Tri-Mamba Architecture Overview

• Tri-Mamba architecture is a design pattern that decomposes neural processing into three coordinated streams to capture local, global, or orthogonal contextual features.
• It is applied across diverse domains—such as speaker verification, 3D medical segmentation, and LiDAR world modeling—with each variant tailoring the three-way integration to its data geometry.
• The approach yields notable performance gains and computational efficiency improvements by reducing errors and FLOPs while adapting to domain-specific use cases.

Searching arXiv for the specified and related Tri-Mamba / Mamba papers to ground the article in current literature. Tri-Mamba architecture denotes a family of Mamba-derived neural designs in which three coordinated state-space processing streams, views, or context sources are used to improve representation quality while avoiding the quadratic cost of full 3D or long-sequence self-attention. In current arXiv usage, the label does not identify a single canonical module. It includes the Tri-Mamba block in MASV for speaker verification, where local bidirectional and global Mamba context are fused inside an ECAPA-TDNN pipeline; Tri-Plane Mamba adapters for adapting frozen SAM encoders to 3D medical volumes; the bidirectional tri-oriented Ortho Mamba block in BiSegMamba; and the tri-path deformable Mamba module in GEM for LiDAR world modeling (Liu et al., 2024, Wang et al., 2024, Shahraki et al., 31 Jan 2026, Zada et al., 29 May 2026, Wu et al., 8 May 2026).

1. Terminological scope and common state-space basis

Across these systems, the recurrent commonality is not a fixed topology but a three-part decomposition aligned with data geometry or signal semantics. In MASV, the three-way organization is local bidirectional context plus global context inside a residual block. In Tri-Plane Mamba for 3D medical imaging, the triad is formed by three orthogonal plane projections. In BiSegMamba, it is three orthogonal scan orientations together with forward and backward sequence processing. In GEM, it is a tri-path split into generic, dynamic, and static feature streams.

System	Three-way organization	Integration point
MASV	LCB-Mamba local context + global Mamba	MFA stages of ECAPA-TDNN
TP-Mamba / TP_MFGC	Three orthogonal planes or plane scans	Residual adapters in frozen SAM ViT
Bi-ToOM	Depth, width, and height scans with bidirectional fusion	Deeper encoder stages of BiSegMamba
GEM Tri-Mamba	Generic, dynamic, and static deformable paths	Four-block latent world-model stack

A formal SSM description is stated explicitly in the adapter-based Mamba-SAM formulation: in continuous time, $h'(t)=Ah(t)+Bx(t)$ and $y(t)=Ch(t)+Dx(t)$; after discretization, $h_k=\bar A h_{k-1}+\bar B x_k$ and $y_k=\bar C h_k+\bar D x_k$. In Mamba, the transition and projection terms become input-dependent, and the per-time-step update in each plane is written as $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$, $y_t^p=C_t^p h_t^p + D u_t^p$, with $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$ (Shahraki et al., 31 Jan 2026).

2. Local-global Tri-Mamba in speaker verification

In MASV, Tri-Mamba is a block-level replacement for the SE-Res2 unit inside ECAPA-TDNN’s Multi-Frame Aggregation stages. The overall pipeline remains front-end Conv1D, MFA stages, Attentive Statistics Pooling, and an embedding head, but the conventional dilated Res2 blocks are replaced by Mamba-derived modules. Each Tri-Mamba block consists, in series, of a $1\times1$ Conv-BN-ReLU projection, a Local Context Bidirectional Mamba (LCB-Mamba), a second single-direction Mamba layer for global context, and a final $1\times1$ Conv-BN-ReLU followed by Squeeze-and-Excitation; the block output is added back to the input through a residual skip. For input $X\in\mathbb{R}^{T\times C}$, the local operator is defined over $y(t)=Ch(t)+Dx(t)$0 frames as $y(t)=Ch(t)+Dx(t)$1, the global context is $y(t)=Ch(t)+Dx(t)$2, and the fusion step is $y(t)=Ch(t)+Dx(t)$3 (Liu et al., 2024).

The LCB-Mamba itself performs forward and backward state-space passes inside a local window, using pre-computed context vectors from a sliding buffer, while the global Mamba applies sequence-level reasoning without downsampling and with constant feature-map dimensions. Hyperparameter details given for the block include channels $y(t)=Ch(t)+Dx(t)$4 such as $y(t)=Ch(t)+Dx(t)$5 or $y(t)=Ch(t)+Dx(t)$6, InstanceNorm before each Mamba, a global Mamba with on-the-fly SSM kernels of length $y(t)=Ch(t)+Dx(t)$7, and an SE ratio $y(t)=Ch(t)+Dx(t)$8. The integration preserves the $y(t)=Ch(t)+Dx(t)$9 interface inside each MFA stage. In the reported ablation for $h_k=\bar A h_{k-1}+\bar B x_k$0, baseline ECAPA-TDNN yields $h_k=\bar A h_{k-1}+\bar B x_k$1 and $h_k=\bar A h_{k-1}+\bar B x_k$2; adding LCB-Mamba reduces EER to $h_k=\bar A h_{k-1}+\bar B x_k$3 and DCF to $h_k=\bar A h_{k-1}+\bar B x_k$4; adding Tri-Mamba further reduces EER to $h_k=\bar A h_{k-1}+\bar B x_k$5 and DCF to $h_k=\bar A h_{k-1}+\bar B x_k$6; and full MASV reaches $h_k=\bar A h_{k-1}+\bar B x_k$7 and $h_k=\bar A h_{k-1}+\bar B x_k$8. The same ablation states that Tri-Mamba alone confers a consistent $h_k=\bar A h_{k-1}+\bar B x_k$9–$y_k=\bar C h_k+\bar D x_k$0 relative reduction in EER by integrating global context with local state-space modeling. Compute growth is modest relative to the baseline: for $y_k=\bar C h_k+\bar D x_k$1, the base ECAPA model has $y_k=\bar C h_k+\bar D x_k$2M parameters and $y_k=\bar C h_k+\bar D x_k$3 GFLOPS, while full MASV has $y_k=\bar C h_k+\bar D x_k$4M parameters and $y_k=\bar C h_k+\bar D x_k$5 GFLOPS (Liu et al., 2024).

3. Tri-plane adapters for frozen SAM encoders

The best-known medical-imaging use of the term is Tri-Plane Mamba, introduced as an adapter for Segment Anything Model backbones in 3D CT segmentation. The design goal is explicit: preserve a frozen pretrained 2D ViT backbone, add lightweight adapters that capture local depth-wise context through multi-scale 3D convolutions, and capture long-range non-causal depth-level representation through a tri-plane Mamba module. In the original formulation, each ViT block contains frozen multi-head self-attention with LoRA, a frozen MLP, and a trainable TP-Mamba adapter. After a channel-reduction Conv3D, four depth-dilated convolutions with dilation scales $y_k=\bar C h_k+\bar D x_k$6 produce a multi-scale tensor $y_k=\bar C h_k+\bar D x_k$7. Tri-plane projection then sums along orthogonal axes to produce three 2D-plane sequences,

$y_k=\bar C h_k+\bar D x_k$8

which are flattened into $y_k=\bar C h_k+\bar D x_k$9, $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$0, and $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$1, passed through three lightweight Mamba blocks, reshaped back, summed, and expanded to the original channel count. The paper contrasts this with naïve 3D self-attention over $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$2 tokens, which has $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$3 FLOPs; for a $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$4 setting, it reports $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$5 GFlops for naïve 3D attention versus $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$6 GFlops per block for TP-Mamba, corresponding to a $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$7 speed-up. With example settings $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$8, $h_t^p=A_t^p h_{t-1}^p+B_t^p u_t^p$9, and kernel size $y_t^p=C_t^p h_t^p + D u_t^p$0, total added parameters are reported as $y_t^p=C_t^p h_t^p + D u_t^p$1M, which is stated as below $y_t^p=C_t^p h_t^p + D u_t^p$2 of the ViT. On BTCV CT, the method is reported to achieve state-of-the-art performance, and with only three CT training samples it attains a Dice score up to $y_t^p=C_t^p h_t^p + D u_t^p$3 higher than conventional 3D segmentation networks (Wang et al., 2024).

A later adapter-based Mamba-SAM framework keeps a frozen SAM ViT-B encoder of approximately $y_t^p=C_t^p h_t^p + D u_t^p$4M weights and injects a small 3D-aware TP-Mamba adapter after each ViT block in residual form, $y_t^p=C_t^p h_t^p + D u_t^p$5. In this formulation, tri-plane processing is combined with either a small 3D CNN local branch or, in the TP_MFGC variant, a Multi-Frequency Gated Convolution branch that replaces the 3D CNN with joint spatial-frequency processing based on 3D DCT, channel-wise pooling, adaptive gating, modulation of frequency components, and inverse DCT reconstruction. The global branch performs three orthogonal plane scans—axial, coronal, and sagittal—each yielding a feature volume that is concatenated with the local branch output and projected back to the SAM token dimension. No cross-attention is added inside TP-Mamba; fusion with the frozen encoder is by simple residual addition. For the TP_MFGC model, Table 5 reports $y_t^p=C_t^p h_t^p + D u_t^p$6M total parameters, approximately $y_t^p=C_t^p h_t^p + D u_t^p$7M trainable parameters, inference speed of $y_t^p=C_t^p h_t^p + D u_t^p$8 FPS per $y_t^p=C_t^p h_t^p + D u_t^p$9 3D volume on an A100 with mixed precision, and peak VRAM of $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$0 GB. On ACDC, the TP_MFGC variant reports Dice scores of $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$1 for RV/Myo/LV and mean Dice $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$2, whereas the dual-branch MambaSAM-Base model reports mean Dice $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$3 and UNet++ reports mean Dice $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$4. The paper explicitly frames TP_MFGC as trading a $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$5 drop in mean Dice for a $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$6 increase in throughput relative to the dual-branch model (Shahraki et al., 31 Jan 2026).

4. Bidirectional tri-oriented volumetric scanning

BiSegMamba generalizes the tri-plane intuition into a bidirectional tri-oriented Ortho Mamba block, abbreviated Bi-ToOM, for 3D medical image segmentation. Bi-ToOM is placed in the deeper encoder stages, downstream of a Progressive Compacting Stem and early-stage Multi-Scale Spatial Mixer blocks. Its defining operation is three-axis scanning with explicit forward and backward sequence modeling. Given an input tensor $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$7, the block constructs axial, coronal, and sagittal views via axis permutations, flattens each into a sequence of length $$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$8, creates reversed copies of all three sequences, concatenates the resulting six streams along the batch dimension, and applies one normalized Mamba operator to all six in parallel:

$$p\in\{\text{Axial},\text{Coronal},\text{Sagittal}\}$$9

After splitting the output back into six groups, the backward streams are reversed to restore original order, and forward and backward results are fused channel-wise for each orientation,

$1\times1$0

where the weights are obtained by a softmax over learned logits. The three orientation-specific feature maps are then fused by Adaptive Directional Fusion, which predicts channel-wise weights over the depth, width, and height branches, applies a $1\times1$1 projection and squeeze-and-excitation, and returns a residual update $1\times1$2 (Zada et al., 29 May 2026).

BiSegMamba’s encoder uses MSSM blocks in stages 1 and 2 for local mixing and Bi-ToOM blocks in stages 3 and 4 for global dependency modeling, with $1\times1$3 patch merging between stages. The paper identifies three shortcomings in earlier volumetric Mamba designs—repeated high-resolution scanning, forward-only sequential modeling, and fixed directional summation—and positions Bi-ToOM and ADF as direct responses to those issues. Reported experiments cover a carotid CTA dataset and the BraTS2023, ACDC, and AMOS-CT benchmarks. Relative to SegMamba-V2, the paper states slightly better performance on BraTS2023, clear improvements on ACDC and the carotid dataset, and up to $1\times1$4 FLOPs reduction (Zada et al., 29 May 2026).

5. Tri-path deformable scanning in LiDAR world models

In GEM, Tri-Mamba takes a different semantic form. The model first tokenizes raw LiDAR sweeps into compact range-map latents, disentangles tokenized features into dynamic and static components in an unsupervised way, and then applies a four-block Tri-Mamba stack. Each Tri-Mamba block carries three streams of identical shape $1\times1$5: a generic feature $1\times1$6 for overall scene context, a dynamic feature $1\times1$7 emphasizing frame-to-frame variation, and a static feature $1\times1$8 emphasizing temporally stable regions. Correspondingly, three scan trajectories are defined in continuous 3D coordinate space: a canonical generic path $1\times1$9, a dynamic path $1\times1$0, and a static path $1\times1$1. For each branch $1\times1$2, the generic feature is bilinearly interpolated along the corresponding path and then processed by one deformable Mamba operation,

$1\times1$3

Fusion is performed by a two-stage gating network. First, dynamic and static outputs are fused,

$1\times1$4

and then the generic stream is updated by

$1\times1$5

The offset MLPs are specified as two Linear layers $1\times1$6 with ReLU and Tanh, and each deformable Mamba block uses hidden dimension $1\times1$7 and state dimension $1\times1$8 (Wu et al., 8 May 2026).

The complete GEM pipeline includes 3D-conv extractors for disentangled streams, an initial gated fusion step before the four Tri-Mamba blocks, a diffusion noise-prediction head, and a decoder back to range maps and then point clouds. The stated rationale is that separate deformable scan trajectories let the model allocate state-space memory differently to moving objects and static background while retaining a generic fallback path. In the reported ablations, removing either dynamic or static deformable branches sharply degrades both Chamfer and $1\times1$9 errors, and replacing the design with a single-path Vision Mamba is reported as approximately $X\in\mathbb{R}^{T\times C}$0 worse (Wu et al., 8 May 2026).

6. Comparative interpretation, trade-offs, and misconceptions

A common misconception is that Tri-Mamba denotes a single standardized architecture. The literature summarized here shows otherwise. In MASV, the triadic structure is local bidirectional context plus global context inside an audio verification block. In TP-Mamba, it is three orthogonal plane projections or scans inside a frozen SAM adaptation framework. In Bi-ToOM, it is three scan orientations with bidirectional sequence modeling and orientation-aware fusion. In GEM, it is a semantic split into generic, dynamic, and static deformable paths (Liu et al., 2024, Wang et al., 2024, Zada et al., 29 May 2026, Wu et al., 8 May 2026).

A second misconception is that Tri-Mamba invariably means “three directional scans.” That description fits the tri-plane and tri-oriented medical-imaging variants, but not MASV’s local-global fusion design and not GEM’s generic-dynamic-static branching. A third misconception is that all such models are direct replacements for transformers. The medical-imaging TP-Mamba variants are explicitly adapters attached to a frozen SAM ViT, sometimes with LoRA on Q, K, and V projections, whereas MASV replaces internal ECAPA-TDNN blocks, BiSegMamba is a full segmentation backbone, and GEM inserts Tri-Mamba inside a latent diffusion world model (Shahraki et al., 31 Jan 2026, Liu et al., 2024, Zada et al., 29 May 2026, Wu et al., 8 May 2026).

The trade-off profile is likewise domain-specific. MASV increases the ECAPA baseline from $X\in\mathbb{R}^{T\times C}$1M parameters and $X\in\mathbb{R}^{T\times C}$2 GFLOPS to $X\in\mathbb{R}^{T\times C}$3M parameters and $X\in\mathbb{R}^{T\times C}$4 GFLOPS while improving EER from $X\in\mathbb{R}^{T\times C}$5 to $X\in\mathbb{R}^{T\times C}$6 (Liu et al., 2024). The TP_MFGC adapter variant improves throughput to $X\in\mathbb{R}^{T\times C}$7 FPS but yields mean Dice $X\in\mathbb{R}^{T\times C}$8, whereas the dual-branch MambaSAM-Base reaches $X\in\mathbb{R}^{T\times C}$9 mean Dice at $y(t)=Ch(t)+Dx(t)$00 FPS (Shahraki et al., 31 Jan 2026). BiSegMamba emphasizes a stronger accuracy-efficiency balance through up to $y(t)=Ch(t)+Dx(t)$01 FLOPs reduction relative to SegMamba-V2 (Zada et al., 29 May 2026). GEM reports that removing specialized branches degrades Chamfer and $y(t)=Ch(t)+Dx(t)$02 errors and that a single-path Vision Mamba is about $y(t)=Ch(t)+Dx(t)$03 worse (Wu et al., 8 May 2026). This suggests that Tri-Mamba is best understood as a design pattern for selecting three complementary long-range scanning views, not as a fixed block diagram. The three branches are chosen to match the dominant structure of the target modality: temporal locality and global sequence context in speech, orthogonal volumetric context in medical images, or dynamic-static scene decomposition in LiDAR world modeling.