Dynamic Tree Scan in UIS-Mamba

Updated 4 July 2026

Dynamic Tree Scan is a vision-specific adaptive tokenization method that dynamically offsets and scales patches to align token support with complex underwater objects.
It employs a two-stage process—adaptive graph deformation and dynamic graph pruning—to construct a weighted 4-connected graph and derive a minimum spanning tree for guiding the scan.
Empirical ablations demonstrate that integrating DTS boosts segmentation metrics, notably increasing mAP and accuracy in challenging underwater instance segmentation tasks.

Dynamic Tree Scan (DTS) is not a single, universally fixed term across the literature. In the sources considered here, its explicit use as Dynamic Tree Scan appears in the computer-vision method UIS-Mamba, where DTS is a module for underwater instance segmentation that dynamically offsets and scales patches, constructs a weighted $4$-connected graph, and uses a minimum spanning tree (MST) to guide scanning within a Mamba-based backbone (Cong et al., 1 Aug 2025). The acronym is simultaneously overloaded elsewhere, including Dyck tiling strip bijection, Dynamic Transaction Storage, Diffusion Tree Sampling, Decoding Tree Sketching, and Digital Twin Synchronization, so any technical discussion of DTS requires immediate contextual disambiguation (Shigechi, 2019, Long et al., 2023, Jain et al., 25 Jun 2025, Xu et al., 1 Nov 2025, Sammartino, 2 Jun 2026).

1. Terminology and disambiguation

The acronym DTS has multiple established meanings in recent work. In the material examined here, only one source uses the phrase Dynamic Tree Scan as the formal name of a method: the UIS-Mamba paper on underwater instance segmentation (Cong et al., 1 Aug 2025). Other works use the same acronym for unrelated concepts in combinatorics, blockchain systems, large-model inference, diffusion-model alignment, and digital twins.

Meaning of DTS	Context	Paper
Dynamic Tree Scan	Underwater instance segmentation with Mamba	(Cong et al., 1 Aug 2025)
Dyck tiling strip bijection	Combinatorics of Dyck tilings	(Shigechi, 2019)
Dynamic Transaction Storage	Blockchain transaction placement	(Long et al., 2023)
Diffusion Tree Sampling / Search	Inference-time alignment of diffusion models	(Jain et al., 25 Jun 2025)
Decoding Tree Sketching	Large reasoning model decoding	(Xu et al., 1 Nov 2025)
Digital Twin Synchronization	6G semantic twin synchronization, as SA-DTS	(Sammartino, 2 Jun 2026)

This terminological overlap matters because several of these methods also involve trees, dynamic updates, or scan-like procedures, yet they address different mathematical objects. The UIS-Mamba usage is a vision-specific module name rather than a general umbrella term for all dynamic tree traversal methods. This suggests that, at present, “Dynamic Tree Scan” is best treated as a local method designation within a particular segmentation architecture rather than as a settled cross-domain algorithmic family.

2. Problem setting in underwater instance segmentation

In UIS-Mamba, DTS is introduced to address a specific weakness of applying Mamba-style state space models to underwater instance segmentation. The paper argues that existing vision-Mamba variants rely on fixed patches, even when they alter scan order. According to that account, merely changing raster, directional, or windowed traversal does not resolve the underlying problem of semantic cutoff due to patch-fixed chunking in the proximity region (Cong et al., 1 Aug 2025).

The underwater setting amplifies this issue. The cited challenges are severely underwater color distortion, blurred instance boundaries, discontinuous object interiors, and complex background interference. In that regime, a rigid patch may mix foreground and background or split a semantically coherent object part across neighboring tokens before sequential modeling even begins. DTS is intended to preserve the internal continuity of the instance objects by allowing patches to dynamically offset and scale, so that token support aligns more closely with object structure rather than with a fixed image grid (Cong et al., 1 Aug 2025).

The module is embedded in UIS-Mamba, described as the first Mamba-based underwater instance segmentation model. Within that architecture, DTS supplies an adaptive scan structure, while a companion module, Hidden State Weaken (HSW), suppresses interference from complex underwater backgrounds through an Ncut-based hidden state weakening mechanism. The backbone outputs are then passed to an FPN and to the same detection and segmentation heads as WaterMask (Cong et al., 1 Aug 2025).

3. Core mechanism and architectural role

DTS operates in two named stages: Adaptive Graph Deformation and Dynamic Graph Pruning. The starting point is a patch set $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ , over which a 4-connected graph is built, with one patch per node and $4$-neighborhood adjacency (Cong et al., 1 Aug 2025).

In the deformation stage, each patch predicts a dynamic offset $(\Delta x, \Delta y)$ and dynamic scaling $(\Delta w, \Delta h)$ . The stated purpose is to move the patch center toward more relevant local content and to resize the patch so that it better captures different parts of underwater instances. The deformed patch $\tilde{\mathbf p}$ is then generated with a bilinear interpolation kernel $G(\cdot)$ , which the paper says preserves gradient continuity at object edges (Cong et al., 1 Aug 2025).

In the pruning stage, DTS computes edge weights on the deformed graph using both Euclidean distance between deformed patch centers and cosine similarity between deformed patch features, with a learnable tradeoff parameter $\alpha$ . From this weighted graph, the method extracts a minimum spanning tree using a Contractive Boruvka algorithm. The paper characterizes this tree as the structure that guides scanning and endows the state space model with a dynamic local receptive field (Cong et al., 1 Aug 2025).

Architecturally, DTS is not a post-processing routine. It is part of the backbone-side Dynamic Tree Topology SSM inside UIS-Mamba. Its graph and MST are also reused by HSW for graph partitioning and hidden-state suppression, so the tree structure is both a scan guide and a substrate for later foreground-background separation (Cong et al., 1 Aug 2025).

4. Mathematical formulation

The reported formulation for the deformation parameters is

$(\Delta x, \Delta y) = \tanh\!\big(\mathbf W_{\text{offset}} f_p(\mathbf p)\big), \qquad (\Delta w, \Delta h) = \operatorname{Softplus}\!\big(\mathbf W_{\text{scale}} f_p(\mathbf p) + \mathbf b\big),$

where $f_p(\mathbf p)$ is a dense prediction function over a patch, $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 0 and $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 1 are learnable projections, and $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 2 is a bias term (Cong et al., 1 Aug 2025). The transformed patch is then written as

$\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 3

with $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 4 the original patch center and $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 5 the bilinear interpolation operator (Cong et al., 1 Aug 2025).

The dynamic edge weight between neighboring deformed patches is reported as

$\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 6

where $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 7 and $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 8 denote deformed patch centers and $\mathcal{P} \in \mathbb{R}^{H \times W \times C}$ 9 balances geometry and semantics (Cong et al., 1 Aug 2025). The tree-selection objective is written as

$4$0

with $4$1 the weighted deformed graph (Cong et al., 1 Aug 2025).

The broader Mamba-style state update used in the architecture is given in standard selective state space form as

$4$2

However, the paper does not provide an explicit traversal rule for linearizing the MST into a scan sequence, nor does it give a DTS-specific asymptotic complexity analysis. The exact stage-by-stage placement of DTS across backbone levels is likewise not enumerated. These omissions matter because the module name foregrounds “scan,” yet the published description is more explicit about patch deformation, graph weighting, and MST construction than about the final tree-traversal kernel itself (Cong et al., 1 Aug 2025).

5. Empirical performance and ablation evidence

The clearest isolated evidence for DTS comes from the UIIS ablation reported for the Mamba backbone baseline. With Mamba only, the paper reports $4$3, $4$4, and $4$5. Adding DTS raises these values to $4$6, $4$7, and $4$8, respectively. In the same ablation, HSW only yields $4$9, $(\Delta x, \Delta y)$ 0, and $(\Delta x, \Delta y)$ 1, and combining both modules gives $(\Delta x, \Delta y)$ 2, $(\Delta x, \Delta y)$ 3, and $(\Delta x, \Delta y)$ 4 (Cong et al., 1 Aug 2025).

A more granular DTS ablation decomposes the module into offset, scale, and dynamic-weight components. Relative to the $(\Delta x, \Delta y)$ 5 $(\Delta x, \Delta y)$ 6 baseline, offset only yields $(\Delta x, \Delta y)$ 7, scale only yields $(\Delta x, \Delta y)$ 8, offset + scale yields $(\Delta x, \Delta y)$ 9, and offset + scale + dynamic weights/MST yields $(\Delta w, \Delta h)$ 0. The paper interprets this as evidence that offset and scale are complementary and that the spatial-semantic weighting step contributes additional improvement (Cong et al., 1 Aug 2025).

At the full-system level, UIS-Mamba is reported to achieve state-of-the-art performance on both UIIS and USIS10K while maintaining a low number of parameters and computational complexity. Against WaterMask R-CNN (ResNet-50), the reported numbers are $(\Delta w, \Delta h)$ 1 versus $(\Delta w, \Delta h)$ 2 $(\Delta w, \Delta h)$ 3 on UIIS, $(\Delta w, \Delta h)$ 4 versus $(\Delta w, \Delta h)$ 5 $(\Delta w, \Delta h)$ 6 on class-agnostic USIS10K, and $(\Delta w, \Delta h)$ 7 versus $(\Delta w, \Delta h)$ 8 $(\Delta w, \Delta h)$ 9 on multi-class USIS10K (Cong et al., 1 Aug 2025). Those gains are attributable to UIS-Mamba as a whole rather than to DTS alone, but the component studies identify DTS as a substantial part of the improvement.

The qualitative discussion associates the method with better recovery of hidden or difficult instances, more accurate boundaries and details, and stronger delineation of salient shapes for categories such as aquatic plants, reefs, wrecks, fish, and starfish. No dedicated visualization of learned tree traversals or MST scan paths is described in the provided material, so the qualitative evidence is presented mainly at the segmentation-output level rather than at the internal graph-construction level (Cong et al., 1 Aug 2025).

DTS in UIS-Mamba should not be conflated with other “dynamic tree” methods in the broader literature. It is distinct from dynamic-search data structures for tree-like partial orders such as the Line-Leaf Tree (Heeringa et al., 2010), from batch-parallel dynamic-tree query frameworks based on RC trees (Ikram et al., 19 Jun 2025), from latent-state Differentiable Tree Search in reinforcement learning (Mittal et al., 2024), and from inference-time search over diffusion trajectories in Diffusion Tree Sampling and Diffusion Tree Search (Jain et al., 25 Jun 2025). Those methods all involve trees, traversal, or dynamic updates, but they target different objects: ordered sets, forests under edge updates, latent planning trees, or diffusion chains rather than adaptive patch graphs for visual state-space modeling.

It is also important not to confuse DTS with unrelated acronym expansions such as Dynamic Transaction Storage in blockchain (Long et al., 2023), Dyck tiling strip bijection in combinatorics (Shigechi, 2019), or Digital Twin Synchronization in the 6G semantic communication framework SA-DTS (Sammartino, 2 Jun 2026). The acronym collision is especially strong because some of those works also describe graph- or tree-like update mechanisms, but they do not define the UIS-Mamba module.

Within its own paper, DTS has visible limitations. The published description does not specify the final scan traversal over the MST, does not provide a DTS-specific complexity derivation, and does not introduce a separate supervision or regularization loss for deformation parameters. The edge-weight formula also leaves an implementation-level ambiguity because the method minimizes an MST objective while using cosine similarity directly in the reported weight expression. These are limitations of specification rather than of empirical outcome, but they delimit how precisely the module can be reconstructed from the text alone (Cong et al., 1 Aug 2025).

More broadly, the present evidence suggests that Dynamic Tree Scan is best understood as a vision-specific adaptive tokenization and tree-guided scan mechanism for underwater segmentation. It is “dynamic” because patch geometry and graph topology depend on the input, and “tree” because the resulting scan structure is an MST rather than a fixed raster order. It is not, in the provided literature, a general-purpose name for scan statistics, dynamic-tree data structures, or tree search across domains.