Mamba-based State-Space Modules

• Mamba-based state-space modules are neural architectures that integrate selective, content-dependent gating with state recurrences to offer efficient alternatives to quadratic attention methods.
• They implement linear-time recurrences via parallel segmented scans and kernel fusion, achieving 2–5× throughput improvements and reduced memory usage.
• The modules are versatile across domains—including vision, language, and time series—and incorporate optimized quantization and compression strategies for robust deployment.

Mamba-based state-space modules are a class of neural sequence architectures that integrate selective state-space modeling with deep learning, providing hardware-efficient, scalable alternatives to attention-based methods for both language and vision domains. These modules leverage continuous-time or discrete-time state-space recurrences, incorporating data-dependent ("selective") gating of parameters, and employ highly parallel and memory-optimized implementations. The growing diversity of Mamba variants addresses fundamental context modeling, resource, and generalization bottlenecks encountered in large-scale sequence tasks.

1. Mathematical Structure and Selective Mechanisms

The prototypical Mamba-based module models input–state–output relations as a continuous-time structured SSM, given by

$$h_t = A h_{t−1} + B x_t\,;\qquad y_t = C h_t + D x_t$$

with learnable parameters $A$ (state transition), $B$ (input), $C$ (readout), and $D$ (direct path). Discretization—typically by zero-order hold—yields

$$\bar{A} = \exp(\Delta A),\qquad \bar{B} = \exp(\Delta A)^{-1}(\exp(\Delta A) - I)\Delta B$$

and thus the final recurrence at each timestep: $$h_t = \bar{A}\,h_{t-1} + \bar{B}\,x_t,\qquad y_t = C\,h_t + D\,x_t.$$

Mamba distinguishes itself by "selective" parameterization: key matrices (such as $B$, $C$, and $\Delta$) are not static, but computed by compact neural networks (e.g., MLPs) on the input $x_t$ at each step, producing content-dependent recurrence dynamics. In vision and multimodal tasks, the module is further adapted to utilize scan-and-fuse strategies or combined with 2D/3D context aggregation.

2. Hardware-aware Linear-time Implementations

A central advantage is the linear computational and memory complexity in sequence length, $O(NT)$ per layer (state size $N$, sequence length $T$), contrasting with the $O(T^2)$ scaling of Transformer-based attention. This efficiency is enabled by:

• Parallel segmented scan: The full sequence is processed in segments in SRAM, ensuring fast prefix scan recurrences are parallelized and recomputed in backward passes for extra memory savings.
• Kernel fusion: Fused custom GPU kernels keep all recurrent parameters, intermediate states, and token representations in high-bandwidth SRAM, minimizing off-chip memory usage.
• Causal or tree-structured scans: Extensions such as Dynamic Tree Scan allow for non-linearizable receptive fields while maintaining efficient recurrence.

When deployed, these kernels result in 2–5× higher throughput compared to naively split implementations or quadratic self-attention designs (Liu et al., 7 May 2024).

3. Domain-specific Adaptations and Extensions

Mamba-based modules are now found across an array of domains, each leveraging the SSM backbone but specializing its architecture:

• Vision (2D/3D/low-level): Spatial-Mamba introduces structure-aware state fusion (SASF) using dilated depthwise convolutions directly in the state space, enabling single-scan 2D modeling and yielding top-1 ImageNet-1K accuracy up to 85.3%, outperforming previous SSM-based vision models (Xiao et al., 19 Oct 2024). Point Mamba utilizes octree-based Morton code ordering for irregular point clouds, preserving spatial proximity and enabling causal recurrences for 3D semantic segmentation and classification at linear cost (Liu et al., 11 Mar 2024). S²Mamba fuses bidirectional spatial and spectral Mamba scans with a mixture gate for hyperspectral image analysis (Wang et al., 28 Apr 2024).
• Multimodal and dialogue: VL-Mamba replaces quadratic attention with vision selective scan (VSS) modules for multimodal language and vision language modeling, supporting both bidirectional and cross-scan strategies reached by refolding 2D vision features into 1D for SSM propagation (Qiao et al., 20 Mar 2024). DA-Mamba applies hierarchical Mamba blocks—modality-group fusion, partner-group fusion, dialogue-aware cross-attention—with constant-chunking and selective SSM merges to linearize computational cost in complex engagement estimation (Kang et al., 22 Sep 2025).
• Time series and operator learning: ss-Mamba incorporates semantic-aware embeddings and spline-based temporal encoding within the SSM block, supporting interpretability and generalization to new series via BERT-projected index features (Ye, 3 Jun 2025). MambaTS enhances selective recurrences by variable scan, convolution-free temporal blocks, and variable permutation training for robust long-term forecasting (Cai et al., 26 May 2024). For dynamical system operator learning and quantitative systems pharmacology, Mamba SSMs provide state-of-the-art interpolation and strict extrapolation accuracy, outperforming RNN, transformer, and neural operator baselines at up to an order-of-magnitude lower cost (Hu et al., 5 Sep 2024).

4. Quantization and Compression: Binzarization and Training Strategies

As Mamba models scale, deployment demands stringent compression. Bi-Mamba presents end-to-end binarization (1-bit quantization) of $\sim$90% of weights, using per-column scaling and bias (FBI-Linear), yet maintains linear time complexity and constant-state memory. Training is conducted via autoregressive teacher-student distillation (minimizing cross-entropy between the teacher's next-token distribution $p^T$ and the student $p^S$ over context), eschewing real-token cross-entropy: $$\mathcal{L}_{\mathrm{Bi-Mamba}} = -\frac{1}{n}\sum_{k=1}^n\langle p^{T}(x^{k+1}),\;\log p^{S}(x^{k+1})\rangle$$ This process realizes an 8–10× overall compression (e.g., the 780M model shrinks from 1.45GB to 0.22GB), with only a $\sim$2–3 PPL loss on standard language benchmarks relative to full-precision Mamba-2 (Tang et al., 18 Nov 2024).

5. Mitigating Contextual and Structural Shortcomings

Recent analysis highlights two key limitations and corresponding remedies:

• Asymmetry bias: The standard Conv1D+SiLU pre-SSM nonlinear convolution in Mamba introduces position-dependent fusion, resulting in failure on tasks (synthetic or real) requiring symmetric pattern or palindrome recognition. Remedies include residual bypass of the convolution (direct skip from linear-projected embeddings to SSM inputs), multiplicative gating, and explicit positional embeddings. These modifications restore Mamba's ability to capture symmetric dependencies (Chen et al., 22 Sep 2025).
• Context-length generalization: Mamba models trained at length $N_{\text{train}}$ deteriorate sharply for $N\gg N_{\text{train}}$. The root cause is tied to the spectrum of the transition matrix $A$; as $|e^{-\alpha\Delta}|$ approaches 1, the hidden state can explode or vanish. Spectrum scaling modulates $A$ post-hoc (e.g., $A' = \lambda^s A$) to contract the spectrum, recovering stable, near-baseline perplexity at 32K–128K context lengths (Lu et al., 23 Sep 2025).

6. Scaling Strategies and Modular Composition

Scaling Mamba modules for large models adopts several approaches:

• Switch-style Mixture of Experts (MoE-Mamba): Sparse MoE FFN layers are interleaved between dense SSM blocks. This architecture achieves the same language modeling quality as dense Mamba in $2.35\times$ fewer training steps, with only marginal active parameter and latency increases per token (Pióro et al., 8 Jan 2024).
• Matryoshka training (MatMamba): Nested (i.e., sliceable) architectures are constructed where each block supports multiple model widths, trained jointly with a superposed loss. Inference can select any prefix size, yielding efficient, elastic adaptation to deployment requirements, without requiring retraining or breaking representation alignment (Shukla et al., 9 Oct 2024).
• Fine-tuning and PEFT: Parameter-efficient methods (e.g., LoRA on prefix-sum buffers) and mixed-precision fine-tuning are fully compatible with Mamba's SSM kernel. Theoretical Lyapunov analysis shows that Mamba's dynamical systems structure makes it inherently robust to rounding perturbations and low-rank updates, outperforming transformer analogs in stability under these adaptations (Halloran et al., 31 May 2024).

7. Empirical Evaluation Across Tasks and Benchmarks

Mamba-based modules now challenge or surpass transformer-based models across an array of benchmarks:

Task	Dataset/Benchmark	Result or Comparison	Reference
Vision	ImageNet-1K (top-1)	Spatial-Mamba-B 85.3%, > VMamba-B, LocalVMamba-B	(Xiao et al., 19 Oct 2024)
	COCO (Detection, Mask R-CNN)	Spatial-Mamba-B box AP 50.4, mask AP 45.1, > VMamba
	Point Cloud (ModelNet40)	Point Mamba: 93.4% accuracy (3.08M params), linear N	(Liu et al., 11 Mar 2024)
Hyperspectral	Indian Pines/Pavia U/Houston 2013	S²Mamba OA 97.9–93.4%, with $<$0.12M params	(Wang et al., 28 Apr 2024)
Language	Wikitext2/PTB/C4 (PPL, 780M–2.7B)	Bi-Mamba within 2–3 PPL of FP16, 8–10× memory reduction	(Tang et al., 18 Nov 2024)
	LLM tasks (VQA, MM-benchmarks)	VL-Mamba 2.8B matches or exceeds 7B–13B Transformer MLLM	(Qiao et al., 20 Mar 2024)
Time Series	ETTh2/Weather/Traffic/etc.	ss-Mamba and MambaTS yield new SOTA and interpretability	(Ye, 3 Jun 2025, Cai et al., 26 May 2024)
Scientific	Dynamical systems (ODEs, PK-PD)	5–10× lower error and compute vs neural operator baselines	(Hu et al., 5 Sep 2024)
Speech	Librispeech+noise+reverb (SI-SNRi)	SPMamba: +2.58dB SI-SNRi, 43% compute, 42% params	(Li et al., 2 Apr 2024)

Key empirical insights include the additive effects of bidirectional scanning, fusion modules (e.g., mixture gates, tree-structured recurrences), and hybridization with local convolutions or MoE. Across domains, the principal bottleneck shifts from quadratic token-token interactions to efficient stateful computation and content-adaptive attention. Open challenges include further improving cross-modal fusion, scaling stability, streaming/causal variants, and on-device hardware specialization.

Summary Table: Representative Mamba-based Module Variants

Module/Class	Domain	Selectivity/Scan	Distinguishing Features
Bi-Mamba	Language	Selective, binarized	1-bit quantization, teacher-student AR distill.
Spatial-Mamba	Vision	Structure-aware fusion	Dilated conv in state space, 1 scan, SASF
S²Mamba	Hyperspectral	Patch/band SSM fusion	Spatial/spectral experts, mixture gating
MoE-Mamba	Language	MoE FFN	Switch-like sparse layers, SSM interleaving
MatMamba	Vision/Language	Nested sub-blocks	Elastic slicing (Matryoshka), shared weights
DA-Mamba	Multimodal	Hierarchical fusion	Dialogue/context fusion, SSM for cross-modal
SPMamba	Speech	Bidirectional, time/freq	BMamba in time/freq domains
Mamba-Adaptor	Vision	Global memory, spatial	Learnable memory augment, depthwise convs

These advances position Mamba-based state-space modules as a robust, extensible, and resource-efficient backbone across sequences, images, multimodal, and operator learning contexts.