Spectral-Integrated Global Mamba (SIGM)

• The paper introduces SIGM as an FFT-based extension to Mamba state-space scanning that mitigates high-frequency noise to improve inlier–outlier separation.
• SIGM employs bidirectional Mamba scans with learnable complex FFT masks and cluster-based ordering to filter out inconsistent features in global correspondence modeling.
• SIGM achieves nearly linear computational complexity while enhancing performance over vanilla Mamba by preserving smooth inlier features and suppressing spurious high-frequency signals.

Searching arXiv for the cited SIGM-related papers to ground the article in current literature. Spectral-Integrated Global Mamba (SIGM) is the global modeling component of SFMambaNet, a two-view correspondence pruning network introduced in “SFMambaNet: Spectral-Frequency Enhanced Selective State Space Model for Correspondence Pruning” (Wang et al., 3 Jun 2026). In that framework, SIGM is a Mamba-based selective state-space block that injects explicit frequency-domain filtering into global sequence modeling. Its stated purpose is to model long-range correspondence context while suppressing the accumulation of high-frequency inconsistent features in hidden states, thereby improving inlier–outlier separability with nearly linear complexity (Wang et al., 3 Jun 2026). More broadly, SIGM belongs to a developing class of spectral-integrated Mamba designs in which state-space dynamics are coupled to spectral structure, frequency transforms, or spectral ordering across vision, hyperspectral, and geometric data (Wang et al., 2024, Bahri et al., 6 Mar 2025, He et al., 2024, Dewis et al., 22 Jan 2026, Gao et al., 10 Sep 2025).

1. Definition and problem setting

In SFMambaNet, correspondence pruning is defined over an initial set of putative two-view matches

$$C = \{c_i\}_{i=1}^N \in \mathbb{R}^{N\times 4},\qquad c_i = (u_i, v_i, u'_i, v'_i),$$

with the objective of classifying each correspondence as an inlier or outlier and estimating the essential matrix for pose estimation (Wang et al., 3 Jun 2026). The network is organized as two cascaded pruning blocks, each followed by a verification block. Within each pruning block, the local component is the Local Spectral-Geometric Attention (LSGA) block, while the global component is the Spectral-Integrated Global Mamba (SIGM) block (Wang et al., 3 Jun 2026).

SIGM receives local spectral-geometric features produced by LSGA and performs global sequence modeling via Mamba-like state-space scanning. Its defining distinction is the insertion of an FFT-based frequency gating mechanism into the state-space pipeline, with learnable complex-valued masks applied in the frequency domain (Wang et al., 3 Jun 2026). The paper characterizes this as explicit suppression of high-frequency noise accumulation within hidden states and mitigation of inconsistent feature propagation (Wang et al., 3 Jun 2026).

This design addresses a specific limitation attributed to vanilla Mamba in correspondence pruning: although Mamba provides global receptive fields and long-sequence modeling capacity, it tends to accumulate substantial inconsistent features in hidden state space, which makes inlier–outlier discrimination more difficult (Wang et al., 3 Jun 2026). SIGM is therefore not a generic renaming of Mamba, but a particular architectural modification in which spectral filtering is inserted between directional state-space scans.

2. Architectural organization within SFMambaNet

SIGM operates after LSGA. LSGA constructs explicit $k$-NN graphs over correspondences, adds spectral-geometric encoding through Fourier features of local relative coordinates, and uses local attention plus a cluster-based Mamba module to produce refined local features $F^{GL}$ with strong local spectral-geometric cues (Wang et al., 3 Jun 2026). SIGM then consumes these features as a global module.

Its input is

$F^{GL} \in \mathbb{R}^{D \times N \times 1},$

which is reordered using a cluster-induced permutation $\Pi$, reused from LSGA’s DiffPool: $$F^{GL}_{ord} = \Pi(F^{GL}) \in \mathbb{R}^{D \times N \times 1}.$$ This reordered sequence is processed in two sequential stages, each composed of a Mamba scan followed by frequency-domain gating, after which forward and backward results are fused with a residual connection and LayerNorm, and the inverse permutation $\Pi^{-1}$ restores the original correspondence order (Wang et al., 3 Jun 2026).

The forward pass is

$F_{fwd} = \text{Mamba}(F^{GL}_{ord}),$

followed by

$$\mathcal{F}_{fwd} = \text{FFT}(F_{fwd}) \odot \text{Interp}(W_{gate}^1), \qquad F^S_{fwd} = \text{IFFT}(\mathcal{F}_{fwd}),$$

where $W_{gate}^1$ is a learnable complex-valued gating weight (Wang et al., 3 Jun 2026). The backward pass flips the refined forward sequence, applies another Mamba scan, and applies a second independent frequency gate: $k$0

$k$1

The final output is

$k$2

The resulting $k$3 is the global frequency-aware feature for each correspondence (Wang et al., 3 Jun 2026).

The paper explicitly summarizes SIGM as a forward–backward Mamba with two FFT-based frequency gates operating on a cluster-ordered sequence (Wang et al., 3 Jun 2026). That ordering is not incidental: the permutation $k$4 is intended to make the sequence geometry-aware, so that smooth inlier patterns and jagged outlier patterns become spectrally distinguishable along the scan axis (Wang et al., 3 Jun 2026).

3. Selective state-space formulation and spectral gating

SIGM adopts the standard selective state-space formulation associated with Mamba. At a high level, the continuous-time system is

$k$5

which after discretization with step $k$6 becomes

$k$7

Mamba introduces data-dependent, time-varying parameters through selective kernels, with projections such as

$k$8

and an output gating pathway

$k$9

while retaining linear complexity in sequence length $F^{GL}$0 (Wang et al., 3 Jun 2026).

SIGM preserves these Mamba scans but inserts a spectral filter after each directional scan. The forward and backward scan outputs $F^{GL}$1 are transformed by FFT along the sequence dimension $F^{GL}$2, channel-wise, multiplied by learnable complex masks, and inverted back to the sequence domain (Wang et al., 3 Jun 2026). The paper stresses that the gate is not a scalar but a frequency-dependent complex mask that can adaptively suppress high-frequency bins and enhance low-/mid-frequency ones (Wang et al., 3 Jun 2026).

This is distinct from the local spectral-geometric encoding in LSGA. There, relative coordinates $F^{GL}$3 are projected via a Gaussian matrix $F^{GL}$4,

$F^{GL}$5

and then mapped to feature space by an MLP (Wang et al., 3 Jun 2026). SIGM does not explicitly reuse these raw Fourier codes. Instead, it receives the already frequency-aware local descriptors $F^{GL}$6, and performs sequence-level spectral filtering on them (Wang et al., 3 Jun 2026).

A plausible implication is that SIGM implements spectral integration at a different level from LSGA. LSGA injects local spectral cues into feature construction; SIGM performs global spectral control over the propagation of those features through the hidden state dynamics.

4. Frequency integration, noise suppression, and sequence semantics

The central interpretive premise of SIGM is a smoothness-driven consensus view of correspondence pruning. Inliers correspond to physically consistent geometric transformations between two views; their motion field tends to be smooth and is therefore associated with low-frequency spatial or graph signals. Outliers violate that consensus and produce random, inconsistent displacements, which manifest as high-frequency variations in the correspondence domain (Wang et al., 3 Jun 2026).

Within SIGM, correspondences are first arranged into a geometry-aware sequence through cluster ordering. Once so arranged, outliers are described as inducing rapid oscillations along the sequence, and these oscillations correspond to high-frequency components in the one-dimensional discrete Fourier transform of the feature sequence (Wang et al., 3 Jun 2026). The frequency gating mechanism then learns, end-to-end, to down-weight spectral regions where outlier energy is concentrated while preserving bins where inlier energy dominates (Wang et al., 3 Jun 2026).

The paper reports a frequency-domain diagnostic in Fig. 12. Before SIGM, inlier features have larger energy in low-frequency bins, while outliers show comparatively more energy in high-frequency bins. After SIGM, outlier high-frequency energy is significantly reduced, and inliers maintain strong low-frequency energy, with sharper separation in low-/high-frequency energy ratio between inliers and outliers (Wang et al., 3 Jun 2026). The authors interpret this as empirical confirmation that the FFT-based gating behaves as a learned spectral low-pass filter tuned to the inlier/outlier statistics of the correspondence domain (Wang et al., 3 Jun 2026).

This explicit frequency-domain intervention distinguishes SIGM from several neighboring Mamba or sequence-modeling strategies. “GlobalMamba” (Wang et al., 2024) also integrates frequency structure with Mamba, but it does so through global image serialization: images are transformed by DCT, segmented into bands, reconstructed by IDCT, tokenized, and concatenated from low to high frequency before standard Mamba processing (Wang et al., 2024). There, frequency enters through input serialization rather than through an internal gate on hidden-state outputs. By contrast, SIGM modifies the sequence processing stage itself via FFT–gate–IFFT operations inside the global block (Wang et al., 3 Jun 2026).

5. Relation to other spectral-integrated Mamba designs

SIGM is one instance of a broader pattern in which Mamba or state-space layers are coupled with spectral structure, though the exact mechanism varies by domain.

“GlobalMamba: Global Image Serialization for Vision Mamba” (Wang et al., 2024) converts images into frequency-domain representations with 2D DCT, partitions the spectrum into bands, reconstructs band images by IDCT, adaptively downsamples them, tokenizes them, and feeds tokens to Mamba in low-to-high frequency order (Wang et al., 2024). This yields a causal sequence whose temporal axis corresponds to frequency scale rather than raster order.

“3DSS-Mamba: 3D-Spectral-Spatial Mamba for Hyperspectral Image Classification” (He et al., 2024) uses 3D spectral-spatial tokens and a 3D-Spectral-Spatial Selective Scanning mechanism with five scanning routes that traverse spatial and spectral dimensions in different priority orders, including a parallel spectral–spatial route that empirically performs best (He et al., 2024). The model thereby performs global spectral-spatial integration within 3D token volumes.

“Clustering-Guided Spatial-Spectral Mamba for Hyperspectral Image Classification” (Dewis et al., 22 Jan 2026) reorganizes spatial tokens through learnable clustering, applies per-cluster local Mamba blocks with attention-driven token selection, and combines them with a spectral Mamba branch and a global spatial Mamba (Dewis et al., 22 Jan 2026). Here, “spectral integration” refers chiefly to the joint use of spatial and spectral branches plus clustering-guided sequence construction.

“Spectral Informed Mamba for Robust Point Cloud Processing” (Bahri et al., 6 Mar 2025) derives traversal orders from graph Laplacian eigenvectors, using spectral geometry to define isometry-invariant sequence orderings for Mamba and hierarchical spectral partitioning for segmentation (Bahri et al., 6 Mar 2025). The spectrum determines traversal and partitioning rather than frequency gating within hidden states.

“Hyperspectral Mamba for Hyperspectral Object Tracking” (Gao et al., 10 Sep 2025) introduces Spectral State Integration (SSI) and the Hyperspectral Mamba (HSM) module, which uses forward, backward, and spectral SSM paths and propagates a spectral hidden state across depth and time (Gao et al., 10 Sep 2025). In that case, spectral integration is realized through directional scanning and recurrent state propagation rather than an explicit FFT mask.

These related models show that “spectral-integrated Mamba” is not a single recipe. In current literature, spectral information can enter through at least four distinct pathways: spectral tokenization or serialization (Wang et al., 2024), spectral scanning routes (He et al., 2024, Gao et al., 10 Sep 2025), graph-spectral ordering (Bahri et al., 6 Mar 2025), and explicit spectral filtering inside the sequence model itself (Wang et al., 3 Jun 2026). SIGM is specifically the fourth type.

6. Empirical behavior, complexity, and limitations

Within SFMambaNet, SIGM is reported to provide robust global context modeling with nearly linear complexity (Wang et al., 3 Jun 2026). The complexity decomposition in the paper is explicit: each Mamba scan is linear in $F^{GL}$7, $F^{GL}$8 up to state-dimension factors, while FFT-based gating costs $F^{GL}$9. The overall complexity is therefore subquadratic and close to linear in practical regimes, remaining cheaper than full self-attention at $F^{GL} \in \mathbb{R}^{D \times N \times 1},$0 (Wang et al., 3 Jun 2026).

The model-level efficiency numbers reported for SFMambaNet are params $F^{GL} \in \mathbb{R}^{D \times N \times 1},$1M, FLOPs $F^{GL} \in \mathbb{R}^{D \times N \times 1},$2G, and average inference time $F^{GL} \in \mathbb{R}^{D \times N \times 1},$3 ms per image pair; the paper compares this favorably with heavier Transformer-based baselines such as BCLNet at 6.65M parameters and 10.93G FLOPs (Wang et al., 3 Jun 2026). The specific implication for SIGM is that the addition of FFT-based gating does not negate the near-linear efficiency advantage associated with Mamba-style sequence modeling (Wang et al., 3 Jun 2026).

Ablations also isolate SIGM’s contribution. On YFCC100M in the camera pose estimation setting with SIFT features, the baseline plus unidirectional Mamba obtains known/unknown mAP5° of 50.21 / 63.18, whereas baseline plus SIGM (without LSGA) reaches 52.21 / 66.60 (Wang et al., 3 Jun 2026). With LSGA fixed, the full SFMambaNet configuration with LSGA + SIGM reaches 62.28 / 73.83, while a variant adding both vanilla Mamba and SIGM on top of LSGA performs slightly worse at 60.91 / 72.18 (Wang et al., 3 Jun 2026). The paper interprets this as evidence that vanilla Mamba can reintroduce ungated noisy propagation, weakening the benefit of frequency gating (Wang et al., 3 Jun 2026).

The scanning-strategy ablation similarly favors SIGM. On the same benchmark, baseline + random scanning Mamba scores 49.20 / 68.99 and 62.50 / 81.46 for known/unknown mAP5°/20°, while baseline + SIGM reaches 52.21 / 73.59 and 66.60 / 83.89 (Wang et al., 3 Jun 2026). This indicates that bidirectionality, geometry-aware ordering, and frequency gating all matter.

The implementation details given for SIGM include channel dimension $F^{GL} \in \mathbb{R}^{D \times N \times 1},$4, Mamba state dimension 16 in SIGM, fixed training sequence length $F^{GL} \in \mathbb{R}^{D \times N \times 1},$5 correspondences, DiffPool-derived cluster number $F^{GL} \in \mathbb{R}^{D \times N \times 1},$6, one forward Mamba plus frequency gate followed by one backward Mamba plus frequency gate, and LayerNorm at output (Wang et al., 3 Jun 2026). Residual connections and cluster-based ordering are identified as stability mechanisms (Wang et al., 3 Jun 2026).

The paper does not enumerate SIGM-specific failure cases in detail, but it identifies several implicit limitations. SIGM relies on meaningful cluster-based ordering; poor clustering may weaken the geometry-aware sequence assumption. It also assumes that outlier effects primarily manifest as high-frequency components; this separation may become more difficult when inlier patterns themselves are high-frequency. Finally, the method uses a one-dimensional FFT along the reordered sequence rather than a graph Laplacian basis or other spectral graph operator, which the paper characterizes as a pragmatic but somewhat heuristic notion of frequency on the graph (Wang et al., 3 Jun 2026). Suggested future directions include graph spectral bases such as Laplacian eigenvectors, multi-dimensional SSMs inspired by S4ND, and more structured or parametric spectral filters (Wang et al., 3 Jun 2026).

Taken together, these results place SIGM as a specialized global Mamba block for robust correspondence pruning: it combines bidirectional selective state-space scanning with explicit sequence-domain spectral filtering, using local spectral-geometric descriptors and cluster-informed ordering as prerequisites for meaningful global frequency separation (Wang et al., 3 Jun 2026).