Hidden State Weaken (HSW) in Underwater Segmentation

• Hidden State Weaken is a module that partitions underwater image patches into foreground and background using DTS outputs and normalized cut.
• It applies a suppression factor (ϕ = 0.7) to downweight background contributions during hidden-state updates while retaining useful context.
• Empirical results show that incorporating HSW with Mamba and DTS significantly improves segmentation accuracy, boosting mAP and AP scores.

Hidden State Weaken (HSW) is a foreground-background aware hidden-state suppression module introduced in "UIS-Mamba: Exploring Mamba for Underwater Instance Segmentation via Dynamic Tree Scan and Hidden State Weaken" (Cong et al., 1 Aug 2025). It is the second key contribution of UIS-Mamba and is designed specifically for underwater instance segmentation, where cluttered backgrounds, severe underwater color degradation, and blurred instance boundaries can cause background patches to contaminate Mamba’s sequential hidden-state propagation. HSW reuses the minimum spanning tree and dynamic edge weights produced by Dynamic Tree Scan (DTS), partitions patches into foreground and background with Normalized Cut (Ncut), and weakens background contributions during hidden-state updates through a suppression factor $\varphi$, with $\varphi = 0.7$ reported as the best setting (Cong et al., 1 Aug 2025).

1. Problem setting and motivation

HSW is motivated by two difficulties identified for applying Mamba to underwater instance segmentation. First, underwater images often contain complex, noisy backgrounds that are visually similar to foreground instances in color and texture. The paper further notes that, due to underwater color degradation, the $R$ channel is severely weakened and images are dominated by green and blue tones. Second, underwater instance boundaries are often blurred by scattering, low contrast, and color distortion, which weakens scene continuity and makes sequential patch propagation more error-prone (Cong et al., 1 Aug 2025).

Within vision Mamba, the core observation is that whatever gets scanned contributes to hidden-state updating. In the underwater case, this means that background patches mixed into the scan sequence can dominate or distort state propagation, interfering with instance understanding. HSW is therefore introduced to suppress background influence during hidden-state updates so that state evolution focuses more strongly on foreground instances (Cong et al., 1 Aug 2025).

This design is specific to the state-propagation behavior of Mamba. The paper’s framing is not that background information is intrinsically useless; rather, background information becomes problematic when it is allowed to propagate through the recurrent hidden-state path with the same strength as instance patches. The choice of weakening, rather than deleting, background contributions reflects that distinction.

2. Ncut-based patch categorization

HSW is a foreground-background separation and suppression mechanism built on Ncut. It operates on the graph structure already created by DTS and explicitly does not reconstruct the graph connection again. Instead, it directly adopts the minimum spanning tree and dynamic edge weights from DTS, which the paper characterizes as more efficient and coherent (Cong et al., 1 Aug 2025).

The inputs to HSW are the minimum spanning tree or graph structure produced by DTS, the dynamic edge weights $w_{ij}$, and the patch set or node set $\mathcal{V}$. On this graph, HSW partitions nodes into two disjoint sets, $A$ for foreground patches and $B$ for background patches, by minimizing the normalized cut objective

$$Ncut(A,B)=\frac{C(A,B)}{C(A,\mathcal{V})}+\frac{C(A,B)}{C(B,\mathcal{V})},$$

where $C(A,B)$ is the total connection from set $A$ to set $\varphi = 0.7$0, $\varphi = 0.7$1 is the total connection from set $\varphi = 0.7$2 to all nodes in the graph, and $\varphi = 0.7$3 is the total connection from set $\varphi = 0.7$4 to all nodes in the graph. The optimal split is

$\varphi = 0.7$5

After partition, each patch receives a binary label: $\varphi = 0.7$6 for foreground and $\varphi = 0.7$7 for background (Cong et al., 1 Aug 2025).

The paper reports that HSW uses the same Ncut settings as Tokencut. That implementation detail is significant because it situates HSW as an adaptation of a known graph partitioning mechanism rather than a wholly separate graph-construction stage. In UIS-Mamba, the novelty lies in the reuse of DTS outputs and the subsequent use of the partition to alter state propagation.

3. Hidden-state weakening mechanism

Once foreground and background patches have been identified, HSW assigns a suppression weight $\varphi = 0.7$8 to each patch: $\varphi = 0.7$9 Foreground patches therefore retain full strength, while background patches are down-weighted by the hyperparameter $R$0. The best value reported in the paper is

$R$1

The paper explicitly states that background information is not removed completely; it is weakened but partially retained, because some background context remains useful for underwater reasoning (Cong et al., 1 Aug 2025).

HSW applies this weighting in the hidden-state update step. After building the minimum spanning tree, it suppresses the weights of edges connected to background patches. For edges $R$2 connecting background patches to foreground nodes, the hidden-state update is reformulated in the paper as

$R$3

and the output is

$R$4

The paper’s notation in this part is described as somewhat malformed in the typeset version, but its intended meaning is stated to be clear: $R$5 is the hidden state at node $R$6, $R$7 is the output state at node $R$8, $R$9 is the output projection, $w_{ij}$0 is the skip-connection matrix, $w_{ij}$1 is layer normalization, and background-related inputs and transitions are multiplied by the weakening weight $w_{ij}$2 (Cong et al., 1 Aug 2025).

Operationally, HSW scales down background contributions before they influence the recurrent state. The paper interprets this as making the update instance-centric: foreground patches propagate normally, background patches contribute less to the hidden state, and the output also uses the weakened patch representation.

4. Relation to standard Mamba and to DTS

The paper places HSW inside the Mamba framework by contrasting it with the standard update

$w_{ij}$3

$w_{ij}$4

HSW modifies this propagation by inserting a foreground/background-aware suppression factor into the hidden-state path. Instead of treating all scanned patches equally, it selectively attenuates background contributions during state evolution (Cong et al., 1 Aug 2025).

Architecturally, HSW is not a standalone module. The overall UIS-Mamba pipeline is described as: backbone feature extraction; Dynamic Tree Scan, which deforms patches, builds a graph, computes dynamic edge weights, and generates a minimum spanning tree; Hidden State Weaken, which runs Ncut on the minimum spanning tree, labels patches as foreground or background, and suppresses background hidden-state updates; and finally WaterMask detection or segmentation heads (Cong et al., 1 Aug 2025).

The relation between DTS and HSW is explicit. DTS reorganizes patch scanning into a tree topology rather than a fixed linear order, with the stated role of maintaining semantic continuity and dynamic local receptive fields. HSW then operates on this tree-based propagation by weakening the contribution of background nodes during the state update. The paper summarizes the design principle as follows: DTS fixes semantic continuity, while HSW fixes background interference in state evolution (Cong et al., 1 Aug 2025).

This division of labor is central to the method. DTS addresses how patches are connected and traversed; HSW addresses how much those traversed patches should influence recurrent state propagation once the graph is available.

5. Empirical behavior and ablation evidence

The paper provides a direct ablation on UIIS with the UIS-Mamba-T backbone. The baseline, WaterMask R-CNN with ResNet-50, achieves mAP $w_{ij}$5, AP50 $w_{ij}$6, and AP75 $w_{ij}$7. Replacing ResNet-50 with Mamba yields mAP $w_{ij}$8, AP50 $w_{ij}$9, and AP75 $\mathcal{V}$0. Adding HSW without DTS yields mAP $\mathcal{V}$1, AP50 $\mathcal{V}$2, and AP75 $\mathcal{V}$3. The full model with Mamba, DTS, and HSW reaches mAP $\mathcal{V}$4, AP50 $\mathcal{V}$5, and AP75 $\mathcal{V}$6 (Cong et al., 1 Aug 2025).

Setting	mAP	AP50 / AP75
WaterMask R-CNN with ResNet-50	26.4	43.6 / 28.8
Mamba backbone only	27.1	45.1 / 29.3
Mamba + HSW	28.2	46.1 / 30.2
Mamba + DTS + HSW	29.4	46.7 / 31.3

Relative to the Mamba-only baseline, HSW alone improves performance by $\mathcal{V}$7 mAP, $\mathcal{V}$8 AP50, and $\mathcal{V}$9 AP75. The full model further improves on that result, which the paper uses to argue that HSW provides a substantial gain and complements DTS (Cong et al., 1 Aug 2025).

The hyperparameter study for $A$0 reports the following UIIS results:

$A$1	mAP	AP50 / AP75
0	27.1	45.1 / 29.3
0.5	27.7	45.5 / 29.6
0.6	28.0	45.6 / 29.9
0.7	28.2	46.1 / 30.2
0.8	27.9	45.7 / 29.7

The reported interpretation is that $A$2 is best, that completely removing background information is not optimal, and that mild weakening is better than hard suppression because underwater context still matters (Cong et al., 1 Aug 2025). The paper does not provide an HSW-only ablation on USIS10K; isolated HSW contribution is only explicitly quantified in the UIIS ablation table.

6. Qualitative effects, computational characteristics, and terminology

The qualitative discussion attributes UIS-Mamba’s improved behavior to better capture of hidden instances, more accurate boundaries, stronger focus on foreground objects, and reduced influence of cluttered underwater background. The paper explicitly states that UIS-Mamba maintains “accurate foreground instance capture” and “background hidden state weakening,” and that it achieves better segmentation of challenging objects and boundaries (Cong et al., 1 Aug 2025). Although a separate HSW-only visualization is not reported, these descriptions support the interpretation that HSW helps prevent background patches from dominating state propagation and preserves instance-centric feature flow.

From an implementation perspective, HSW is presented as computationally efficient because it does not rebuild the graph. It directly uses the minimum spanning tree $A$3 and dynamic edge weights $A$4 from DTS, and it uses the same Ncut settings as Tokencut. This suggests that its added cost is tied primarily to partitioning and weighting on already-available graph structure rather than to a second graph-construction pass (Cong et al., 1 Aug 2025).

The term should also be distinguished from other contemporary uses of “hidden state” in the literature. In UIS-Mamba, Hidden State Weaken denotes a foreground-background-aware suppression mechanism for state propagation in underwater vision Mamba (Cong et al., 1 Aug 2025). This is different from hidden state as latent dynamical coordinates in state discovery (Chen et al., 2021), from hidden-state filtering used as a pre-inference jailbreak defense in LLMs (Qian et al., 2024), and from hidden-state poisoning attacks against Mamba-based LLMs (Mercier et al., 5 Jan 2026, Mercier et al., 12 Mar 2026). A plausible implication is that the phrase “hidden state” is architecture-dependent across subfields, whereas HSW in UIS-Mamba has a narrow and concrete meaning: attenuation of background-driven recurrent propagation during underwater instance segmentation.