Structural Flux Block (SFB)

• Structural Flux Block (SFB) is a modular element that enables topology-aware and anisotropic feature representation, particularly for geological lineament segmentation.
• It integrates four specialized submodules (ASG, PMF, HSR, and HFFU) that collaboratively optimize dynamic information flow and robust noise suppression.
• Empirical results show that SFB enhances segmentation accuracy up to 89.87% mIoU while maintaining low computational overhead, making it ideal for multi-source remote sensing tasks.

The Structural Flux Block (SFB) is a fundamental architectural component introduced within the Fluxamba model for topology-aware, anisotropic feature representation, particularly in the context of geological lineament segmentation in multi-source remote sensing. SFBs address limitations inherent in classical State Space Model (SSM)–based encoders, whose axis-aligned serialization pipelines induce topological mismatches with curvilinear targets. By integrating four specialized modules—Anisotropic Structural Gate (ASG), Prior-Modulated Flow (PMF), Hierarchical Spatial Regulator (HSR), and High-Fidelity Focus Unit (HFFU)—the SFB enables dynamic, geometry-adaptive information propagation and robust noise suppression without sacrificing the computational advantages of SSMs (Bai et al., 24 Jan 2026).

1. Architectural Role and High-Level Composition

Within Fluxamba’s four-stage encoder, each stage comprises a sequence of SFBs, which transform an input feature tensor $X_{base} \in \mathbb{R}^{C \times H \times W}$ through a cascade of geometric probing (ASG), anisotropic trajectory rectification (PMF), scale-adaptive realignment (HSR), and spectral noise filtering (HFFU). This macro-level differentiable rectification preserves near-linear complexity while aligning context aggregation with the intrinsic, potentially non-Euclidean geometry of linear and curvilinear features. The SFB replaces the rigid, axis-aligned information flow of PlainMamba encoders with a content- and geometry-aware pipeline that better retains boundary integrity and long-range continuity (Bai et al., 24 Jan 2026).

2. Mathematical Structure and Module Formulation

Each SFB consists of four tightly integrated submodules:

2.1 Anisotropic Structural Gate (ASG)

ASG decouples orientation from spatial position through dual-branch processing:

• Coordinate-Aware Branch: Computes horizontal and vertical average pooling, producing $$F_{coord}(x, y) = [\mathrm{AvgPool}_H(X_{base});\mathrm{AvgPool}_W(X_{base})]$$.
• Strip-Pooling Branch: Applies elongated (“strip”) convolutional kernels ($F_{strip} = \mathrm{StripPool}(X_{base})$).

These outputs are concatenated and passed through a $1 \times 1$ convolution and a sigmoid activation: $$G_{ASG} = \sigma(\mathrm{Conv}_{1 \times 1}([F_{coord}; F_{strip}])) \in [0, 1]^{C \times H \times W}$$.

A residual attention mechanism modulates the input: $X_{ASG} = X_{base} + X_{base} \odot G_{ASG}$.

2.2 Prior-Modulated Flow (PMF)

PMF generates a “virtual” anisotropic trajectory over the grid:

• Feature maps are serialized via Four-directional Selective 2D Scan (FS2D) in four cardinal directions to yield $Y_k$ for $k=1\ldots4$.
• A geometric prior $M_{raw}$ is built from $X_{ASG}$ using both local and global convolutions, with global average pooling (GAP) for context.
• $M_{raw}$ is split via softmax into four gating maps $\{M_k\}_{k=1}^4$, satisfying $\sum_k M_k(i, j) = 1$.
• The output is $X_{PMF} = \sum_{k=1}^4 Y_k \odot M_k$.

This design enables superposition of axis-aligned flows, achieving rotational robustness without explicit input resampling.

2.3 Hierarchical Spatial Regulator (HSR)

HSR realigns features to maintain boundary and semantic coherence across scales. A shallow variant, Lightweight Modulation Refinement (LMR), operates in early stages, employing multi-rate dilated convolutions and gating; deeper stages employ a Global Transformer Reorganizer (GTR), harnessing multi-head self-attention along spatial axes.

2.4 High-Fidelity Focus Unit (HFFU)

HFFU applies dual gating for selective amplification:

• Channel Gate: $$G_{ch} = \sigma(\mathrm{Conv}_{excite}(\mathrm{GAP}(X_{HSR})))$$
• Spatial Gate: $G_{sp} = \sigma(\mathrm{Conv}_{spatial}(X_{HSR}))$

Its output is $$X_{out} = (G_{ch} \odot X_{HSR}) + (G_{sp} \odot X_{HSR})$$. By omitting an identity skip, HFFU forces the model to only propagate features passing channel or spatial confidence thresholds, effectively purging residual noise.

3. Orientation–Location Decoupling and Differentiable Rectification

The ASG acts as the central decoupling mechanism, independently modeling “where” and “how” information is aggregated. In classical convolutions, orientation and spatial position are coupled by the filter geometry; ASG, however, employs $F_{coord}$ for spatial saliency and $F_{strip}$ for orientation-sensitive context. Concatenation and gating (see Equations 1–2) yields a soft attention that boosts responses aligned with latent curvilinear structures. Downstream, PMF exploits this prior for directionally-weighted propagation. This design enables SFBs to flexibly align information flow with arbitrary topologies, overcoming the limitations of static raster or snake path serialization (Bai et al., 24 Jan 2026).

4. Algorithmic Implementation and Computational Complexity

The following pseudocode summarizes one SFB forward pass, with $s$ denoting the encoder stage to select the appropriate HSR variant:

def SFB(X_base, s): # 1. ASG F_coord = CoordPool(X_base) # horizontal & vertical avg pools F_strip = StripPool(X_base) # multi-scale strip convolutions G_ASG = sigmoid(Conv1x1(concat(F_coord, F_strip))) X_ASG = X_base + X_base * G_ASG # 2. PMF for k in range(4): # directions Y_k = FS2D_direction_k(X_base) M_raw = Conv_loc(X_ASG) + broadcast(Conv_glob(GAP(X_ASG))) {M_k} = split_softmax(M_raw) X_PMF = sum(Y_k * M_k for k in range(4)) # 3. HSR if s <= 2: # LMR F_cat = concat([DilatedConv_r(X_PMF) for r in R]) F_proj = Conv_proj(F_cat) G_LMR = sigmoid(Conv_gate(F_proj)) X_HSR = (1 - G_LMR) * X_base + G_LMR * F_proj else: # GTR X_in = X_PMF + X_base X_H = MSA_H(LN(X_in)) + X_in X_W = MSA_W(LN(X_H)) + X_H X_HSR = FFN(LN(X_W)) + X_W # 4. HFFU G_ch = sigmoid(Conv_excite(GAP(X_HSR))) G_sp = sigmoid(Conv_spatial(X_HSR)) X_out = (G_ch * X_HSR) + (G_sp * X_HSR) return X_out

For complexity, a single SFB (ASG+PMF+HSR+HFFU) requires 350 MFLOPs and 0.5M parameters on average, compared to 300 MFLOPs and 0.3M parameters for a standard PlainMamba block. The Fluxamba-Tiny configuration ([1,1,2,1] SFB per stage) totals 3.39M parameters and 6.25 GFLOPs (Bai et al., 24 Jan 2026).

5. Noise Suppression and Module Interactions

While PMF and HSR restore geometric continuity, serialization can introduce noise—particularly under low signal-to-noise ratios. The HFFU provides final noise purification via dual-polarized gating. Ablations indicate that exclusion of HFFU from SFB results in a notable 2.53% drop in mIoU, establishing its necessity for filtering regolith and texture noise that upstream modules cannot eliminate. HFFU’s absence allows weak, spurious activations to persist, whereas its inclusion enforces robust selective propagation.

6. Empirical Impact and Ablation Findings

Benchmarking on the LROC-Lineament validation set confirms the distinct contributions of each SFB module:

Variant	mIoU (%)	Gain vs. Base
Base Mamba block	79.33	–
+PMF only	88.10	+8.77
+ASG only	80.66	+1.33
+HSR only	85.15	+5.82
+HFFU only	84.07	+4.74
PMF+ASG+HSR+HFFU	89.87	+10.54

Combining only PMF and HFFU, without explicit ASG or HSR, still yields 89.32% mIoU, highlighting the dominant role of flow rectification and spectral filtering. Additionally, the FS2D plus PMF approach outperformed static multi-path templates by 2.54 points, underscoring the benefits of content-aware rectification.

7. Significance and Applications

The SFB architecture enables Fluxamba to achieve state-of-the-art results for geological lineament segmentation, with an F1-score of 89.22% and mIoU of 89.87% on LROC-Lineament, running at over 24 FPS and requiring only 3.39M parameters and 6.25 GFLOPs. This establishes a new Pareto frontier between segmentation fidelity and computational efficiency. Empirical findings demonstrate that SFB-driven dynamic anisotropic information flux is essential for topological fidelity, boundary continuity, and noise robustness in complex, multi-source remote sensing scenarios (Bai et al., 24 Jan 2026).