HyMamba: Hybrid Mamba Architectures

• HyMamba is a family of architectures that hybridize Mamba’s selective state space backbone with an added organizing principle (e.g., geometric, hypergraph) to address domain-specific challenges.
• These variants employ modifications like hyperspectral scanning, dynamic graph ordering, and hyperbolic embeddings to enhance performance and maintain linear-time complexity.
• Empirical evaluations across tasks such as 3D pose lifting and medical image segmentation demonstrate HyMamba’s effective efficiency–accuracy trade-offs.

HyMamba denotes an emergent but non-canonical cluster of Mamba-derived architectures rather than a single universally fixed model. In current arXiv usage, the label may refer explicitly to a hyperspectral object tracking network equipped with Mamba (Gao et al., 10 Sep 2025), to the “HyperGCN–Mamba” shorthand used for HGMamba in 3D human pose lifting (Cui et al., 9 Apr 2025), or to broader hybrid, hypergraph, hyperbolic, and hyperspectral Mamba designs in medical imaging, graph learning, and remote sensing (Xu, 2024, Pan et al., 2024, Zhang et al., 14 May 2025). This suggests that “HyMamba” functions primarily as a family-resemblance term for architectures that retain Mamba’s selective state space backbone while introducing an additional structural prior, geometric prior, or domain-specific factorization.

1. Terminological scope and naming variability

The term is semantically unstable across papers. Some works use it directly, some use it as shorthand, and some explicitly note that the term does not appear in the paper even though the architecture would be described informally as a “HyMamba”-style design.

Usage in literature	Domain	Interpretation
HGMamba / “HyperGCN–Mamba” (Cui et al., 9 Apr 2025)	3D human pose lifting	Hybrid Hyper-GCN and Mamba
HC-Mamba / HyMamba (Xu, 2024)	Medical image segmentation	Hybrid convolutional Mamba
HeteGraph-Mamba (Pan et al., 2024)	Heterogeneous graph learning	Heterogeneous graph Mamba via two-level tokenization
HMamba / “Hyperbolic Mamba” (Zhang et al., 14 May 2025)	Sequential recommendation	Mamba in Lorentz hyperbolic space
HyMamba (Gao et al., 10 Sep 2025)	Hyperspectral object tracking	SSI- and HSM-based hyperspectral tracking

The ambiguity is not incidental. HS-Mamba states that the term “HyMamba” does not appear in that paper and should be treated as a generic label unless a specific citable architecture is supplied (Peng et al., 22 Apr 2025). HyM-UNet likewise states that the paper does not explicitly use the term “HyMamba,” even though it embodies what many practitioners would informally call a “Hybrid Mamba” design (Chen et al., 22 Nov 2025). GraphMamba makes a related distinction: the overall network is “GraphMamba,” while the spectral sequence encoder module is called “HyperMamba,” not “HyMamba” (Yang et al., 2024).

A common misconception is therefore to treat HyMamba as a single named baseline analogous to Mamba or VMamba. The literature instead supports a narrower statement: HyMamba is a recurrent naming pattern for Mamba systems that hybridize selective state space modeling with another organizing principle.

2. Shared state-space backbone

Despite the terminological variability, the architectures grouped under HyMamba are united by a common control-theoretic substrate. Multiple papers formulate the underlying state space model in continuous time as

$\dot{x}(t) = A x(t) + B u(t), \qquad y(t) = C x(t)$

or, in variants with an explicit skip term,

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

followed by zero-order-hold or equivalent discretization into

$$x_k = \bar{A} x_{k-1} + \bar{B} u_k, \qquad y_k = C x_k,$$

with convolutional or scan-based implementations for parallel training (Cui et al., 9 Apr 2025, Xu, 2024).

The distinctiveness of Mamba-style models lies in selectivity: parameters such as $B$, $C$, and the discretization step $\Delta$ are made input-dependent. HGMamba states this in the form

$$B = \mathrm{Linear}_N(x), \qquad C = \mathrm{Linear}_N(x), \qquad \Delta = \tau_\Delta(\mathrm{Parameter} + s_\Delta(x)),$$

while related graph and vision variants describe equivalent token-conditioned gates or per-step projections (Cui et al., 9 Apr 2025, Pan et al., 2024). The practical consequence is linear-time sequence modeling in sequence length, in contrast to the quadratic complexity of global self-attention.

What changes across HyMamba variants is not the selective state space core but the way non-sequential data are converted into sequences and the auxiliary modules used to compensate for causal order bias, lost locality, heterogeneity, or geometry. Vision variants use SS2D and directional scans; graph variants impose metapath-based orderings; hyperspectral models reorder spectral bands or construct dual spatial-spectral streams; hyperbolic variants transport hidden states on the Lorentz manifold rather than in Euclidean space (Zhang et al., 14 May 2025).

3. Hybridization as the dominant design pattern

The most explicit “HyMamba” formulation appears in HGMamba, where the model is built from dual-stream blocks: a Hyper-GCN stream for local skeletal structure and a Shuffle-Mamba stream for global spatio-temporal scanning. The Hyper-GCN stream uses multi-granularity hypergraphs, with body-scale and part-scale hyperedges, and the Mamba stream uses bidirectional forward/backward aggregation together with stochastic layer-wise spatial shuffle regularization. The two streams are fused adaptively by

$$\alpha_m, \alpha_{hg} = \mathrm{softmax}(W_{\ell}[X^{m}_{\ell-1}, X^{hg}_{\ell-1}]), \qquad X_{\ell} = \alpha_m \odot X^{m}_{\ell-1} + \alpha_{hg} \odot X^{hg}_{\ell-1},$$

so that local physiological priors and global temporal coherence are balanced at each joint-time feature (Cui et al., 9 Apr 2025).

Medical-image variants realize the same local/global compromise with different modules. HC-Mamba uses an HC-SSM branch centered on SS2D and a convolutional branch built around dilated convolutions with a “sawtooth” dilation-rate schedule of $1,2,3,1$, followed by channel shuffle after branch concatenation. Depthwise separable convolution is inserted to reduce parameters and computational cost while preserving spatial localization (Xu, 2024). HyM-UNet adopts a hierarchical encoder in which shallow stages are CNN-based Residual Convolution Blocks and deep stages are Visual Mamba blocks with SS2D, while the Mamba-Guided Fusion Skip uses deep semantic features as gating signals to suppress shallow background noise (Chen et al., 22 Nov 2025).

The same motif extends to volumetric segmentation. HybridMamba introduces Slice–Local Mamba, which combines slice-oriented Mamba for global dependencies and local-oriented Mamba for local window traversals and across-slice continuity, then augments this with an FFT Gated Mechanism that fuses spatial and frequency-domain features through

$$g = \sigma\!\left( \mathrm{Conv}_{3\times 3\times 3}([x_s, x_{\mathrm{fre}}]) \right), \qquad x_{\mathrm{out}} = g \odot x_s + (1-g) \odot x_{\mathrm{fre}}.$$

Here again, the hybridization strategy is explicit: long-range modeling alone is treated as insufficient for precise boundaries and small-lesion fidelity (Wu et al., 18 Sep 2025).

4. Graph, geometric, and hyperspectral lineages

In graph learning, HeteGraph-Mamba generalizes the HyMamba idea from local/global fusion to heterogeneity-aware sequencing. It defines a heterogeneous graph $$\frac{d\mathbf{x}(t)}{dt} = A\,\mathbf{x}(t) + B\,\mathbf{u}(t), \qquad \mathbf{y}(t) = C\,\mathbf{x}(t) + D\,\mathbf{u}(t),$$0, constructs metapath-centered tokens, then performs two selective scans: an inner scan within each node type ordered by meta-path count, and an outer global scan across all types ordered by node degree. Type-specific linear projections and metapath attention preserve heterogeneous semantics before the Mamba scans are applied (Pan et al., 2024). This is structurally different from HGMamba, but the shared principle remains the same: selective SSMs are paired with a domain-specific organizing prior.

HMamba pushes the idea into geometry. It places the selective state space in the Lorentz model of hyperbolic space,

$$\frac{d\mathbf{x}(t)}{dt} = A\,\mathbf{x}(t) + B\,\mathbf{u}(t), \qquad \mathbf{y}(t) = C\,\mathbf{x}(t) + D\,\mathbf{u}(t),$$1

uses the exponential map at the origin to lift Euclidean embeddings into hyperbolic space, and updates hidden states through curvature-aware parallel transport and curvature-normalized discretization. The result is a “hyperbolic selective state space” designed for hierarchy-aware sequential recommendation (Zhang et al., 14 May 2025).

Hyperspectral work constitutes the densest concentration of HyMamba-like usage. HS-Mamba combines a dual-channel spatial-spectral encoder with a lightweight global inline attention branch. The DCSS-encoder uses non-overlapping patches and multi-groups Mamba to process spectral-priority and spatial-priority sequences, while the LGI-Att branch operates on the whole image to provide channel and spatial weights before gated fusion (Peng et al., 22 Apr 2025). HSRMamba, aimed at hyperspectral super-resolution, replaces naïve flattening with Local Spatial-Spectral Partitioning and a Global Spectral Reordering Mechanism based on spectral similarity, then applies bidirectional SSMs to restore both local and global spatial-spectral structure (Chen et al., 30 Jan 2025). GraphMamba complements this line by coupling a HyperMamba spectral encoder with SpatialGCN and Weighted Multi-hop Aggregation, using a Global Mask and AutoRes to manage spectral clutter and adaptive residual fusion (Yang et al., 2024).

The explicit HyMamba tracker for hyperspectral object tracking is built around Spectral State Integration and the Hyperspectral Mamba module. SSI propagates a recurrent spectral hidden state across both layer depth and time, while HSM uses forward, backward, and spectral directional scanning SSMs. Its Multi-Directional Fusion Module combines joint and hyperspectral activations through six element-wise interaction terms, thereby integrating temporal dependencies, cross-depth interactions, and spectral continuity directly from raw hyperspectral inputs (Gao et al., 10 Sep 2025).

5. Representative architectures and reported performance

Across domains, HyMamba-labeled or HyMamba-adjacent models are evaluated not merely as architectural novelties but as efficiency–accuracy trade-off mechanisms. The reported results are task-specific and not directly comparable across domains, but they illustrate how the naming pattern spans a wide methodological range.

Model	Task	Headline reported result
HGMamba-B (Cui et al., 9 Apr 2025)	3D human pose lifting	P1 errors of 38.65 mm on Human3.6M and 14.33 mm on MPI-INF-3DHP
HC-Mamba (Xu, 2024)	Medical image segmentation	ISIC18: mIoU 80.72%, DSC 89.26%; Synapse: mean DSC 81.58%, HD95 26.34 mm
HGMN (Pan et al., 2024)	Heterogeneous node classification	ogbn-mag 0.5763 ± 0.0043 accuracy; DBLP 0.9602 ± 0.0010 F1
HMamba (Zhang et al., 14 May 2025)	Sequential recommendation	3–11% improvement while retaining Mamba’s linear-time efficiency
HS-Mamba (Peng et al., 22 Apr 2025)	Hyperspectral image classification	OA 94.65±0.91, 96.43±1.35, 96.64±0.79, and 96.10±0.74 on four benchmarks
HyMamba (Gao et al., 10 Sep 2025)	Hyperspectral object tracking	HOTC2020: 73.0% AUC and 96.3% DP@20
HyM-UNet (Chen et al., 22 Nov 2025)	Skin lesion segmentation	IoU 81.82%, Dice 88.97%, HD 4.03 mm, Precision 90.91%
HybridMamba (Wu et al., 18 Sep 2025)	3D medical image segmentation	LC dataset: 75.34 Dice and 44.52 HD95

Efficiency claims are equally central. HGMamba-B reports 64.5G MACs versus MotionBERT’s 174.8G MACs at similar Human3.6M accuracy, while HC-Mamba reports 13.88M parameters in ablation and frames its design around reduced parameter count through depthwise separable convolution (Cui et al., 9 Apr 2025, Xu, 2024). HS-Mamba reports parameter counts from 177.26K to 236.64K across datasets and states 26–40% fewer FLOPs than MambaHSI on medium/high-resolution datasets, with about 52% faster inference on medium/high-resolution datasets (Peng et al., 22 Apr 2025). HybridMamba argues that selective scans plus limited FFT overhead preserve linear scaling in sequence length for volumetric segmentation (Wu et al., 18 Sep 2025).

These results do not imply a single performance profile for “HyMamba.” Rather, they show that the label consistently appears where Mamba is modified to recover structure that a plain 1D causal scan would otherwise underrepresent.

6. Limitations, misconceptions, and research directions

The first limitation is taxonomic. “HyMamba” is not a standardized architecture or benchmark entry, and conflating HGMamba, HC-Mamba, HMamba, and the hyperspectral tracker under one fixed definition obscures major differences in geometry, tokenization, and task formulation. A plausible implication is that future literature will either formalize the term more narrowly or abandon it in favor of domain-specific names.

The second limitation is methodological: most variants are introduced precisely because vanilla Mamba is order-sensitive or locality-deficient on non-sequential data. HGMamba notes that gains over transformer baselines are smaller on estimated 2D poses than on GT-2D and that the hypergraph topology is static even though hyperedge weights are learned (Cui et al., 9 Apr 2025). HeteGraph-Mamba identifies sensitivity to sequence ordering and the burden of predefined metapaths as open issues (Pan et al., 2024). HMamba fixes curvature $$\frac{d\mathbf{x}(t)}{dt} = A\,\mathbf{x}(t) + B\,\mathbf{u}(t), \qquad \mathbf{y}(t) = C\,\mathbf{x}(t) + D\,\mathbf{u}(t),$$2 in experiments and leaves broader curvature sensitivity and Riemannian optimization analysis for future work (Zhang et al., 14 May 2025).

The third limitation is domain dependence. HC-Mamba does not exhaustively describe decoder or head details, and its paper does not specify optimizer, learning-rate schedule, batch sizes, or epochs (Xu, 2024). HS-Mamba and HSRMamba both report sensitivity to patch size, group count, window size, or spectral similarity estimation (Peng et al., 22 Apr 2025, Chen et al., 30 Jan 2025). The hyperspectral tracking HyMamba is constrained by the scarcity of large-scale HS video datasets, which is reflected in its decision to freeze most of the pretrained backbone and train only ASD, SSI, and HS-specific patch embedding (Gao et al., 10 Sep 2025).

The research directions proposed across these papers are strikingly consistent. They include adaptive or learned hypergraph structures, smarter joint-time scanning orders, attention–SSM hybrids, explainable analysis of decision mechanisms, dynamic graph ordering, learned spectral affinity, 3D selective scans, multi-person or cross-view extensions, and broader deployment across additional modalities (Cui et al., 9 Apr 2025, Xu, 2024, Pan et al., 2024, Peng et al., 22 Apr 2025, Chen et al., 30 Jan 2025). Taken together, these directions reinforce the central encyclopedic point: HyMamba names a class of attempts to make selective state space models structurally aware, not a single canonical network.