Design and Behavior of Sparse Mixture-of-Experts Layers in CNN-based Semantic Segmentation

Mixture-of-Experts (MoE) networks promise favorable accuracy-compute trade-offs, yet practical vision deployments are hindered by expert collapse and limited end-to-end efficiency gains. We study when sparse top-$k$ routing with hard capacity constraints helps in vision classification, evaluated under multi-seed protocols on four benchmarks (CIFAR-10/100, Tiny-ImageNet, ImageNet-1K). We observe a compute-leverage pattern: positive accuracy gaps require a substantial fraction $ρ$ of total FLOPs to be routed; at ImageNet scale this is necessary but not sufficient, as multi-expert routing ($k \geq 2$) is additionally required. Two controlled experiments isolate these factors. A hidden-size sweep on CIFAR-10 yields both predicted sign reversals across standard and depthwise backbones, ruling out backbone family as the active variable. An ImageNet-1K ablation that varies only top-$k$ -- holding architecture, initialization, and $ρ$ fixed -- reverses the gap from positive to negative across all five seeds. A per-sample variant of Soft MoE that softmaxes over experts rather than the batch rescues CIFAR-100 above the dense baseline, identifying batch-axis dispatch as the dominant failure mode in per-sample CNN settings. Code and aggregate results: https://github.com/libophd/sparse-moe-vision-rho.

Sparse Mixture-of-Experts (MoE) architectures route each token through a subset of experts at each layer independently. We propose viewing MoE computation through the lens of expert paths -- the sequence of expert selections a token makes across all layers. This perspective reveals that, despite $N^L$ possible paths for $N$ experts across $L$ layers, tokens in practice cluster into a small fraction of paths that align with linguistic function, yet the vast majority of paths remain unexplored, representing a statistical inefficiency. This motivates architectures that constrain the effective path space to amplify this natural concentration. As one instantiation, we introduce \pathmoe{}, which shares router parameters across blocks of consecutive layers. Analysis confirms that \pathmoe{} amplifies the emergent path structure: it produces more concentrated path clusters, better cross-layer consistency, and greater robustness to routing perturbations. Experiments on 0.9B and 16B parameter \pathmoe{} models demonstrate consistent improvements on perplexity and downstream tasks over independent routing, while eliminating the need for auxiliary losses. These results establish expert paths as a useful design axis for MoE architectures, complementary to existing work on independent routing mechanisms.

Mixture-of-Experts (MoE) scales language models by routing each input through a small set of independently parameterized experts. We show that copying this design into convolutional networks fails for a structural reason: parallel convolutional experts that read the same input channels learn nearly identical filters. We therefore move the expert axis from operator duplication to channel selection. We introduce Mixture of Channel Experts (MoCE), a structured sparse channel-mixing layer, inspired by MoE, that replaces pointwise (1x1) channel-reduction projections. In MoCE, an expert is a single output channel with a learned sparse support of k << C input channels. The selected channels are combined by a softmax whose temperature is predicted per input, so each expert can move between mean-like and max-like aggregation. A residual expert summarizes the unselected channels, and a load-balancing loss keeps channel coverage complete. MoCE replaces a dense projection whose cost is quadratic in C with a mechanism whose relative cost scales as k/C, and the predicted savings hold in measured wall-clock time. Across ResNet backbones on ImageNet-1K and CIFAR-100, transfer learning, EfficientViT, and a strong modern training recipe, MoCE matches or exceeds dense baselines and prior channel-selection methods while reducing MACs by 16.7% and end-to-end latency.