Efficient Sparse Scaling of Mamba Layers

• Efficient sparse scaling of Mamba layers integrates Mixture-of-Experts with SSMs, reducing per-token compute and achieving up to 2.35× faster training.
• The approach leverages shared routing and structural sparsity to cut active parameters by up to 2.3× while maintaining performance on large-scale tasks.
• Adaptive grouping, bidirectional local scans, and domain-specific extensions enable robust applications in sequence, vision, and multimodal models.

Efficient sparse scaling of Mamba layers is a rapidly advancing area within deep learning, targeting the challenge of increasing model capacity and expressiveness while maintaining tractable computation and memory requirements. Mamba layers, rooted in state-space model (SSM) formalism, have demonstrated strong performance in sequence modeling via linear-time complexity. However, scaling their representational power to rival the largest modern models requires sophisticated sparsification and modularization strategies. This entry surveys key methodologies, technical details, experimental findings, and theoretical implications, focusing on strategies that enable efficient, sparse scaling of Mamba and SSM-derived architectures.

1. Hybrid Sparse Scaling with Mixture-of-Experts

Mixture-of-Experts (MoE) integration has emerged as a principal technique for efficient sparse scaling of Mamba layers. MoE-Mamba architectures interleave SSM-based layers with sparsely-activated expert modules. Each expert in the MoE layer is a distinct feed-forward network, and a trainable router selects the most relevant expert for each input token:

• The router computes $\mathbf{h}(\mathbf{x}) = W\mathbf{x}$, applies softmax normalization to obtain $p_i(\mathbf{x})$, and selects $I = \arg\max_i p_i(\mathbf{x})$ (Switch routing, $k=1$).
• Output is $y = p_I(x)\cdot E_I(x)$—only one expert is active per token, ensuring constant per-token compute.

This architecture decouples the unconditional, recurrent sequence integration of SSMs from conditional, expert-driven computation. The principal advantage is support for parameter growth (by increasing the number of experts) without commensurate growth in inference cost—modeling capacity scales sublinearly with hardware demands (2401.04081).

Key observations include:

• MoE-Mamba matches vanilla Mamba’s performance with 2.35× fewer training steps.
• Increasing expert count improves perplexity monotonically.
• Inference remains efficient: only a small, constant subset of parameters is used per token.

2. Sparse Projections and Shared Routing in SSMs

Routing Mamba (RoM) extends sparse scaling by restructuring SSM projection layers themselves as sparse mixtures of linear experts. Rather than naively adding independent MoE routers to each projection—often leading to performance degradation due to fragmented expert activation—RoM employs a shared routing strategy:

• A single router computes routing weights for all principal projection layers (Convolution, Gate, Output).
• Each expert is a parameterized linear module, and the router activates only a selected top-$K$ experts per token.
• For token $t$, routing weights are: $$\mathcal{R}_i(X_t) = \mathcal{P}(X_t)\cdot \mathbb{1}\{i\in \text{Top}K(\mathcal{P})\}$$, with $$\mathcal{P}(X_t) = \operatorname{Softmax}(X_t \cdot W_r)$$.

The expert computations are sparse and coherent across the layer:

$$O_t = \sum_{i} \mathcal{R}_i(X_t) \cdot E_i(Y_t, X_t) \ E_i(Y_t, X_t) = Y_t \odot (G W_{\text{out}, i})$$

This approach provides gains such as:

• For 115M-scale models, RoM achieves the same perplexity as dense Mamba with up to 2.3× fewer active parameters.
• For hybrid models, FLOPS are reduced by 23% over dense scaling for similar LLMing performance.
• The shared router design allows efficient scaling of both SSMs standalone and hybrids with attention (2506.18145).

3. Architectural Decomposition and Groupwise Sparsification

Vision-specific state-space models benefit from groupwise and multi-directional sparse processing. GroupMamba introduces channel grouping and multi-directional Visual Single Selective Scanning (VSSS):

• The input channels are split into groups (e.g., four groups at $C/4$ channels each), and each group is processed with a VSSS block scanning in a distinct spatial direction (left-to-right, right-to-left, top-to-bottom, bottom-to-top).
• Aggregation across group outputs uses Channel Affinity Modulation (a two-layer nonlinearity with sigmoid output applied to groupwise pooled channel stats).
• This reduces both parameter count and computational cost, while ensuring strong spatial modeling and cross-group communication (2407.13772).

Mathematically, the VSSS block is:

$$Z'_{\text{out}} = Z_{\text{in}} + \mathrm{Mamba}(\mathrm{LN}(Z_{\text{in}})),\quad Z_{\text{out}} = Z'_{\text{out}} + \mathrm{FFN}(\mathrm{LN}(Z'_{\text{out}}))$$

The grouped variant:

$$X_{GM} = \mathrm{Concat}\{\mathrm{VSSS}(X_{LR}), \mathrm{VSSS}(X_{RL}), \mathrm{VSSS}(X_{TB}), \mathrm{VSSS}(X_{BT})\}$$

4. Structural and Unstructured Sparsity via Parameterization and Pruning

Sparse scaling in Mamba layers can be achieved by directly structuring the parameter space:

• Sparse Mamba enforces canonical controllable or observable forms for the SSM state matrix $A$, where only $n$ values are free in an $n \times n$ matrix. For example:

$$A = \begin{bmatrix} 0 & 1 & 0 & \dots & 0 \ 0 & 0 & 1 & \dots & 0 \ \vdots & \vdots & \ddots & \ddots & \vdots \ -a_{n-1} & -a_{n-2} & \cdots & -a_0 \end{bmatrix}$$

This reduces parameter count and computation, and when paired with enforced stability (e.g., $a_i = -1\times 10^{-5}$ if $a_i \geq 0$), establishes predictable dynamical behavior with improved perplexity and training speed (2409.00563).

Unstructured sparsity is addressed via pruning strategies (2505.08299):

• Gradient-aware magnitude pruning ranks each parameter $w_{ij}$ by $$S(w_{ij}) = |w_{ij}| (|\partial \mathcal{L}/\partial w_{ij}|)^\alpha$$.
• Iterative (cubic) pruning schedules increase sparsity gradually, and a global pruning threshold allocates sparsity unevenly per-layer to preserve sensitivity in critical blocks.
• Stability preservation is enforced by bounding eigenvalue shifts in pruned state matrices.
• Up to 70% parameter reduction is possible with <5% loss in performance and up to 2.45× inference speedup.

5. Bi-directionality and Locality in Sparse Scanning

SSM-based models traditionally compute forward-only (causal) scans. LBMamba addresses the absence of “future” context by embedding lightweight, local backward scans within each forward scan window. In practice:

• For each local window of length $M$, a backward state $h_t^b$ is computed recursively within the window, initialized as $B^f x_t$ at new window boundaries.
• States are merged as $$h_t = h_t^f + (h_t^b - B^f x_t),\ y_t = C^f h_t + D x_t$$.

This locally bi-directional approach preserves the parallel efficiency of Mamba—since all operations remain within per-thread registers—and achieves higher accuracy and throughput relative to full global forward-backward scans (2506.15976). For example, LBVim (the backbone) exceeds prior backbones by up to 1.6% top-1 accuracy under identical compute budgets.

6. Task-Specific Sparse Scaling: Vision and Multimodal Extensions

Sparse scaling is adapted to domain-specific requirements:

• In high-resolution diffusion models, DiM and related bidirectional SSM architectures incorporate multiple scan directions, learnable padding, and lightweight convolutional mixing, maintaining linear scalability even for images $1536\times 1536$ (2405.14224, 2405.15881).
• In hyperspectral imaging, sparse deformable sequencing (SDS) uses adaptive attention-based token selection for spatial and spectral feature learning, minimizing computation on irrelevant regions and boosting detail preservation (2504.09446).
• For multimodal and sequential recommendation, multi-scale Mamba integrates time-domain SSMs with frequency-domain (FFT) analysis and LLM features, fused with an adaptive gating mechanism for dynamic reliability weighting (2505.04445).

7. Implications and Future Directions

Efficient sparse scaling of Mamba layers reveals a broad suite of design patterns for large-scale, yet tractable, sequence and vision models:

• Mixture-of-Experts projections and shared routing broadly enable sublinear compute scaling with model capacity.
• Structural sparsity—especially in state matrices—enables controlled, interpretable, and stable model design.
• Layer grouping, bi-directional locality, and cross-layer aggregation allow parameter-efficient vision backbones.
• Hardware-friendly quantization and FPGA acceleration (e.g., FastMamba) leverage sparse patterns for deployment on edge devices by transforming linear layers via Hadamard transforms and power-of-two quantization, supporting efficient computation under quantization constraints (2505.18975).
• Continued innovation in routing, expert selection, and hybridization with attention or convolutional modules is expected, alongside efforts to optimize load balancing, expert utilization, and stability.

Efficient sparse scaling of Mamba layers thus constitutes a core methodological advance for scaling SSM architectures to modern datasets and tasks, bridging the gap between tractable resource usage and state-of-the-art learning capacity.