Bidirectional Mamba Network

• Bidirectional Mamba Network is a design pattern using forward and reverse scans to integrate both past and future context for improved non-causal processing.
• It adapts the original causal Mamba formulation to various domains like vision, audio, and biomedical imaging by tailoring scanning directions and fusion methods.
• Empirical results across applications show that bidirectional architectures enhance performance while necessitating careful trade-offs between computational efficiency and model complexity.

Searching arXiv for papers on bidirectional Mamba networks and related variants across vision, audio, graphs, and sequence modeling. Bidirectional Mamba Network denotes a class of Mamba-based selective state-space architectures in which information is propagated in more than one scan direction, typically by pairing a forward scan with a reverse-order scan, or by extending that idea to multiple spatial, spectral, task, or volumetric axes. In the recent literature, the concept is used across image backbones, speech and music systems, medical imaging, recommendation, graphs, and scientific time-series analysis. This suggests that “Bidirectional Mamba Network” is best understood as a design pattern for adapting the originally causal, 1D Mamba formulation to non-causal or offline settings in which both earlier and later context are useful (Xu et al., 2024, Ibrahim et al., 11 Feb 2025).

1. Conceptual scope and defining rationale

Original Mamba is introduced in the visual surveys as a selective structured state-space model with linear scalability in sequence length, but its default formulation is causal and sequence-order dependent. In the vision setting, the surveys state that this causes a mismatch with non-causal image sequences, and motivates bidirectional or multi-directional scanning so that a token can aggregate information beyond the already scanned prefix (Xu et al., 2024, Ibrahim et al., 11 Feb 2025).

The literature uses several closely related meanings. In the narrowest sense, a bidirectional Mamba network runs one Mamba path in natural order and another on a reversed sequence, then fuses the two outputs. This is the clearest pattern in Vim-style blocks, GCAMba, MambaNet, BMACE, XLSR-Mamba, and several biomedical or audio systems (Ibrahim et al., 11 Feb 2025, He et al., 10 Nov 2025, Luan et al., 23 Jan 2026, Yuan et al., 5 Jan 2026, Xiao et al., 2024). In a broader sense, visual and volumetric systems generalize bidirectionality into multi-directional scan sets: VMamba performs bi-directional scanning along horizontal and vertical axes; BIM combines task-first and position-first scanning with forward and reversed task order; BiSegMamba creates forward and backward scans for each of three orthogonal 3D orientations (Xu et al., 2024, Cao et al., 28 Aug 2025, Zada et al., 29 May 2026).

Across application papers, bidirectionality is usually introduced when the task is described as offline, non-causal, or inherently spatial. The music-separation model TS-BSMAMBA2 is explicitly non-causal and uses bidirectional Mamba-2 because source separation can use both past and future context; ABS-Mamba argues that medical images are noncausal spatial fields; MambaNet states that subcarrier channel gains are non-causal; BiT-MamSleep uses both past and future EEG context for sleep staging (Bai et al., 2024, Yuan et al., 12 May 2025, Luan et al., 23 Jan 2026, Zhou et al., 2024).

2. State-space substrate and bidirectional constructions

The common substrate is the state-space model. The visual Mamba survey gives the continuous-time form

$$h'(t)=\mathbf{A}h(t)+\mathbf{B}x(t), \qquad y(t)=\mathbf{C}h(t),$$

with zero-order-hold discretization

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

and discrete recurrence

$$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$

The same survey states that Mamba makes the model selective by letting $$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$, so the effective dynamics become input-dependent (Xu et al., 2024).

Bidirectional variants preserve this substrate but alter the scan wrapper. In the Vim-style block summarized in the survey fragment, each direction $o \in \{\text{forward},\text{backward}\}$ computes direction-specific $\text{Conv1d}_o$, $B_o$, $C_o$, and $\Delta_o$, forms $\bar A_o$ and $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$0, applies

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

gates both directional outputs with $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$2, then sums them and adds a residual projection (Ibrahim et al., 11 Feb 2025). This is the canonical “two directional scans, one fused block” pattern.

Other papers make the bidirectional recurrence explicit. MambaNet defines a forward scan

$$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$3

and a backward scan

$$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$4

then fuses them by

$$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$5

before output gating and projection (Luan et al., 23 Jan 2026). LBMamba instead embeds a local backward recurrence inside the forward selective scan: $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$6 and then alternates global scan direction across layers through explicit sequence reversal (Zhang et al., 19 Jun 2025). This is not full bidirectionality in one layer, but an efficiency-oriented approximation.

A recurring feature is that the internal selective-SSM equations are often omitted once the architecture moves into domain-specific papers. Several works specify the forward/backward wrapper, the fusion rule, and the surrounding convolutions or projections, but not the low-level selective scan kernel, state size, or exact gating internals. This suggests that the field treats bidirectionality primarily as an architectural adaptation around an already accepted Mamba core.

3. Architectural motifs in the literature

One motif is the dual-path sequence block. ABS-Mamba reshapes a 2D feature map into a spiral-ordered sequence $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$7, constructs $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$8, applies two independent Mamba modules, and fuses the outputs through a residual convolutional block with $$\overline{\mathbf{A}}=\exp(\Delta\mathbf{A}), \qquad \overline{\mathbf{B}}=(\Delta\mathbf{A})^{-1}(\exp(\Delta\mathbf{A})-\mathbf{I})\Delta\mathbf{B},$$9 and $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$0 convolutions (Yuan et al., 12 May 2025). XLSR-Mamba’s DuaBiMamba uses two entire Mamba columns, one on the original utterance sequence and one on the reversed sequence, reverses the backward output back to original order, and concatenates the two directional outputs (Xiao et al., 2024). BMACE follows a similar high-level pattern: two Mamba blocks with opposite masking directions, concatenation, a fully connected layer to restore dimensionality, and residual connections (Yuan et al., 5 Jan 2026).

A second motif is bidirectionality along more than one axis. TS-BSMAMBA2 applies bidirectional Mamba-2 first along the temporal dimension $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$1 and then along the band dimension $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$2 inside BMAMBA2-DualNet, so the system is dual-axis bidirectional rather than merely temporal (Bai et al., 2024). TF-Mamba similarly places BiMamba in both a per-frame frequency-sequence module and a per-frequency time-sequence module, thereby factorizing time-frequency modeling into two bidirectional 1D scans (Xiao et al., 2024). BIM serializes multi-task dense-prediction features in task-first order and then in position-first order, while also running a backward branch that reverses task order; the two branches are finally concatenated along channels (Cao et al., 28 Aug 2025).

A third motif is task-aware or efficiency-aware departure from full reverse scanning. SIGMA’s PF-Mamba does not reverse the whole sequence; it reverses the first $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$3 items while preserving the last $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$4 items in original order, then fuses original and partially flipped Mamba outputs with an input-dependent Dense Selective Gate (Liu et al., 2024). LBMamba avoids a second full sweep and confines the backward recurrence to local chunks of size $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$5, relying on cross-layer direction alternation to recover a global receptive field over depth (Zhang et al., 19 Jun 2025).

A fourth motif is orientation-specific bidirectionality in 3D. BiSegMamba flattens each feature tensor into three orthogonal views $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$6, constructs reversed sequences for all three, concatenates the six sequences along the batch dimension, processes them by one Mamba call, then fuses forward and backward outputs per orientation with learnable channel-wise weights before a second adaptive fusion across orientations (Zada et al., 29 May 2026).

4. Representative instantiations across domains

The breadth of the design pattern is visible in recent application papers.

Domain	Representative architecture	Bidirectional mechanism
Music source separation	TS-BSMAMBA2 (Bai et al., 2024)	Bidirectional Mamba-2 along time $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$7 and band $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$8; two-stage mask plus residual refinement
Medical image translation	ABS-Mamba (Yuan et al., 12 May 2025)	Spiral sequence plus reversed sequence, two Mamba branches, residual convolutional fusion
Speech anti-spoofing	XLSR-Mamba (Xiao et al., 2024)	Dual-column Mamba on original and reversed utterance features, concatenation fusion
Sound source localization	TF-Mamba (Xiao et al., 2024)	BiMamba in both frequency-sequence and time-sequence paths; directional outputs averaged
Sequential recommendation	SIGMA / PF-Mamba (Liu et al., 2024)	Original order plus partially flipped prefix, DS Gate weighting, FE-GRU parallel branch
3D medical segmentation	BiSegMamba (Zada et al., 29 May 2026)	Forward/backward scans for each of $$h_t=\overline{\mathbf{A}}h_{t-1}+\overline{\mathbf{B}}x_t, \qquad y_t=\mathbf{C}h_t.$$9 orientations, then adaptive directional fusion

Other domains confirm that the same idea is not tied to one modality. BiT-MamSleep uses separate forward and backward temporal Mamba paths over EEG features, gates both with the same $$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$0, and fuses them with an output projection and residual connection (Zhou et al., 2024). The anomalous-diffusion model Bi-Mamba processes original and time-flipped trajectory features in two Mamba branches, concatenates the outputs, and feeds them to a feedforward layer before downstream segmentation and regression (Lavaud et al., 2024). DMbaGCN contains a Global Context-Aware Mamba branch

$$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$1

which is explicitly bidirectional over the serialized node sequence, even though the overall graph model is dual-path rather than a single bidirectional encoder (He et al., 10 Nov 2025). MambaNet applies forward and backward selective scans because OFDM subcarrier gains are described as non-causal (Luan et al., 23 Jan 2026).

This distribution of examples suggests that bidirectional Mamba is not domain-bound. What changes from paper to paper is the definition of the sequence itself: temporal samples, image tokens, band sequences, node trajectories across GNN depth, task-ordered dense features, or flattened 3D voxels.

5. Empirical performance and efficiency

The strongest evidence is domain-specific rather than universal. In music source separation, TS-BSMAMBA2 (SS) reports 9.56 cSDR / 8.71 uSDR average on MUSDB18-HQ, compared with 8.59 cSDR / 8.14 uSDR for the first stage alone; its efficiency table reports 35.52M parameters and 212.11 G/s MACs, compared with 146.57M and 611.01 G/s MACs for BSRNN (Bai et al., 2024).

In medical image translation, ABS-Mamba reports SSIM 0.935±0.009 and PSNR 31.70±0.56 on BraTS2019 T1-to-T2 translation. Its ablation indicates that the configuration with SIE, 2 BRMN, and RFFN reaches 0.935 SSIM, while 1 BRMN + SIE + RFFN gives 0.926 and 3 BRMN + SIE + RFFN gives 0.931, suggesting an optimum at two BMRN modules in that setup (Yuan et al., 12 May 2025).

In speech and spatial audio, the bidirectional effect is directly quantified. XLSR+DuaBiMamba reaches LA EER 0.93, LA min t-DCF 0.208, DF EER 1.88, and average EER 1.41, improving over plain XLSR+Mamba at average EER 1.79. TF-Mamba’s best configuration reports ACC($$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$2) 98.9, ACC($$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$3) 96.9, and MAE 2.52°, whereas the w/o BiMamba ablation gives 97.1, 93.6, and 2.84° (Xiao et al., 2024, Xiao et al., 2024).

The efficiency–accuracy trade-off is particularly explicit in LBMamba. Compared to vanilla Mamba’s CUDA kernel, LBMamba increases FLOPs by about 27% while reducing throughput by only 1.9\%-2.3\%, with unchanged GPU memory. At matched throughput, widened LBVim variants improve over Vim by 0.8% to 1.6% top-1 on ImageNet-1K, 0.6% to 2.7% mIoU on ADE20K, and 0.9 AP$$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$4 plus 1.1 AP$$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$5 on COCO (Zhang et al., 19 Jun 2025). The paper’s argument is not that local bidirectionality matches full bidirectionality exactly, but that the saved runtime can be reinvested in model size more effectively.

BiSegMamba shows the same trade-off in volumetric vision. On BraTS2023, compared with SegMamba-V2, parameters drop from 138.77M to 47.38M and FLOPs from 1853.19G to 410.28G. In the ACDC ablation, moving from + Patch Merging to + Bi-ToOM improves DSC 92.20 → 92.35 and HD95 1.16 → 1.11, while the subsequent addition of adaptive directional fusion improves to DSC 92.53 and HD95 1.08 (Zada et al., 29 May 2026).

6. Ambiguities, misconceptions, and open directions

The literature does not use the term in one uniform way. Some papers describe a conventional forward/backward inference architecture; others use partial reversal, local backward windows, task-order reversal, or bidirectional distillation. TransMamba, for example, is primarily a Transformer-to-Mamba adaptation framework whose bidirectional contribution is an Adaptive Bidirectional distillation strategy for bidirectional visual Mamba students, rather than a newly proposed bidirectional inference block (Chen et al., 21 Feb 2025). This suggests that “Bidirectional Mamba Network” should be read as a family resemblance rather than a single canonical module.

A second recurring issue is incomplete specification. TS-BSMAMBA2 states “the superiority of bidirectional Mamba-2” but does not provide a separate ablation against unidirectional Mamba-2, and it does not specify the exact internal bidirectional fusion rule inside BMAMBA2 (Bai et al., 2024). ABS-Mamba introduces a spiral transformation matrix $$\mathbf{B},\mathbf{C},\Delta = Linear(\boldsymbol{x})$$6 and a bidirectional Mamba residual network, but does not give the explicit spiral indexing algorithm or all low-level Mamba hyperparameters (Yuan et al., 12 May 2025). DiM-3D states that each DiM block uses bidirectional sequence modeling and merges the two directions, yet leaves the exact fusion operator unspecified (Mo, 2024). BiT-MamSleep presents an inconsistency between an averaging-style bidirectional equation and an algorithm that performs gated summation plus projection and residual addition (Zhou et al., 2024). BMACE, as a short extended abstract, omits the internal Mamba equations and several architectural hyperparameters (Yuan et al., 5 Jan 2026).

A third issue is that bidirectionality is not always isolated experimentally. TS-BSMAMBA2, ABS-Mamba, and DiM-3D all present strong end-to-end gains, but the provided text does not include a clean bidirectional-versus-unidirectional ablation for the core Mamba block itself (Bai et al., 2024, Yuan et al., 12 May 2025, Mo, 2024). By contrast, TF-Mamba, XLSR-Mamba, BiT-MamSleep, SIGMA, and BiSegMamba do provide more direct evidence that the bidirectional wrapper contributes materially to performance (Xiao et al., 2024, Xiao et al., 2024, Zhou et al., 2024, Liu et al., 2024, Zada et al., 29 May 2026).

Finally, bidirectionality and efficiency remain in tension. Full reverse sweeps add computation and may erode Mamba’s efficiency advantage. LBMamba is the clearest response: it replaces a full backward sweep with a local backward recurrence in per-thread registers and recovers global context across layers via sequence reversal (Zhang et al., 19 Jun 2025). A plausible implication is that future bidirectional Mamba research will continue to separate exact non-causal bidirectionality from hardware-aware approximations, and will standardize how scan order, fusion, and ablation are reported.