolution architecture, from ShuffleNet to MobileNetV2's expand-project blocks.