Linear-MoE Systems: Scalable Neural Networks

• Linear-MoE systems are neural architectures that combine linear sequence modeling with Mixture-of-Experts layers to enable scalable, long-context processing.
• They employ sparse expert routing and advanced parallelization techniques like sequence parallelism and ZeRO optimization to reduce memory and computation costs.
• These systems achieve competitive accuracy and robust interpretability while supporting efficient deployment on both high-end clusters and resource-constrained edge devices.

A Linear-MoE system is a class of neural network architectures and associated system frameworks that integrate linear sequence modeling (LSM) modules—such as linear attention, state-space models, or linear recurrent units—with Mixture-of-Experts (MoE) layers, where expert routing is typically (but not necessarily) governed by linear routers. This design achieves parameter- and computation-efficient modeling for tasks requiring long-context or high-capacity architectures, and enables scalable deployment through algorithmic and system-level innovations.

1. Architectural Foundation: Unifying Linear Sequence Modeling and Sparse Experts

Linear-MoE systems are characterized by a compositional architecture where, instead of the standard Transformer block with quadratic-cost self-attention, the core sequence module implements an LSM technique—examples include blockwise linear attention, modern continuous state-space models (SSMs), retention modules, gated linear units, and recurrent variants (e.g., HGRN2, RWKV). These are inserted as plug-and-play modules within a single unified recurrence-based framework, parameterized as: $O = \varphi(Q) \left(\varphi(K)^{T} V\right)$ where $Q$, $K$, and $V$ are linear projections of the input $X$, and $\varphi$ is an elementwise nonlinear transformation (Sun et al., 7 Mar 2025).

Integrated within or after these sequence modules are MoE layers. An MoE layer consists of $n$ experts $E_1, ..., E_n$, each usually (but not necessarily) implemented as a feed-forward block or a specialized linear module. Sparse activation is achieved by a gating function $G$, typically a linear router: $p(e | x) = \mathrm{softmax}(W x + b)$ where $x$ is the input token state, $W$ projects onto expert logits, and $b$ is a bias vector (Harvey et al., 19 Jun 2025). For each token, only $k \ll n$ experts are selected (top-$k$), yielding the MoE output: $y = \sum_{i = 1}^k G(x)_{e_i} E_{e_i}(x)$ This sparse, linear interplay between token and experts yields sublinear compute scaling in parameter count, and—due to the linear-complexity sequence backbone—sublinear complexity in sequence length.

Hybrid architectures (“LLLNLLLN...”) further interleave Linear-MoE and standard Transformer-MoE layers, leveraging the efficiency of LSM and the in-context learning benefits of softmax attention (Sun et al., 7 Mar 2025).

2. System and Parallelization Techniques

Linear-MoE systems employ a suite of advanced system-level parallelization strategies to make trillions of parameters tractable on modern hardware:

• Multi-dimensional Parallelism: Data, tensor, pipeline, and expert parallelism are combined. Notably, Linear-MoE leverages “Sequence Parallelism” (SP), which exploits the associativity of linear operators to distribute sequence computation across devices in both forward and backward passes while keeping memory and compute requirements linear in the sequence length (Kim et al., 2021, Sun et al., 7 Mar 2025).
• Zero Redundancy Optimizer (ZeRO): Partitioning of optimizer states, parameters, and gradients across devices allows much larger models to be trained efficiently, an approach realized in the DeepSpeed library and extended for MoE architectures (Kim et al., 2021).
• Sequence Parallelism and “Right-Product Kernel Trick”: SP enables streams of Q/K/V computations using partitioned weight matrices, with recombination via all-gather and reduce-scatter operations. This substantially relaxes the memory bottleneck for long-context sequences in LSM-based MoE blocks (Sun et al., 7 Mar 2025).
• Expert Parallelism: Expert parameters are sharded across GPUs, so that no device needs to store all experts. Only the selected experts for a given token are activated, further reducing compute and memory costs.
• Offload/Hybrid Memory Systems: For inference, Linear-MoE deployments on memory-constrained hardware use mixed CPU–GPU strategies, weight paging, and runtime expert prediction/prefetching to avoid loading all parameters into GPU memory (Cao et al., 18 Nov 2024, Yuan et al., 12 Apr 2025, Tairin et al., 10 Mar 2025).

3. Routing Strategies and Variants

The routing function critically determines both computational path selection and expert load balance. Empirical comparisons highlight the following:

• Linear Routers: Offer fast, parameter-efficient inference but are less expressive. Inference latency can be as low as 0.07 ms per token (6,144 parameters), at the expense of moderate “routing entropy” (≈1.95) and less specialized token–expert assignments (Harvey et al., 19 Jun 2025).
• MLP, Attention, and Hybrid Routers: Adding depth or attention mechanisms increases the expressiveness and sharpens expert selectivity, but at increased computational cost.
• Graph-based Routers (GNN): Recent advances use graph neural networks to facilitate expert collaboration, with Poisson and Normal-distribution regularization for routing outputs to balance specialization and load (see GMoE) (Bai et al., 18 Dec 2024).
• Activation/Basis Decomposition: To compress routers and expert parameters, shared basis decompositions (e.g., $W^i = A^i f(\sum_j \alpha^{(i,j)} B^j)$) are used, significantly reducing storage and compute (Chen et al., 7 Aug 2025).

4. Training, Efficiency, and Scaling

Linear-MoE systems demonstrate several training and deployment advantages:

• Sublinear Scaling: Both parameter and data parallelism result in near-linear throughput with increasing cluster size.
• Sample Efficiency: Expert selection strategies such as Random Token Selection (RTS) for unbiased slot allocation, and expert aggregation (AoE) for checkpoint initializers, yield much faster convergence and better sample efficiency than dense or non-specialized approaches (Kim et al., 2021).
• Communication Efficiency: Algorithms such as LSH-MoE cluster similar tokens using locality-sensitive hashing and transmit only cluster summaries, cutting all-to-all communication by up to 88% and accelerating training by 1.28–2.2× with minimal quality loss (Nie et al., 13 Nov 2024).
• Adaptive Configuration for Heterogeneous Hardware: Workload division formulas (such as $B_i = \frac{1 / t_i}{\sum_j 1 / t_j} B_{global}$) allocate more work to faster devices, supporting practical multi-GPU, heterogeneous deployments (Luo et al., 2 Nov 2024).

5. Memory and Inference Optimization

Several strategies are employed to address the memory limitations in deployment and inference:

• Caching and Prefetch Strategies: Activation-aware, sequence-level expert caches (MoE-Infinity, HOBBIT, DuoServe-MoE) learn recurrent expert activation patterns, allowing only relevant experts to be loaded or kept on device at each step, yielding up to 20× reduction in per-token latency and 70–80% memory reduction (Xue et al., 25 Jan 2024, Tang et al., 3 Nov 2024, Tairin et al., 10 Mar 2025, Zhang et al., 9 Sep 2025).
• Mixed Precision and Runtime Compression: Systems such as HOBBIT dynamically substitute low-precision experts when routing weights are small (based, e.g., on gating output magnitude), allowing up to a 4× reduction in expert loading time with <1% accuracy loss (Tang et al., 3 Nov 2024).
• Expert Aggregation and Basis Decomposition: Techniques such as MoBE reduce parameter count by 24–30% with only 1–2% accuracy loss, using shared basis factorizations per MoE layer (Chen et al., 7 Aug 2025). CoMoE’s collaborative aggregation strategies are adapted for real-time deployment on mobile edge devices, enabling up to a 70% reduction in memory (Li et al., 10 Aug 2025).
• Performance Modeling: Hierarchical roofline-based models (MoE-Lightning, MoE-Lens) explicitly analyze memory and compute bottlenecks, enabling scheduling and batching policies that reach up to a 10.3× increase in throughput and close to the hardware throughput bound (Cao et al., 18 Nov 2024, Yuan et al., 12 Apr 2025).

6. Empirical Performance and Applicability

Empirical results across language, vision, and time series forecasting tasks demonstrate:

• High Throughput and Scalability: Linear-MoE models scale linearly in both number of experts and sequence length; inference and training speed remain stable as context length increases, contrary to quadratic scaling of standard attention (Kim et al., 2021, Sun et al., 7 Mar 2025).
• Competitive Accuracy: On MMLU, ARC, WinoGrande, GSM8K, and related tasks, MoE-augmented LSMs and hybrid models are reported to match or exceed classic Transformer baselines of comparable active parameter size (Sun et al., 7 Mar 2025, Wu et al., 11 Aug 2025).
• Robustness and Interpretability: Especially in time series (e.g., Super-Linear), spectral gating across frequency-specialized linear experts yields strong zero-shot results and transparent interpretability, with clear mapping from input periodicity to gating weights (Nochumsohn et al., 18 Sep 2025).
• Dynamic Activation and Resource Adaptation: Mechanisms such as Grove MoE’s adjugate experts and dynamic top-k allocation improve efficiency for tokens of variable complexity. Adaptive scheduling and aggregation at the edge (CoMoE) are essential for real-world deployments under fluctuating resource constraints (Wu et al., 11 Aug 2025, Li et al., 10 Aug 2025).

7. Theoretical Insights, Limitations, and Outlook

Theory and empirical studies on linear mode connectivity (LMC) establish that, upon alignment of expert and gating permutations, the loss landscape of independently trained MoE models is flat and connected, facilitating model merging, ensembling, and federated learning applications (Tran et al., 14 Sep 2025). This property is robust across dense and sparse gating regimes and up to hundreds of layers.

Identified limitations and open challenges include:

• Quality–Compression Tradeoffs: Aggressive compression or expert merging must balance parameter reduction with preservation of rare expert specializations; future work is needed on adaptive compression, improved basis sharing, and dynamic distillation (Chen et al., 7 Aug 2025, Li et al., 10 Aug 2025).
• Load Balancing Under Distribution Shift: While RTS and advanced router schemes help, catastrophic imbalance can still occur, motivating research into graph-based routing and coordination penalties (Bai et al., 18 Dec 2024).
• Edge and Mobile Adaptation: Deployment on resource-constrained, network-variable edge devices requires real-time expert aggregation/offloading and fail-safe routing, as pioneered by CoMoE (Li et al., 10 Aug 2025).
• Sequence Parallelism in Non-Transformer LSMs: Efficient scaling is strongly dependent on the sequence kernel structure; generalizing advanced parallelism techniques to new LSMs is an ongoing research direction (Sun et al., 7 Mar 2025).

In summary, Linear-MoE systems achieve scalable, efficient, and expressive modeling by combining sublinear-complexity sequence modules with sparsely activated expert layers, enabled by modern parallelization, efficient routing, and deployment-aware system optimizations (Sun et al., 7 Mar 2025, Kim et al., 2021, Luo et al., 2 Nov 2024, Tairin et al., 10 Mar 2025, Harvey et al., 19 Jun 2025). Their efficacy is underpinned by detailed empirical results, theoretical understanding of model symmetry, and a growing catalog of compression and deployment frameworks appropriate for both high-end clusters and constrained edge hardware.