SSD-Mamba2: Structured SSM Backbone

• SSD-Mamba2 is a family of architectures that leverages selective state-space duality to combine per-step recurrences with structured semiseparable matrix operations for efficient long-context modeling.
• It employs input-dependent parameters, head-wise dynamics, and parallel chunk-based scanning to optimize state transitions for streaming inference and diverse application domains.
• Its design preserves linear-time complexity and enhances hardware efficiency by balancing state storage, memory bandwidth, and non-matmul operations through innovative state pruning and quantization.

SSD-Mamba2 denotes a family of architectures built on Mamba2 under Structured State-Space Duality (SSD), in which a selective state-space model is simultaneously viewed as a per-step recurrence for streaming and as a structured semiseparable matrix operator for parallel training. In this formulation, a continuous-time linear state-space model

$$\frac{d h(t)}{dt} = A h(t) + B(t)x(t), \qquad y(t) = C(t) h(t) + D x(t)$$

is discretized under zero-order hold, yielding a recurrence whose Mamba2 specialization uses structured $A$, input-dependent $\Delta,B,C$, chunkwise evaluation, and linear complexity in sequence length. Across the recent literature, SSD-Mamba2 is best understood not as a single canonical network, but as a design pattern for long-context, streamable, and hardware-aware sequence modeling that has been specialized to surgical video, genomics, LLMs, robotics, dense vision, anomaly detection, and accelerator design (Oh et al., 14 May 2026).

1. Formal basis: selective state spaces and structured duality

The mathematical core of SSD-Mamba2 is the selective state-space model (SSM) together with its SSD reformulation. Under zero-order hold with step $\Delta$, the exact discrete update is

$$h_n = \bar A\,h_{n-1} + \bar B\,x_n, \qquad y_n = C\,h_n + D\,x_n,$$

with

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

In Mamba and Mamba2, $\Delta,B,C$ are input-dependent, while $A$ is structured; in Mamba2, the SSM inner dimension is split into heads and each head has a scalar $A_h<0$. A sequence of length $L$ is split into chunks of size $A$0; within each chunk, the SSD scan is executed in parallel, and a single head-wise state tensor is passed between chunks. The chunked scan is algebraically equivalent to the step-wise recurrence, so the same operator supports both training-time parallelism and streaming inference (Oh et al., 14 May 2026).

This duality is also the basis for Mamba2’s role in long-range language and sequence models. HybriDNA describes the SSD layer as a multi-head recurrence

$A$1

with $A$2, and notes that the corresponding operator $A$3 is semiseparable, enabling $A$4 algorithms rather than quadratic attention. TurboS likewise frames Mamba2 as a linear-time sequence module with complexity $A$5, in contrast to attention’s $A$6, and explicitly relies on chunk-based parallelism in prefill and selective state updates in decode (Ma et al., 15 Feb 2025, Team et al., 21 May 2025).

A useful comparative development is the gated delta rule. Gated DeltaNet identifies Mamba2’s state transition as effectively diagonal in the fast-weight view and introduces a more expressive update,

$A$7

combining Mamba2-style global adaptive forgetting through $A$8 with DeltaNet-style targeted overwrite through $A$9. This situates SSD-Mamba2 within a broader trajectory from diagonal selective dynamics toward low-rank structured state transitions that remain scan-friendly (Yang et al., 2024).

2. Architectural motifs built on SSD-Mamba2

A recurrent theme in SSD-Mamba2 research is that the base recurrence is retained while domain-specific structure is introduced around it. SurgicalMamba is the most explicit example: it keeps Mamba2’s per-head scalar $\Delta,B,C$0, selective $\Delta,B,C$1, and SSD scan, then adds three SSD-compatible components aimed at long surgical videos: a dual-path SSD block, intensity-modulated stepping, and state regramming. The dual-path block separates a slow path that carries SSM state and convolution buffer across clips from a fast path that resets at clip boundaries but is conditioned on the slow-path output. The result is a two-timescale recurrence in which long-horizon memory and short-term reactivity coexist without changing the $\Delta,B,C$2 per-frame streaming cost (Oh et al., 14 May 2026).

Its second addition, intensity-modulated stepping, interprets a learned scalar $\Delta,B,C$3 as a continuous-time time warp,

$\Delta,B,C$4

and implements this by scaling the selective step size: $\Delta,B,C$5 Because $\Delta,B,C$6, increasing $\Delta,B,C$7 strengthens decay and induces explicit forgetting near phase transitions. Its third addition, state regramming, applies a per-chunk orthogonal rotation

$\Delta,B,C$8

to the head-wise state, where $\Delta,B,C$9 is a low-rank skew-symmetric matrix predicted from chunk summaries. This preserves norm, opens cross-channel mixing in an otherwise axis-aligned recurrence, and leaves the SSD rank bound intact (Oh et al., 14 May 2026).

Other works modify SSD-Mamba2 in different directions while preserving its long-range backbone role. HybriDNA uses a layer-wise hybrid with 7 Mamba2 blocks per 1 Transformer block, with the first block being Mamba2 and no positional encoding of any kind. TurboS interleaves 57 Mamba2 layers, 7 Attention layers, and 64 FFN layers inside AMF and MF block patterns, using Mamba2 as the dominant sequence-modeling component while sparse attention layers act as global checkpoints. Gated DeltaNet-H2 goes further by explicitly stacking Mamba2 + Gated DeltaNet + sliding window attention, and the paper reports that this ordering gives the best average perplexity and zero-shot accuracy among the tested permutations (Ma et al., 15 Feb 2025, Team et al., 21 May 2025, Yang et al., 2024).

A broader implication, stated explicitly in several papers, is that SSD-Mamba2 is increasingly treated as a modular backbone rather than a self-sufficient monolith. Hybridization with attention, local convolutions, or specialized branches is not a departure from the paradigm; it is one of its dominant engineering patterns (Ma et al., 15 Feb 2025, Hu et al., 22 Jun 2026).

3. Sequence construction, scanning, and positional structure

Because SSD-Mamba2 is inherently sequential, the way higher-dimensional data are serialized into sequences becomes part of the model definition. Different domains have therefore produced distinct scanning and ordering mechanisms.

In genomics, HybriDNA adopts strict base-level tokenization with A/C/G/T as four tokens and no k-mer or BPE, producing contexts up to 131,072 tokens (131 kb). It also uses no positional encoding—no sin/cos, RoPE, ALiBi, or learned positions—and instead relies on the direction of the autoregressive process and the state evolution of Mamba2 for order information. This makes the SSM recurrence itself the primary positional mechanism (Ma et al., 15 Feb 2025).

In visual domains, several SSD-Mamba2-style systems engineer the scan explicitly. MambaBEV performs BEV feature discrete rearrangement in four directions—forward-left, forward-upward, reverse-left, and reverse-upward—before applying Mamba2, then reshapes and averages the outputs. The paper reports that four-direction rearrangement outperforms single-direction by +1.02% NDS and +1.28% mAP, indicating that sequence order materially affects 2D global context formation in BEV space (You et al., 2024). Surgical-MambaLLM introduces Surgical Instrument Perception (SIP) scanning, a radial, center-out traversal tailored to the geometry of robotic surgery, and uses it inside a Cross-modal Bidirectional Mamba2 Integration (CBMI) module for visual–text fusion (Hao et al., 20 Sep 2025).

MambaADv2 treats scanning as a scale-dependent design variable. It serializes 2D features with Hilbert curves and proposes semantics-adaptive progressive scanning, with a per-stage direction budget $\Delta$0 satisfying $\Delta$1. Its default configuration is $\Delta$2, so scanning complexity decays along the feature pyramid. The paper reports that this setting improves image-AUROC and AU-PRO over fixed Hilbert-8 while reducing redundant scanning (Hu et al., 22 Jun 2026).

Related work outside strict SSD-Mamba2 nomenclature reaches analogous conclusions. SDMamba for hyperspectral image classification formulates Sparse Deformable Sequencing (SDS), in which tokens are ranked by angular similarity to an anchor, top-$\Delta$3 selected, and ordered into a sparse deformable sequence before being fed to Mamba. The paper explicitly describes this as a natural conceptual template for “SSD-/SD-type Mamba” design in vision, suggesting that selective token routing and data-dependent ordering are likely to remain central in future SSD-Mamba2 image models (Xu et al., 13 Apr 2025).

4. Computational profile, bottlenecks, and systems behavior

The principal computational claim of SSD-Mamba2 is linear scaling in sequence length together with bounded streaming cost. SurgicalMamba states this as linear complexity $\Delta$4 in sequence length $\Delta$5 and model dimension $\Delta$6, with constant per-frame cost $\Delta$7 in streaming because the state is updated once per new frame. TurboS makes the same complexity distinction against attention, using Mamba2 to make 256K-context training and inference feasible. HybriDNA similarly uses Mamba2 as the efficient majority of layers so that 131 kb context can be processed at single-nucleotide resolution (Oh et al., 14 May 2026, Team et al., 21 May 2025, Ma et al., 15 Feb 2025).

Profiling work shows, however, that linear complexity does not make all components equally cheap. PerfMamba reports that the SSM component dominates FLOPs, latency, memory, and I/O in both Mamba-1 and Mamba-2. In Mamba-2 prefill, the Gated MLP becomes the main bottleneck, but in decoder mode the critical path remains the SSM recurrence

$\Delta$8

The same study introduces $\Delta$9-guided structured state pruning, where states with low average gate activity are removed. On Mamba2-130M, this yields up to 1.14× speedup and 11.5% memory reduction on long-sequence state updates, with a “safe pruning region” at $$h_n = \bar A\,h_{n-1} + \bar B\,x_n, \qquad y_n = C\,h_n + D\,x_n,$$0 showing mean accuracy loss of about 0.7 percentage points across the reported tasks (Asif et al., 28 Nov 2025).

Hardware co-design papers push SSD-Mamba2 further toward deployment. FastMamba targets FPGA execution of Mamba2 with Hadamard-based 8-bit quantization for linear layers, power-of-two quantization for the SSM and convolution, and first-order approximations for SoftPlus and exp. On Xilinx VC709 FPGA, for the input prefill task on Mamba2-130M it achieves 68.80× and 8.90× speedup over Intel Xeon 4210R CPU and NVIDIA RTX 3090 GPU, respectively; in the output decode experiment with Mamba2-2.7B, the abstract reports 6× higher energy efficiency than RTX 3090 GPU (Wang et al., 25 May 2025). SpecMamba extends FPGA acceleration to speculative decoding for Mamba, proposing hybrid backtracking, FIFO-based tree verification with tiling, and a dataflow that computes linear layers in parallel and SSM layers in series; on AMD FPGA platforms it reports 2.27× speedup over GPU baselines, 2.85× improvement compared to prior FPGA solutions, and 5.41× and 1.26× higher energy efficiency, respectively (Zhong et al., 24 Sep 2025).

A consistent systems-level conclusion emerges from these papers: the decisive optimization target in SSD-Mamba2 deployments is usually not the existence of recurrence itself, but the interaction among state storage, memory bandwidth, chunking strategy, and non-matmul operators (Asif et al., 28 Nov 2025, Wang et al., 25 May 2025, Zhong et al., 24 Sep 2025).

5. Major application domains

SSD-Mamba2 has been specialized across a wide range of problem classes. The table summarizes representative instantiations and outcomes already reported in the literature.

Domain	Model	Representative result
Online surgical phase recognition	SurgicalMamba	94.6%/82.7% on Cholec80 and 89.5%/68.9% on AutoLaparo under strict online evaluation
DNA language modeling	HybriDNA	Processes sequences up to 131 kb and reaches 0.74 AUROC on Causal eQTL with 131k-context pretraining
Large language modeling	Hunyuan-TurboS	256K context, 1.8× speedup over Hunyuan-Turbo at inference, Arena score 1356
Robotic surgery VQLA	Surgical-MambaLLM	EndoVis-18: 0.6964 Acc, 0.4110 F-Score, 0.8027 mIoU
Camera-only 3D detection	MambaBEV	51.7\% NDS and 42.7\% mAP on nuScenes
Unsupervised anomaly detection	MambaADv2	87.2 mAD on MVTec-AD and 80.1 on VisA
End-to-end motion control	SSD-Mamba2 RL	Thin Obstacles with Goals: 537.67 ± 307.79 return, 193.70 ± 93.61 collisions, 10.50 ± 5.36 m distance

In online surgical phase recognition, SurgicalMamba is the most explicit domain-specialized “SSD-Mamba2” system. It addresses procedures spanning tens of thousands of frames, non-uniform temporal flow, and highly correlated channels in narrow visual domains. Across seven public SPR benchmarks, it reports state-of-the-art online results, including 94.6% Acc / 82.7% Jac on Cholec80 and 89.5% Acc / 68.9% Jac on AutoLaparo, at 119 fps on a single GPU (Oh et al., 14 May 2026).

In long-range genomics, HybriDNA shows how SSD-Mamba2 can dominate a hybrid backbone rather than merely replace attention. Its decoder-only architecture uses a 7:1 Mamba2:Transformer ratio, no positional encoding, and context-length warm-up from 8,192 to 32,768 and 131,072 tokens. On the long-range benchmark, HybriDNA-300M improves Causal eQTL AUROC from 0.71 at 8k pretraining context to 0.74 at 131k (Ma et al., 15 Feb 2025).

In LLMs, TurboS demonstrates SSD-Mamba2 at industrial scale: a 56B activated (560B total) hybrid MoE with 57 Mamba2 layers, 7 Attention layers, and 64 FFN layers, trained on 16T high-quality tokens and supporting 256K context length. It reports an overall top-7 rank on LMSYS Chatbot Arena with a score of 1356, and an average of 77.9% across 23 automated benchmarks (Team et al., 21 May 2025).

In visual robotics and dense perception, Surgical-MambaLLM uses Mamba2 as a cross-modal fusion front-end between CLIP-ViT-B/32 and InternLM-7B for surgical visual question localized-answering, improving EndoVis-18 over prior work. MambaBEV uses Mamba2 for temporal BEV fusion and a Mamba-based DETR head, reporting 51.7\% NDS and 42.7\% mAP on nuScenes. MambaADv2 places an SSD-based, Mamba3-style HSS core inside a decoder for multi-class unsupervised anomaly detection and reports state-of-the-art mean mAD on six benchmarks, including 87.2 on MVTec-AD and 49.0 on COCO-AD (Hao et al., 20 Sep 2025, You et al., 2024, Hu et al., 22 Jun 2026).

In reinforcement learning for motion control, the SSD-Mamba2 paper frames the architecture directly as a vision-driven cross-modal RL backbone. In the Thin Obstacles with Goals environment, it reports 537.67 ± 307.79 return, 193.70 ± 93.61 collisions, and 10.50 ± 5.36 m distance, outperforming the reported Transformer proprio-vision baseline. On zero-shot transfer to Sphere Obstacles with Goals, it reports 608.47 ± 344.02 return and 158.77 ± 117.62 collisions (Tao et al., 9 Sep 2025).

6. Misconceptions, limitations, and research directions

A common misconception is that SSD-Mamba2 names a single standardized architecture. The literature instead uses it as a family resemblance term: SurgicalMamba is an SSD-Mamba2 specialization for online surgical video; HybriDNA is a hybrid Transformer–Mamba2 long-range DNA LLM; TurboS is a hybrid Transformer–Mamba2–MoE LLM; MambaADv2 explicitly describes itself as following the SSD-based Mamba lineage while incorporating Mamba3-style position-aware state-space modeling (Oh et al., 14 May 2026, Ma et al., 15 Feb 2025, Team et al., 21 May 2025, Hu et al., 22 Jun 2026).

A second misconception is that linear-time recurrence makes attention unnecessary. Several papers argue the opposite. HybriDNA reports that a pure Mamba2 model at 300M parameters has worse pretraining loss than the 300M hybrid, and TurboS retains sparse attention layers because too few attention layers degrades performance while too many hurt efficiency and KV cache size. Gated DeltaNet-H1 and H2 similarly obtain their strongest results by combining recurrent layers with sliding window attention or Mamba2 layers rather than replacing all other mixers (Ma et al., 15 Feb 2025, Team et al., 21 May 2025, Yang et al., 2024).

A third misconception is that positional structure is automatic once recurrence is present. Some systems do omit positional encodings altogether, as in HybriDNA, but others add explicit mechanisms precisely because serialization alone is insufficient: SurgicalMamba uses time-warped stepping and chunk-boundary rotations; Surgical-MambaLLM introduces SIP scanning; MambaADv2 adds RoPE into the SSD-style SSM and uses semantics-adaptive progressive scanning; MambaBEV uses four-direction BEV rearrangement (Oh et al., 14 May 2026, Hao et al., 20 Sep 2025, Hu et al., 22 Jun 2026, You et al., 2024).

The main limitations reported across the literature are similarly concrete. TurboS notes that attention remains quadratic even when reduced to 1/8 of layers, so extremely large contexts still incur some quadratic cost. HybriDNA observes that OMIM variant effect prediction remains difficult for all models despite 131k context. MambaADv2 identifies spatial information loss, frequency blind spots, and representational redundancy as limitations of earlier Mamba-lineage anomaly detectors, motivating RoPE, frequency branches, and progressive scanning. PerfMamba shows that even efficient SSD-style models remain bottlenecked by SSM state dimension and memory traffic, which is why pruning and hardware-specific co-design continue to matter (Team et al., 21 May 2025, Ma et al., 15 Feb 2025, Hu et al., 22 Jun 2026, Asif et al., 28 Nov 2025).

The dominant research directions are therefore not merely “larger Mamba2 models,” but richer state dynamics, better hybridization, more informative scans, and more specialized systems support. Existing papers already point to multi-timescale SSD blocks, adaptive time-warping, orthogonal state rotations, low-rank transition updates, hybrid SSM–attention stacks, state pruning, FPGA quantization, and speculative decoding as concrete extensions. This suggests that SSD-Mamba2 is evolving less as a fixed architecture than as a general computational substrate for long-sequence models that need both streaming efficiency and task-specific structure (Oh et al., 14 May 2026, Yang et al., 2024, Zhong et al., 24 Sep 2025).