Dynamic-Capacity MoE: Adaptive Neural Networks

• Dynamic-Capacity MoE is an architecture that dynamically assigns expert modules per input using adaptive, input-conditioned gating mechanisms.
• It employs techniques such as embedding-based routing, token importance metrics, and hierarchical structures to optimize computational efficiency and model accuracy.
• Empirical results demonstrate that this approach improves performance in tasks like image classification, machine translation, and speech recognition while managing resource constraints.

A Dynamic-Capacity Mixture-of-Experts (MoE) system is an advanced neural network architecture in which model capacity—measured as the number of active experts, activated channels, or computed parameters—can be dynamically allocated per input, token, or regime, enabling adaptivity to varying complexity and computational constraints. This adaptive sparsity framework has led to significant representational, efficiency, and deployment benefits across computer vision, natural language processing, speech, and wireless communication tasks.

1. Core Principles of Dynamic-Capacity MoE

Dynamic-capacity in MoE architectures refers to mechanisms where the selection, activation, or scaling of experts is determined on a per-sample or per-token basis, informed by input content, token importance, routing confidence, or contextual statistics. Traditional MoE systems used fixed-K routing (e.g., Top-1 or Top-2), leading to rigid expert utilization regardless of data complexity. Dynamic-capacity MoEs generalize this by:

• Allowing variable numbers of experts to be activated for different tokens or samples, proportional to calculated difficulty or importance (e.g., (Huang et al., 12 Mar 2024, Aghdam et al., 10 Sep 2024)).
• Assigning dynamic, input-conditioned routing weights to experts, often with explicit sparsity constraints enforced during training (Wang et al., 2018, You et al., 2021, Gao et al., 25 Jan 2025).
• Supporting specialized architectures (stratified/hierarchical gating, hypernetwork-based expert generation, or periodic adaptation of active expert pools), providing granular control over model capacity per input and context (Xu et al., 2023, Zhao et al., 20 Feb 2024, Jing et al., 28 May 2025).

A generic dynamic routing paradigm computes a vector of gating weights $g(x)$ per input (or token) $x$, which parameterizes the contribution of each expert:

$y = \sum_{i=1}^N g_i(x) \cdot E_i(x)$

where $E_i(x)$ is the output of expert $i$. $g(x)$ may be sparse and input-dependent, and the number and type of experts activated are dynamically determined.

2. Architectural Realizations and Algorithms

Several mechanisms have been explored for enabling dynamic capacity within the MoE framework:

a) Embedding- and Context-Based Gating

In DeepMoE (Wang et al., 2018), a shallow embedding network first computes a latent semantic vector $e$ for each input. For each convolutional layer $l$, a layer-specific gating vector is given by:

$G^l(e) = \text{ReLU}(W_g^l \cdot e)$

with $W_g^l$ learned, and ReLU and L1 regularization promoting sparsity so that only a subset of channels/experts in each layer is activated per input.

b) Token-Wise and Task-Based Dynamic Routing

In language and vision transformers, dynamic gating functions depend on token representations and attention properties. For example, "Harder Tasks Need More Experts" (Huang et al., 12 Mar 2024) computes a softmax over experts and accumulates them by decreasing gating confidence until a threshold $p$ is surpassed, resulting in a per-token dynamic-K routing:

$P = \text{Softmax}(W_r x^\top)$

Experts are sorted by $P_i$, and selected until $\sum_{j=1}^t P_{I_j} \geq p$.

DA-MoE (Aghdam et al., 10 Sep 2024) leverages the Transformer attention weights to define token importance:

$$\text{token\_importance}_k = \frac{1}{H} \sum_{j=1}^{H} \max_d A(i, j, k, d)$$

The number of experts for each token is then proportional to its calculated importance, allowing adaptivity across sequence positions.

c) Adaptive Gating and Pool Management

DynMoE (Guo et al., 23 May 2024) introduces a "top-any" gating scheme, where binary gating per expert is computed as:

$g(x) = \text{sign}(\sigma (s(x)) - \sigma (G))$

with $s(x)$ the cosine similarities between tokens and expert prototypes and $G$ a vector of trainable thresholds. Experts are added or pruned during training, based on utilization statistics, further tuning the expert pool to the demands of the data distribution.

d) Hierarchical/Stratified Structures

SMoE (Xu et al., 2023) partitions experts across multiple strata. Tokens are routed through different quantities of experts over multiple stages, where "easier" tokens exit early (after few experts) and "harder" tokens receive increased capacity, leading to efficient parameter utilization.

e) Knowledge Transfer and Specialization

HyperMoE (Zhao et al., 20 Feb 2024) extends dynamic capacity by transferring knowledge from unselected experts using hypernetworks, essentially "blending" latent expert information to enrich the prediction without diminishing selection sparsity.

CoMoE (Feng et al., 23 May 2025) and MoDE (Xie et al., 31 Jan 2024) introduce auxiliary objectives (contrastive learning and mutual distillation) to increase the specialization and effective capacity of active experts, allowing more nuanced and robust dynamic capacity assignments.

f) Capacity-Constrained Routing and Inference Adaptation

Capacity-aware techniques (He et al., 7 Mar 2025) enforce runtime capacity constraints during inference by dropping or rerouting tokens to prevent expert overload (the "Straggler Effect"), while others (Huang et al., 13 Oct 2025, Imani et al., 19 Jul 2024) combine expert quantization and on-the-fly dynamic gating for fine-grained, resource-aware capacity control.

3. Training Objectives and Regularization

Dynamic-capacity MoE models often use explicit regularizers to control sparsity, load balancing, and expert utilization:

• L1 gating regularization (e.g., $L_g = \sum_l \|G^l(M(x))\|_1$ in DeepMoE) penalizes wide expert activation, encouraging per-sample compactness (Wang et al., 2018).
• Entropy-based penalties on routing distributions temper "cheating" by excessive activation (Huang et al., 12 Mar 2024).
• Balanced utilization regularizers (mean importance, load balancing, auxiliary-loss-free mechanisms) ensure no expert is starved, stabilizing convergence (You et al., 2021, Li et al., 19 Sep 2025).
• Auxiliary loss for contrastive or distillation objectives, maximizing specialization while promoting knowledge sharing across experts, is critical for robust generalization (Xie et al., 31 Jan 2024, Feng et al., 23 May 2025).

4. Empirical Results and Performance Metrics

Dynamic-capacity MoE models have demonstrated superior accuracy and efficiency across modalities and tasks:

• DeepMoE (Wang et al., 2018) achieves 1–4% accuracy improvements over comparable dense baselines across ImageNet and CIFAR benchmarks, with lower FLOPs and improved segmentation mIoU.
• SpeechMoE (You et al., 2021) realizes 7–23% relative CER reductions in ASR while scaling expert capacity without increased computation.
• Stratified SMoE (Xu et al., 2023) outperforms vanilla MoE and Switch Transformer by 0.74–1 BLEU points in machine translation, with fewer parameters.
• DA-MoE’s adaptive expert allocation yields substantial GLUE benchmark improvements (up to 8.6% on some tasks), robustness in both pre-training and fine-tuning settings (Aghdam et al., 10 Sep 2024).
• Capacity-aware inference schemes achieve up to 1.94$\times$ inference speedup with minimal accuracy loss (<0.2–0.9% degradation), by balancing expert workloads and suppressing overload (He et al., 7 Mar 2025).

A selection of characteristic results is summarized:

Model	Task/Benchmark	Dynamic Capacity Mechanism	Metric	Improvement
DeepMoE	ImageNet, CIFAR	Channel-wise dynamic gating	Top-1 error, FLOPs	–1% error (ImageNet), +3–4% acc
SMoE	MT (M4, M15, OPUS100)	Stratified multi-strata, var k	BLEU, Params	+0.75–1 BLEU, halved params
DA-MoE	GLUE	Attention-informed var K/token	Accuracy, F1	+8.6% (max), 7/8 tasks outperformed
DynMoE	Vision, Lang, VL	Top-any gating, expert pop mgmt	Throughput, Acc, FLOPs	15% fewer params, no perf. loss
MC#	DeepSeek-VL2	Integer-program quant., OTP prune	Size, Acc, throughput	6.2× smaller; –1.7% acc; 20% fewer experts

5. Implementation and System-Level Considerations

Efficient deployment of dynamic-capacity MoE models requires architectural and framework support for:

• Asynchronous computation graph adjustment and sample assignment caching (DynaMoE, (Kossmann et al., 2022)); decoupling expert assignment and expert computation for improved throughput.
• Adaptive expert quantization and resource scheduling for runtime memory and throughput control (Imani et al., 19 Jul 2024, Huang et al., 13 Oct 2025).
• Task- and prompt-aware expert load prediction and selective loading (eMoE, (Tairin et al., 10 Mar 2025)).

In practice:

• Hardware-aware strategies (e.g., partial offloading to CPU, mixed-precision experts, rerouting on overflow) are essential for scaling dynamic MoEs to resource-constrained or latency-sensitive environments.
• Layer-wise and expert-population adaptation provide further fine-tuning, with dynamic capacity varying not only by token but also by network stage.
• Specialized frameworks facilitate dynamic recompilations and metric-based graph modifications, accommodating the mutable expert workload distribution (Kossmann et al., 2022).

6. Theoretical and Practical Implications

Theoretical analyses provide strong justifications for dynamic-capacity MoE:

• MoE architectures separate latent cluster structures, reducing effective information exponent and enabling sample/rate-optimal learning in heterogeneous or multimodal settings (Kawata et al., 2 Jun 2025).
• Adaptive capacity modulation mitigates interference (e.g., catastrophic forgetting in multi-domain adaptation, (Li et al., 21 Sep 2025)) and is essential for accurate generalization in dynamic-system tasks (Nzoyem et al., 7 Feb 2025).
• Aggressive model compression is attainable with optimized static and dynamic capacity mechanisms, permitting large-scale MoE deployment on non-datacenter hardware (Huang et al., 13 Oct 2025, Imani et al., 19 Jul 2024).

Dynamic capacity also fosters new research avenues in parameter-efficient learning, hierarchical meta-learning (Nzoyem et al., 7 Feb 2025), scalable multi-domain adaptation (Li et al., 21 Sep 2025), and edge-cloud resource orchestration.

7. Future Directions

Several open directions are evident:

• Advanced token- and task-conditioned gating, possibly incorporating richer semantic, contextual, or multi-modal cues.
• Further exploration of hierarchical, stratified, or hypernetwork-driven capacity allocation to maximize model expressiveness and efficiency.
• Framework-level support for elastic, low-latency MoE execution, including robust capacity-aware training and runtime scheduling.
• Deeper integration of continuous knowledge transfer and domain isolation techniques to maximize adaptivity and resist catastrophic forgetting in ever-changing task landscapes.

Dynamic-capacity Mixture-of-Experts architectures thus represent a flexible, domain-spanning paradigm for scaling neural network capacity, offering both theoretical soundness and practical deployment efficiency in complex, real-world scenarios.