Enabling True Global Perception in State Space Models for Visual Tasks
Authors: Jie Hui
Zhenxiang Zhang
Wenyu Mi
Jianji Wang
Venue: ICLR 2026 Poster (2026)
Keywords: State Space Model
Frequency Domain Modulation
Global Image Modeling
Mathematical Definition
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Despite the importance of global contextual modeling in visual tasks, a rigorous mathematical definition remains absent, and the concept is still largely described in heuristic or empirical terms. Existing methods either rely on computationally expensive attention mechanisms or are constrained by the recursive modeling nature of State Space Models (SSMs), making it challenging to achieve both efficiency and true global perception. To address this, we first propose a mathematical definition of global modeling for visual images, providing a theoretical foundation for designing globally-aware and interpretable models. Based on in-depth analysis of SSMs and frequency-domain modeling principles, we construct a complete theoretical framework that overcomes the limitations imposed by SSMs' recursive modeling mechanism from a frequency perspective, thereby adapting SSMs for global perception in image modeling. Guided by this framework, we design the Global-aware SSM (GSSM) module and formally prove that it satisfies definitional requirements of global image modeling. GSSM leverages a Discrete Fourier Transform (DFT)-based modulation mechanism, providing precise front-end control over the SSM's modeling behavior, and enabling efficient global image modeling with linear-logarithmic complexity. Building upon GSSM, we develop GMamba, a plug-and-play module that can be seamlessly integrated at any stage of Convolutional Neural Networks (CNNs). Extensive experiments across multiple tasks, including object detection, semantic segmentation, and instance segmentation, across diverse model architectures, demonstrate that GMamba consistently outperforms existing global modeling modules, validating both the effectiveness of our theoretical framework and the rigor of proposed definition. Code is available at \url{https://github.com/Xinmu-Tantai/GMamba-GSSM}

Published as a conference paper at ICLR 2026
ENABLING TRUE GLOBAL PERCEPTION IN STATE SPACE MODELS FOR VISUAL TASKS
Jie Hui'
Zhenxiang Zhang' Wenyu Mi!
Jianji Wang"*
State Key Laboratory of Machhne Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi'an an Jiaotong University, China hui mnijie__ ust... x xjuu. .du...du... cn, 22x2024 www..xed.tu...........oo wenyu.mi @ 63, com, wangjianj @mail x xjtu. edu.cn
ABSTRACT
Despite the importance of global contextual modeling in visual tasks, rigorous mathematical definition remains absent, and the concept is still largely described in heuristic empirical terms. Existing methods either rely computation- ally expensive attention mechanisms or are constrained by the recursive modeling nature of State Space Models (SSMs), making it challenging achieve both effi- ciency and true global perception. To address this, we first propose a mathematical definition of global modeling for visual images, providing a theoretical foundation for designing globally-aware and interpretable models. Based on in-depth analy- sis of SSMs and frequency-domain modeling principles, construct complete theoretical framework that overcomes the limitations imposed by SSMs' recur- sive modeling mechanism from frequency perspective, thereby adapting SSMs for global perception in image modeling. Guided by this framework, we design the Global-aware SSM (GSSM) module and formally prove that satisfies def- initional requirements of global image modeling. GSSM leverages a Discrete Fourier Transform (DFT)-based modulation mechanism, providing precise front- end control over the SSM's modeling behavior, and enabling efficient global im- age modeling with logarthogari complexity. Building upon GSSM, we de- velop GMamba, aod--and-ply module that be seamlessly integrated at any stage of Convolutional Neural Networks (CNNs). Extensive experiments across multiple tasks, including object detection, semantic segmentation, and instance segmentation, across diverse model architectures, demonstrate that GMamba con- sistently outperforms existing global modeling modules, validating both the effec- tiveness of our theoretical framework and the rigor of proposed definition. Code is available https: /ttpt/ggttttttt///////ee/gtabhht com/ X nmu Tantai /GMambaaGaasa
INTRODUCTION
In visual tasks, capturing long-range dependencies is essential for accurate object recognition and semantic understanding. However, despite the central role global image modeling in improving visual perception, rigorous mathematical definition that guarantees true global awareness is still lacking. Thus, existing studies typically rely on extensive ablation experiments, performance com- parisons, posterior feature visualizations assess global modeling capabilities, treating global image modeling as an empirical and somewhat ambiguous concept, without systematic theoretical derivations or proofs. This lack of formal definition limits interpretability and theoretical support.
Through extensive research, existing global modeling methods be categorized into types: Transformers (Han et al., 2021; Liu et al., 2021) based on self-attention and Mamba (Gu & Dao, 2023) based on state space models. Transformers can capture global information through parallel modeling, but their quadratic complexity limits their applicability in resource-constrained environ- ments (Guo et al., 2020), as shown in Fig. (a)) In contrast, Mamba, recently proposed in Natural Language Processing (Fanni et al., 2023), offers linear complexity and efficient sequeee mod- eling via a novel SSM-based architecture. The core of Mamba lies in combining SSM with selec- tion mechanism to selectively process input sequences in hardware-aware manner, while utilizing
"Coreepoodingg Author: Jianji Wang (wangjianji @ @miilxxtu.eddu.c)

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(a) Self
Attention
(b) Vanilla (SM
(c) Vim(SSM)
Spich
Bidirectional Scon
Complesiiy: Paraliel Modeting
Complexity (+)
Recursive Modeling
Complexity
Recursive Modeling
(d) GMamba(GGSM) (Ours)
legend
FPI Y nae of
rill m
Hlattened
Transform Medulation
Feature Napp
Peature Naps
Global Perception
Each pixell information
from all other piae and exhibitx global percuption
Complexity
Global Perception Modeling
Existing global modeling approaches include: (a) Self-Attentio,, capturing global de- pendencies in parallel with Onn²) complexity; (b) Vanilla Mamba, adopting recursive SSMs with linear (n) complexity but limited receptive fields; (c) Vim, which enhances modeling capacity via Bidirectional SSMs; and (d) our proposed GMamba, introducing DFT-based pre-modulation to embed global perception into features, guiding SSMs for truly global modeling.
Figure 1:
SSM's recurrence to model image information, as shown in Fig. 1(b). Recently, many studies (Wang et al., 2025a; Xu et al., 2024; He et al., 2025) have applied Mamba to vision tasks, fully leveraging its linear complexity advantage. However, applying Mamba to vision tasks faces two critical issues: (1) The modeling process of SSM employs step-by-step state update mechanism, where each step's computation only depends on the current input and historical state, meaning the model must rely on multi-step indirect propagation obtain global context. Its perceptual capability remains limited to local rather than explicit global modeling. (2) SSM's state update mechanism is suitable for time- series data with clear causal structure, while pixel relationships in images are non-causal, creating a structural conflict with SSM's modeling assumptions, thereby limiting its performance in image modeling. To address these issues, some methods (Li al., 2025a; Wang et al., 2025b; Zhang al., 2025; Pei et al., 2025; Shi et al., 2024) attempt to compensate for the limitations of unidirectional scanning in image tasks by modifying various scanning strategies. For example, Vim (Zhu et al., 2024a), as shown in Fig. I(c). In fact, existing methods that modify various scanning strategies (Zhu et al., 2024b) have not significantly alleviated the inherent limitations of SSM.
To tackle these issues, we propose for the first time a mathematical definition of global image model- ing, based on in-depth analysis of its behavior. Motivated by the extensive of frequency-domain analysis in computer iasion-particularly the DFT (Sundararajan, 2001; Pei & Ych, 1998; Winograd, 1978), where each frequency component inherently aggregates global information and provides natural global receptive capability- we explore a frequency-doman global modeling. Building thorough analysis of SSM mechanisms and rrequency-domain trans- formation principles, we establish the theoretical foundation for frequency-domat modulated SSM and rigorously prove the global properties of the DFT, thereby constructing complete theoretical framework for frequency-guides
perspective for more effective
SSM. Guided by this theoretical basis, we design the GSSM mod- ule (Figs. I(d) and 2) and demonstrate that it strictly satisfies the proposed mathematical definition of global image modeling. The module injects global semantic information into the SSM through a learnable 2D-DFT-based frequency-dome domain rremmodulation mechanism. By introducing global semantics at the front end and adaptively controlling the guidance and fusion between frequency- domain and spatial features, GSSM enables precise regulation of state selection and hidden-state updates in the SSM. This design allows the modeling process to go beyond historical states and, without complex scanning strategies, achieve efficient global modeling guided by global perception, while maintaining Ainaarlogarithmic computational complexity.
Based on GSSM, we further design the GMamba block, which can be flexibly embedded into any stage of CNNs to enhance the network's 's understanding of global context. We conduct evaluations on multiple mainstream CNN backbones, covering four remote sensing datasets (for semantic seg- mentation) and MS-COCO (Lin et al., 2014) (for object detection and instance segmentation). Ex- perimental results demonstrate that GMamba exhibits superior generalization capabilities across
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different tasks and network architectures, achieving better performance than other global model- ing modules while introducing fewer parameters. This validates the universality and effectiveness of the proposed theoretical framework and the rationality of our mathematical definition for global modeling in images, laying the foundation for designing globally-aware image models with stronger theoretical grounding and interpretability.
THE PROPOSED METHOD
In this section, we first propose a mathematical definition of global image modeling, then establish complete theoretical framework for frequency-domal modulation that endows SSMs with global properties, and finally provide detailed descriptions of the proposed GMamba and GSSM modules.
2.1 GLOBAL PERCEPTION MECHANISM
Global Perception Property for Images: Here, we propose a formal definition to precisely char- acterize the notion of global perception in image modeling.
Motivated by the inherent unstructured nature of image data (Yu & Wang. 2025) and the fact that derivative captures the sensitivity of outputs with respect input variables (Bishop, 2006), introduce the following mathematical definition.
Definition: For an image modeling function f RRXWXC + BH which is differen- tiable almost everywhere in D,, and a global influence function I {L.... H} x fl...., W x {I...., C} + R++ whose derivative exists all points in D,, the Frobenius norm of the derivative of f with respect to any input pixel is greater than I, then f exhibits global gradient dependency.
Of(x)
2 I(i,j,,) 0, v(I.i.c) E Dy;
inf j(i,j.c) 2 2 0. (5.3.c)
(1)
0Xij.
where ji..e represents the pixel value position (i.j) and channel e in the input image X x#x xC, || ||r denotes the Frobenius norm of the gradient tensor which measures the degree of influence of input pixels at different positions on the output image, D, denotes the set of points where both f and I are differentiable, inf represents the infimum, and t ensures that each input pixel exerts a stable and non-negligible influence on the reconstructed output.
Constraint: For function f. due to the absence of inherent sequential regularity in image features, f should not impose strict prder-dependent constraints on the input.
Our proposed mathematical definition of image global modeling. together with its constraints, estab- lishes rigorous and guaranteeable architectural criterion. This definition provides fundamental framework for encompassing and evaluating existing heuristic methods. Self-attention-basel ap- proaches achieve image globality only when their learned weights happen to satisfy >> O, yet their architectures do not enforce this property. In contrast, SSM-based models face an inherent structural conflict: their causal architectural assumption is incompatible with the non-causal nature of images, making it impossible to satisfy the non-sequential constraint while simultaneously guaranteeing a gradient lower bound (i.e., avoiding exponential decay). Thus, our definition transforms image glob- ality from an unstable, empirically observed emergent property into a theoretical property that can be rigorously analyzed and guaranteed at the architectural design stage. This shift greatly enhances the interpretability and theoretical grounding of image global modeling and lays the foundation for designing architectures that truly provide global guarantees.
2.2 WHY DOES DFT ENDOW SSMS WITH TRUE GLOOBAL. PERCEPTION?
We conduct an in-depth analysis of the modeling mechanisms and frequency- domain modeling be- havior of SSMs, thereby establishing the theoretical foundation for frequency-dome domain modulated SSMs. We provide two proofs: (i) 2D-DFT possesses inherent global properties in image tasks, and (ii) DFT-based modulation mechanisms can endow SSMs with true global perception capabilities.
2.2.1 SSM IN FREQUENCY DOMAIN
The modeling mechanism of SSMs. Classical SSMs describe continuous time systems. However, in deep learning, SSMs must be discretized by introducing time scale parameter A R and applying the widely used zero-order hold method. The discrete-time SSM is defined as follows:
Á(A)= = EA B(A) ( er dc B A= 1)B,
It = A(A)a111 + B(A) A = C.t-
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where A N B RRRM, and C RP are the continuous- time system parameters. The matrices A(A) and ((A) are the discretized state transition and input matrices, respectively. This discrete formulation enables efficient sequence modeling in neural networks by evolving the hidden state de over discrete time steps with step size A.
Meanwhile, SSM can be equivalently expressed in convolution form as:
y/2
K
where K2 CA(A))
Local Perception Limitation of SSMs in Image Tasks: SSM exhibits local perception limitations in image tasks due to its sequential processing mechanism and exponential decay of long-range influence coefficients. In image tasks, SSM flattens the pixel grid into sequence, where the spatial distance between two pixels (i1, and (i2. in the flattened sequence is defined as d li2
W + j2 - i1 W j1|- The influence coefficient follows the bound [Ka I |C||A where p(A) < 1. As the spatial distance d increases, [aa exhibits exponential decay. Furthermore, SSM relies on sequential state transitions to capture global contextual information. While can achieve global information access, its perception inherently local rather than truly global modeling.
Equivalence between SSM and Frequency Domain Representation. We observe that SSM es- sentially models the input sequence through step-by-step dynamic convolution (Eq. 3), where volution fundamentally serves as a form of filtering. From this perspective, SSM can be regarded as performing dynamic filtering the input. Frequency-domain analysis provides effective tool to characterize filter behavior in modeling. Based on this, we further aim to regulate the SSM modeling mechanism from a rrequency-domain perspective. For a causal and stable discrete-time SSM with p(A) < 1, we derive the riqueencyddomate transfer function as follows. The detailed derivation is provided in the Appendix.
((w) = --)
(4)
The frequency-doman transfer function of an SSM mathematically equivalent to the discrete-time Fourier transform of its convolution kernel.
R(w)= = Σ Kie-iwk jwk = =C(1 - ((l-Ae-Juy Jw) B =
e H(w).
(5)
The convergence of the geometric series p(A) <.
Ee (Ae -ight (1- -e-Ae-Ju-- is guaranteed when
Theoretical Foundation of Frequency-Domase Modulated SSM. Based on the established equiv- alence (Eq. 5), we further present three theoretical propositions that elucidate the rationality of frequency-domain modulation in SSM.
Information Preservation: The encoded hidden state information x, in SSMs can be transformed into a convolutional form Ks. where trenuency-transformmed information of K₂ directly maps with original information, ensuring frequency domain operations preserve the representational capacity of the original model.
Bidirectional Convertibility: The dynamic convolution kernel K₂ of SSM and its frequency do- main transfer function (w)) form Fourier transform pair, enabling lossless bidirectional version between time-domain and frequency-domain representations.
Linear Information Propagation: Both the discrete convolution ye Σt Ex KRU, and the
frequency-doman domain multiplication (w)) (w)) (w) are linear relations, ensuring consistent and stable linear information propagation through the network in either domain.
This theoretical foundation justifies the use of rrquency-domaid modulation in SSMs while pre- serving the original computational paradigm of SSM.
The Global Property of the Discrete Fourier Transform: In frequency-domain analysis, the DFT provides natural mechanism for global modeling, as each frequency coefficient depends on all positions of the input sequence. For a one-dimensional signal x E R. the DFT is defined as:
N-1
((w))= = Σ Tne juin
Wh
2T k, N
0, N 1
(6)
n=0
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Global Property: Each frequency component X (wi) depends all positions simultaneously through the exponential terms e Juhn. This creates an explicit global dependency structure where:
(we) - # 0 for all frequency indices and positions n. Position Invariance Property: The DFT exhibits uniform positional treatment where the contribution of each position to the frequency domain representation maintains consistent magnitude |e - = 1 across all positions. This ensures that no position inherently privileged or degraded in the frequency domain representation. Global Reconstruction: Through the inverse DFT, any position p in the reconstructed signal depends on all frequency components:
DE.
N N-1 Σ
X(wn)ewur..
The DFT models information from time steps and, through its position invariance property, en- sures that the information at each position contributes meaningfully to the output, without imposing any restrictions on the input. Furthermore, we observe that the definition of the DFT is analogous to that of the non-local operation (Wang et al., 2018): non-local operation computes the response at a position as a weighted sum of the features at all positions in the input feature maps. This further supports the global property of the DFT. In the appendix, we provide proof of the global properties of the DFT and prove that its extension to 2D-DFT satisfies the proposed Definition.
Extension 2D-DFT for Image Tasks: For image modeling tasks, the 2D-DFT preserves the global characteristics of the ID-DFT while extending them to capture spatial dependencies in both dimensions (height and width). The 2D-DFT for an image X E I Nx defined as:
H W
X = X
X e
2 i WW), u O....... 1 1, v = O..... W-1 -1 (8)
1=0
1=
2.2.2 THEORETICAL DESIGN OF GSSM MODULE
Global Perception of GSSM: Based on the feasibility of frequency-domain modulated SSM theory in Sec. 2.2.1 and the global properties of the 2D-DFT as proved in Sec. 2.1, we theoretically designed the GSSM module, adopting a frequency-guided modulation strategy to precisely control the update process of input states and hidden states in SSM. The following is our theoretical design of GSSM. First, we apply the 2D-DFT to the input features to inject global awareness.
free = FrD Hirreg
{x):
x F2)(X)
where Fon and and denote the 2D-DFT and its inverse transform, and Hfree( represents learnable frequency domain transformations.
Then employ adaptive modulation mechanism adjust contributions of original features and frequency-domain global features across different inputs and network stages.
X modulated 9(X, , glahal) = an (Fgohhat) O X + or2 F giohatt)
globaa
(10)
where Falobat Concat X, F Free] aggregates the original features with frequency-derived global features, and 01, 02 E (0, 1) are adaptive modulation weights derived from F globat- This adaptive learning design can be effectively applied to different inputs in visual image tasks.
The complete GSSM process can be expressed as:
Y= = SSSMM X= (FD (F2()))))
(11)
where G(-) denotes the global modulation function defined in Eq. 10, which precisely regulates input and state update processes of SSM. Although this design is simple, the effectiveness of GSSM in global modeling will be validated by both theoretical proof and experimental validation in the following subsections.
Further justification for our -hroee- design. We further analyze and prove that GSSM satisfies the proposed Definition.
Proving for Definition: The gradient of the GSSM output Y,.g with respect to the input X..j. can be decomposed, according to the chain rule, into two components: the SSM processing of the mod-
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ulated imput, and the global ieqquency-domatle modulation.
oYp4
oY
OX momoullated
(12)
OX modulated
SSM process
Global Modulation
We first demonstrate that the Global Modulation satisfies Definition. According to the modulation formulation in Eq. 10, the gradient can be decomposed as follows:
0X madulated
0x
OF freq
0Xije
01
02
0Xije
(13)
direct path
global frequency path
Spatially Uniform Global Influence: The gradient of F (req respect to X can be written
OF freg = F2D 0.....c
iMlreg
OX
(14)
0x
Since ax
aXini (w1, w2) = e ((wr)+wa)) and |e- (== for all spatial positions, the magnitude
of frequency-domain coupling is location-independen.. Hence establish spatially uniform lower bound:
0x @Xmodulated min(a1, a2) T >>> 0
(15)
0Xig.
where 7 independent of spatial location (1, c). yielding the global influence function I(i,j, c) min(a1,,0) 022)
=
We then demonstrate that the SSM process of the modulated input satisfies Definition. The se- quential state update mechanism of the SSM models global information through autoregressive formulation [x, = A(A),,,1 + B(A)u.). Each state xy accumulates information from all previous inputs U1 ......., Ue through the recurrent updates. This can be explicitly written as:
I4
B(A)) A=1
(16)
Since the output Yp.g CET is calculated from the final state (where T is the sequence length), and ør incorporates information from all input positions, we have:
0Yp.g. C'A(A)T(T (B(() 0Xij.c
Ouk + O,
(17)
OX..j.
where A corresponds to the sequential index of pixel (i,j, c) in the flattened input sequence. More- over, each pixel X modulated contains information from all other pixels, enabling the SSM update process to be guided by global context, thus eliminating the constraints of recursive modeling.
Therefore, the SSM's ability to propagate information through its hidden states ensures that every input pixel contributes to the final output, establishing:
OY p.g
8>>0
(18)
Xxmodulated
where 3 is a positive constant determined by the SSM system matrices.
aY.. is greater than zero. There exists a global From this, we can prove that the Frobenius norm of ax,,ee
influence function (i, min[min(a) 02) T, 3] that satisfies the conditions of our proposed Definition.
Analysis of Constraint: The GSSM employs a Das-based modulation mechanism to perform paral- lel global modeling of the input and further modulates the input to the SSM. As result, the GSSM no longer relies on local state information for stepwise modeling but instead regulates the input and state update process with global awareness. Consequently, the GSSM imposes no sequential constraints and satisfies the proposed Constraint.
Conclusion: The integration of DFT-based global coupling and adaptive modulation ensures that GSSM satisfies Definition and Constraint, thereby theoretically possessing global perception.

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FGMM
Specinan Images
ef + B.A,
Eigs
Nask
Yes Cualter
Window Severse & Prediction
aware
GSSM
Inpul Image
FGMM
Plation & Linur Projecioon
CORV Layer
Gobal taadaligg
GMamba Block
Global SSM Module
Overview of the GMamba Block, The input image is first segmented into multiple patches and projected into a token sequence, which is then processed by the GSSM module. Unlike vanilla SSM, GSSM exhibits true global perception capabilities through DFT-based pre-modulation using FEM and FGMM, while providing linear logarithmic complexity. Finally, MLP is applied for further semantic processing.
Figure 2:
2.3 GMAMBA OVERALL ARCHITECTURE
Based on the theoretical exploration in Sec. 2.2 on endowing SSMs with global perception through rrequency-guider modulation, we implemented the design of GMamba and GSSM, whose overall architecture is shown in Fig. 2.
Specifically, for an input image X E HXxxxC we first partition it into patches of size P x P. HxW obtaining N = P2 patch tokens. represented as {x1, .2...... IN J. where each 2; E R PC Subsequently, through linear projection, these tokens are mapped the feature space, yielding the projected feature sequence Z E NxD, The feature sequence is then fed into the GSSM module for global contextual modeling, with its output features further processed through Multi- layer Perceptron (MLP) to extract semantic information, and finally restored to spatial dimensions R xHxw'X xD through window reconstruction operations. The overall process of GMamba Block is:
Z (aandowPartition()) Z = Z + DropPath(7i GSSM(Norm) (2))), Z Z + DropPath(72 MLP MLP (Norrm2 (Z)),, ) and X Window (Z), where ?1 and 72 are learnable scaling factors for GSSM and MLP branches, respectively, Norm and N Norm2 represent layer normalization opera- tions, and DropPath is stochastic depth regularization.
2.4 GSSM MODULE
GSSM consists of two key modules: Frequency Encoding Module (FEM) and Frequency-Guue Guided Modulation Module (FGMM), as illustrated in Fig. 2. FEM applies 2D-DFT to input features, ex- tracting high- and low-frequency components, then adaptively recalibrates using learnable weights. This injects global semantics while guiding the model to focus on critical regions. FGMM leverages modulation coefficients a and ag to adaptively interact frequency-domain and spatial features be- fore spatial modeling, enabling grquunccygguideee modulation. Resulting features are subsequently processed by SSM. The appendix provides detailed algorithmic flow of GSSM, along with analysis of its logart-loa computational complexity.
EXPERIMENTS
In this section, conduct experiments on five datasets across multiple backbones and tasks (seman- tie segmentation, object detection, instance segmentation) to validate GMamba's 's effectiveness. We compare it with existing global modeling methods and analyze the design from various perspectives.
3.1 SEMANTIC SEGMENTATION ON VAIHINGEN, POTSDAM, LOVEDA, AND UAVID
Our semantic segmentation experiments are conducted on four remote sensing datasets: Vaihingen (Rottensteiner et al., 2020), Potsdam (Rottensteiner et al., 2020), LoveDA (Wang et al., 2021), and UAVid (Lyu et al., 2020). Detailed descriptions of each dataset are provided in the appendix.
Backbones. We use the ResNet (He et al., 2016), Swin Transformer (Liu et al., 2021), and Con- vNeXt (Woo et al., 2023) families for experiments, covering lightweight CNNs, larger CNNs, and global modeling architectures. Specifically, we choose ResNet34 (Koonce, 2021), Swin Trrasfoommr- (Swin(T)), and Son-NeXt-Small (ConyNeXt(S)) the backbones.

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Table I: Performance comparison on Vaihingen, Potsdam, LoveDA and UAVid datasets. GMamba consistently improves performance across different backbone architectures.
Caegars
Vakinges Molel
Potidaa Matied
xFT(S)
DAVS1
xF1(3)
(A/S)
Eiattoree (Wongge (001)
81:11
93.51
$3.50
Envelimmee (Morger (003)
1.1
07:17
91:31
34
93.55
3023)
03
ofiic 2010
Maboda
SerhNe ei al, 2004)
$4:38
91:12
01.26
SEUTNA Chang al. 2044
06.33
02.05
01:31
AFFNNe SSlancc el, 20220
64:55
91544
91.67
AFENN Oflanc al. 20050
07:90
91.34
92.09
Nowerks
Baotiz
UNasCher Nob059
07:01
$3:31
84:15
92.19
43.18
92.30
8:04
$3.09
01:30
91.43
94:33
Denl
Unet weciiaaalleeaccc (iMande
UNe 1-CMlashy
91.56-2.00
06-3--1
Uivestta Nette Caande
26.
02.88-123
126
91,0011 1.0
UNer No Gatanba
12.3
01.9
Cor Ghaana
91.83
Canggrry
LoveDA Method
LovEDA
Method
mloU(S)
(15)
Laeplabrie (Surtbulls 2019)
64,97
66.05
WNerlwamr
67.50
STEUNa (Ho ei al., 2022)
54.43
87.18
MFIN (Ches & Lus, 2024)
69.70
Exitting
MankFunner (Cheng et al. 2022)
$0.79
66.57
70.82
Urb (Ni et all, 2004)
69.00
Methods
ForkeFommer (Ching et al., 2003)
51.14
64.52
71.55 95
MA-DIPAN (Yen atl 70044
70.01
MBT (Xu et al., 2003
54.92
09.64
72.34
CAGNe: (Wass ct al. 2014)
69.00
GLOTS (Luu es 2023)
35.63
67.42
UMFFomer (Li ah., 20250g
67.00
Bucclin:
Networks
UNet ReaNe:44
Swier))
51.05
$0.37
66.09
66.79
67.82
UNs ResNet34
UNes
65.73
Ouns
(-GManbba)
UNet ConNNNXiS) -GMambo
ReNNed4-GMaal
57.17 2230
52.90:240
54,00:144
68
69.33:356
72.17 2:70
78.46:7700
69.92:
74.57
LINen Sonn-SSinTTS--MMaaa D'-Mambb
UNer Cun GManba
UNes ResNe134 GMamba
67.62
70.23/1
(6,38:22113
Experimental Setup. In experiments, we select UNet as the baseline network and insert GMamba in a residual connection manner at each stage of the network encoder and decoder, with a total of
7 GMamba modules inserted. We compare against state-of-the-art global modeling methods: (1) attention-based: Swin Transformer (Swin) (Liu et al., 2021), Swin Transformer V2 (SwinV2) (Liu et al., 2022), and (2) SSM-based: Vim (Zhu al., 2024a), VMamba (Liu et al., 2024b), Tiny Vim (Ma et al., 2024). All methods use identical insertion strategies. For fair comparison, we employ publicly available code and common training/testing settings from GeoSeg (Wang et al., 2022). All models use identical configurations: batch size, training epochs, etc. Details are in the appendix.
Table 2: Performance comparison of GMamba and other global modeling modules on the Vaihingen dataset across different backbones.
Model Variant
Params (M)
FLOPs
mloU (%)
mPF (%)
OA (%)
UNet- NeNN-RR (Raseline)
25.33
30:32
81.65
89:24
91.86
Swin (X7)
35.81
43.45
83.24 (11.5)
90.63 (71.9%
93.08 (11.22)
SwinV2
35,86
43
83.10
90.5 54 (11
95.04
VIM (x
35.81
(11.3)
(11.27
92.93 (1107)
VMambu (xx)
32.45
38.49
83.24 (11
90.62 (71.30
93.04 (11.3)
VMM (x7)
31.19
36.51
83.17 (11:2:
90.59 (11.25)
92.99 (1115)
Marnh Version (x7)
34,87
39.78
83.20
62
93.00
Sputial Mamnaa (x7)
30.92
35.3
82.90 25:
92.85 (1000)
FregMamba (x7)
31.98
36.21
85.00 en M5
90.55 50 211:60
92,90 (11.00
Group Mamba (x7)
29.72
35. 15
82,99
90.41
92.85 86
GMamba (x7) (Ours)
30.96
36.30
84.74
(10,52)
93.72 (11.60
UNet Swint TI (Buseline)
36.48
44.46
82.44
89.75
92.
Swin(xx)) (xT)
60.01
73.27
83,70 760
90.92 (11.17)
93.12 (1090)
Swin (x7)
60.07
73.28
(11.19)
(11.0)
VIM (x7)
42,83
57.99
83.62 19:
(11
(1007)
VMambaa (x7)
$2,06
61.99
81.07 (11
91.14 (11.9%)
93.32 (1114)
VIM (x7)
49.38
58.01
84.04
91.13
11.28
Manna Version (x7)
52.47
62.95
(41
(11.15)
93.10 (1002)
Spatial Maroba (x7)
48.93
$6.88
83.40 (r se
90.70 70 (10or))
92.92 m7170
FregMambu (x7)
49.95
$7.98
83.55 e11:11
90.52 (1144))
93.00 (1452)
Group Mumba (x:)
46.31
$5.15
83.51
80
92.97
GMarmba (x7) (Ours)
49.13
57.81
84.83 (12.99)
91.61 (11.900
93.65 (11-4)
UNdt-oonNeeitS) (Bascline)
$8.42
68.
83.11
90, 19
92.
Swin (x7)
81.95
97.69
84.82
91.59 11.599mmm
93.57
SwinV2 (x6)
81.77
93.61
84.36 25:
211.15)
(11.7)
VIM (x7)
64.76
78.09
84.24
ct 13:
91.22 21.22.20 (T1ur))
93.37 (117))
VMamho (x7)
73.99
86.41
84.56 65)
91 45 c11.70
93.56 30
Timy (X7)
71.31
(11.14)
(11ID)
Marnha Version (x7)
74.87
88.47
80 Mio
91.5 55 (11.360
93.55 (11.55
Spatial Mamba (x7)
70.93
B1.92
81.50 (11.399
91.33 (11.15)
93.35 (1125)
FregMamba (x
71.95
85.
84.60
91.44 .2
93.42
Group Mamba (x
79.60
48:
(11.25)
(1185)
GMamma 2) (Ouns)
71.06
85.66
86.00 e77 se:
92.31 (17.17)
93.99 (11.0)
Results Comparison. Table I presents semantic segmentation performance results of GMamba on four remote sensing datasets using different backbone networks. GMamba achieves consistent mloU improvements across all datasets and backbones, demonstrating universality and plug-and-pla play char- acteristics for both CNN and Transformer- based backbones. GMamba particularly excels when paired with the powerful ConyNeXt(S) backbone, surpassing existing methods on all datasets. To
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Published as a conference paper at ICLR 2026
validate GMamba's effectiveness, compare it with various global modeling modules using UNet baseline on Vaihingen dataset. Table shows that while Transformer and Mamba-base modules im- prove accuracy lightweight ResNet34, Transformer variants (Swin, SwinV2) introduce substan- tial parameters and FLOPs due to quadratic complexity. Mamha variants (Vim, VMamba, Tiny Vim) show limited global modeling capability with modest gains. In contrast, GMamba achieves superior accuracy-efficient trade-off. On global modeling backbones (Swin(T)), GMamba extracts fine- grained global information to enhance performance. On complex CNN backbones (ConvNeX((SS)), it achieves optimal results. Complexity and qualitative analysis is provided in Appendix.
3.2 OBJECT DETECTION AND INSTANCE SEGMENTATION ON MS-COCO
To verify the effectiveness of the GMamba Block other downstream tasks, we conduct exper- iments on object detection and instance segmentation using the 2017 MS-COCO dataset, which contains 118,000 training and 5,000 validation images, covering 80 object categories.
Experimental Setup. We use the MMDetection (Chen et al., 2019) framework and conduct experi- ments on the MS-COCO dataset. For object detection, we adopt pre-trained ResNet50 and Swin(T) as the backbone networks of the detectors and employ Faster R-CNN (Ren et al., 2016) and Mask R-CNN (He et al., 2017) as the detection models, with Feature Pyramid Network (FPN) (Lin al., 2017) as the neck structure. For instance segmentation, we use Mask R-CNN with Swin(T) as the backbone and FPN as the neck. We insert the GMamba module into the first three stages of the back- bone through residual connections to provide global information. All comparison modules (Swin, SwinV2, Vim, VMamba, and Tiny Vim) adopt the same insertion strategy and training configuration. Further experimental details and insertion strategies are provided in the appendix.
Table 3: Comparison of GMamba and other global modeling modules inserted into the first three stages of different backbones (ResNet50 / Swin(T)) on the MS-COCO object detection task with Faster R-CNN and Mask R-CNN.
Model Varian
(S)
APss (3)
APrs (9)
APs (9)
APar (8)
(8))
Peenn (M)
FLOPX (C
Fintor R-CN
Baseline (RteNNetO)
-win 5)
58.7
210.17(70.88
TinyM33 (x33
58.6
61.40.41.1
208.37/78
VMaznbo (K3)
37.6
58.8
40.
21.5
41.4
00 (4.77
205167/79.100
Mambo
30.7
58.
41.4
(5.40X45.11
209521199400
Spotial Mamba (C3)
38.6
40.
21.4
41.2
45.3
64.30X
206.270 (9./10)
PregMaamee 3)
57.6
58.
4019
21.5
41.3
45.4
64500 (55666666)
29.057279000
Group Manba (x3)
$7.5
58.5
40.5
21.3
41.0
45,5
64.80.4433
209.37((7888))
GMambo (X3) (Ours)
38.5
39.6
42.2
22.1
42.0
49.9
61.40441.3
210.22/79.06
Raseline (hwin (T)
41.6
64.
45.2
25.2
44.8
55.4
45115/29.5
213300966 10)
(MMambe (x 3 (Om))
42,9
68.6
46.9
27.1
46.4
56.4
55.05090.61
216. (58.15)
Must. R. CMN
Bascline (ResNa50))
37.5
58.1
41.3
21.2
40.9
45.3
46.45:23.5)
260.14,76.500
Swin 5)
59.3
41.7
21.6
42.2
49.5
19:15006.11 A1
263 (0)
(winV)(xx))
59.1
41.7
23.2
43.9
49.6
79.59/56.61
263.44/79 X0)
38.2
58.8
41.6
21.5
41.6
49.9
6410041.1
VMunta (x3)
59.1
41.9
23.5
40.8
49.8
67.65.4.7)
262.74
Maniia Misiion
38.2
59.8
22.3
42.0
40.2
263.04 68.05/45.11
Sponia (C3)
262.36
ProgMMames (x:5)
22.1
262
Unoup Mambe (Chme)
068..70 79.65)
Buseline (SwiaiT)
64.7
47.79
256.000
GMaumb (x3)
57,89637.6)
269 299.15)9.225)
Table 4: Comparison of GMamba and other global modeling modules with Mask R-CNN (Swin(T) backbone) on MS- COS-CCCO instance segmentation
Model Variar
AP (%)
APhs (%)
APss
APs
APsr
APr. (16)
Phramm
PLOP% (C3)
Mash R-CHV
Baseline (SwinIT))
38.7
61.3
41.5
20.2
41.6
55.7
256,00660100 47.79227.5)
Swin (X3)
38.4
19.2
41.7
21.6
42.2
49.3
06.49 06.2)
259.50 (0)
SwinV2
19.1
61.9
42.0
21.3
42.3
57.4
07.4K 66.31
269. 209.3899..00 41)
TIny (x33
58.2
58.8
41.6
21.5
41.6
49.9
58 31
267.80897 90)
VMomha (x:3
$6.9
61.8
41.9
1988
41.7
56.9
40.59 40
268 71)
Mumbe Version (x3)
39.0
61.2
42.0
21.0
43.6
57.0
66,39 11
209.50899 99.00)
Spotia Mambu (xC3)
38.5
60.7
41.6
20.6
43.5
50.5
66.1943359 51
200 260.20 30)
DregMaams (x3)
614
43.2
21.1
41.7
59.2
66.29 00,00
2601 40)
Gropp Mamba (x.1)
619
41.9
20.2
41.9
51.2
63.9966355
268 (0)
GManba (X3) (uus)
39.8
62.7
20.1
42.7
55.0
$7.89/37.6)
269.15)99.25)
Results Comparison. From the results in Tables 3 and 4, GMamba provides consistent performance
improvements on both object detection and instance segmentation tasks. On Faster R-CNN and Mask R-CNN with a pre-trained ResNet-50 backbone, GMamba achieves an APL improvement of 1.9% and 2.0% over baseline, demonstrating its strong global modeling capability. Our method also significantly outperforms other global modeling modules when integrated with Swin(T). Due to space constraints, the comparison results between GMamba and other global modeling modules

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Published as a conference paper at ICLR 2026
using the Swin(T) backbone object detection are provided in the appendix. GMamba exhibits strong performance on instance segmentation, achieving the best results on most AP metrics.
3.3 ABLATION STUDIES
Finally, we conduct extensive ablation studies on the Vaihingen dataset using UNet with ConvNeet- Small as the baseline validate the effectiveness of the GSSM module design.
Table 5: Ablation Study of GSSM Components
Model Variun
BSSM Medule
Perfomence
FGMM
SSM
Parama
(L)
(A6
SSM NoNoSSal
53.42
83.11
68.31
$2.00
84.01
REM + SSM
70.30
$5.30
85.30
91.89
93.51
(DFT)) FGMM SSM
68.62
82.24
84.79
91.58
93.51
CSSM Midtilo (All)
71.06
35.66
86.00
92.31
93.99
Table 6: Ablation Study on Scan Strategies in GSSM
Scun Strategy
Parums (M)
FLOPs (G)
mloU
mF1
OA (96)
Bidirectional Scan
75.75
88.50
85.73
92.15
93.88
Four-way Scun
78.50
91.00
85.98
92.30
93.98
Single-direction (Ours)
71.06
92.31
93.99
Table 7: Effect of Replacing Global Modeling Module in GMamba
GMamba Variant
Params (M)
F1.OPs (G)
mloU (%)
mFI (%)
OA (%)
GMamba w/ Self-Altention
74,87
91.20
84.78
91.57
93.62
GMamba VSSM (Mamba)
68.3
82.00
84.01
91.01
93.38
GMamba w/ GSSM (Ours)
71.06
85.66
86.00
92.31
93.99
Effectiveness of GSSM components. As shown in Table 5, SSM alone achieves +0.90% mIoU improvement, demonstrating effective global information capture. Adding FEM significantly boosts performance to 85.30% mloU, validating its global semantic injection capability. Replacing FEM with simple DFT and adding FGMM drops performance to 84.79% mloU, indicating the necessity of adaptive mechanisms. The complete GSSM module achieves optimal performance with reasonable computational overhead, validating the theoretical design.
The Impact of Scan Strategies in GSSM. We modified GSSM to incorporate bidirectional and four-way scanning, as shown Table 6. The results demonstrate that GSSM can achieve genuine global perception through frequency-domain modulation using only unidirectional scanning, with- out the need for more complex scanning mechanisms. Introducing additional scanning strategies mercly increases computational overhead.
Effectiveness of GSSM for global modeling. As shown in Table 7, our GSSM not only demon- strates superiority in theoretical analysis but is also empirically shown to outperform existing global modeling modules. Although it introduces slightly higher computational complexity compared to the complexcy VSSM, it achieves substantial performance improvement. Compared with standard self-attention, GSSM maintains significantly lower complexity while delivering the best overall performance.
More Ablations. In the Appendix, we provide additional ablation studies, including: (1) the impact of applying GMamba different layer positions: (2) the analysis of GMamba's receptive field; (3) the effect of frequency-domat information; (4) the robustness evaluation; (5) the efficiency analysis of GSSM; and (6) the impact of different frequency-domen integration strategies, among others.
CONCLUSION AND DISCUSSION
This paper first formulates a rigorous mathematical definition of image global modeling, laying the foundation for designing globally aware models with stronger theoretical grounding and inter- pretability, We establish a comprehensive theoretical framework for frequency-domain modulation, resulting in an SSM architecture that is explicit, uniform, non-causal, and mathematically well- defined, making it more suitable for the global modeling of images. Guided by this theory, we design the GSSM module and, based on construct the and-play GMamba module. By in- troducing DFT-based global attribute modulation mechanism, the SSM overcomes the lack of an explicit non-causal global perception mechanism. Both theoretical analysis and empirical evaluation demonstrate that this module exhibits excellent global modeling capability and strong adaptability across multiple tasks. See the appendix for details on LLM usage.
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ACKNOWLEDGEMENTS
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 62495091, 62125305, and 52508037).
ETHICS STATEMENT
This study does involve human subjects, personally identifiable information, sensitive data. The experiments are conducted on publicly available datasets that have been widely used in prior research. We adhere the dataset licenses and usage agreements and do not raise any additional ethical concerns. The proposed methods are intended solely for academic research and do introduce foresecable harmful applications.
REPRODUCIBILITY STATEMENT
We have taken several measures to ensure the reproducibility of our experiments. All model archi- tectures, training procedures, and hyperparameter settings are described in comprehensive detail. Dataset preprocessing strictly follows the official guidelines and standard protocols. All theoretical derivations and proof's are provided in the appendix. To further support reproducibility, we provide anonymized source code the supplementary materials.

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Published as a conference paper at ICLR 2026
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APPENDIX
In Sec. A, we describe the use LLMs. In Sec. B, we discuss the related work. In Sec. C, we present the complete derivation of the discrete-time SSM frequency-donee domain transfer function. Sec. D, we provide full proof of the global properties of the DFT, and in Sec. E, we give detailed proof that the 2D-DFT satisfies our proposed definition for global image modeling. detail the algorithm of the GSSM module and analyze the computational complexity of GMamba. In Sec. H. we describe the datasets and experimental settings in detail. In Sec. we provide addi- tional experiments
Sec. F and Sec. G, we
semantic segmentation tasks, including (1) comparisons of model complexity, (2) ablation studies for integrating GMamba at different stages, and (3) visual result analysis. In Sec. present further experiments object detection and instance segmentation, including (1) comprehensive comparisons for object detection, (2) ablation studies for inserting GMamba at dif- ferent stages, and (3) visualization analysis. Sec. K, conduct additional analyses on the GSSM module. Finally, in Sec. L, we analyzed the failure cases.
A THE USE OF LARGE LANGUAGE MODELS
To improve the quality of the manuscript, LLMs were used to assist with writing and editing, limited solely to language polishing. The authors remain fully responsible for the content.
B RELATED WORK
B.I STATE SPACE MODELS IN VISUAL TASKS
State Space Models offer linear computational complexity and efficiently capture long-range de- pendencies, making them a promising alternative to Transformers in computer vision. However, SSMs rely on autoregressive formulations suited for causal sequences, a property that image data inherently lacks (Yu & Wang, 2025). To address this, several improvements (Liu al., 2024a; Chen et al., 2024a; Cheng et al., 2024; Shi et al., 2025b; Deng & Gu, 2024; Xu et al., 2025; Hui et al., 2025; Shaker al., 2025a; Ma et al., 2026) have been proposed.
To better capture 2D spatial context, many works have focused on modifying the scanning mecha- nism. For instance, Vim (Zhu al., 2024a) uses bidirectional SSMs enhance spatial understand- ing by modeling forward and backward directions, but at high computational cost and with limited fusion effectiveness. Mamba Vision (Hatamizadeh & Kautz, 2025) preserves the one-directional SSM formulation but incorporates self-attention model global image dependencies, which also increases the computational complexity. VMamba (Liu et al., 2024b) introduces a two-dimensional selective scanning mechanism to capture context from multiple directions. Further addressing the 2D spatial structure challenge, Spatial- (Xiao et al., 2025) introduces a structure-aware state fusion equation, leveraging dilated convolutions to directly enhance spatial context modeling within the state space. Similarly, GroupMamba (Shaker et al., 2025b) employs grouped scanning mecha- nisms to improve the representation of spatial relationships.
Despite these advances, existing methods still face limitations. Approaches like VMamba, Spatial- Mamba, and GroupMamba attempt to capture 2D context by complicating the spatial scanning or fusion mechanisms, which can increase computational overhead (Zhu et al., 2024b) and still rely on autoregressive mechanisms to progressively build global representations. In contrast, our GSSM of- fers a simpler, more efficient design by adopting unidirectional modeling and integrating frequency- domain global modeling to guide state selection and updates, enabling true global awareness tailored for image tasks.
B.2 FREQUENCY LEARNING
The Discrete Fourier Transform (Bone et al., 1986; Pei & Yeh, 1998; Winograd, 1978; Sundararajan, 2001: Feng et al., 2023) is a classical technique for analyzing the frequency-domain characteristics of digital signals. providing global representation. Recent studies (Mao et al., 2023; Liu et al., 2025: Cai et al., 2021; Gao et al., 2024; Feng et al., 2024) have explored combining frequency and spatial information for visual tasks. For example, AFENet (Gao al., 2025a) introduces adaptive
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trequency-spatie interaction module, and SFFNet (Yang al., 2024) fuses frequency components
with CNNs. Other works propose novel frequency- based operators. SPANet (Yun et al., 2023) designs frequency-balanccin token mixer using spectral modulation. FAD (Shi et al., 2025a), addressing cross-domain learning, proposes a Frequency Diversion Adapter that partitions features into frequency bands and adapts each band separately. Similarly, Freq (Zou et al., 2024), designed for image deraining, introduces a "triple interaction structure" with parallel spatial Mamba, "frequency band Mamba," and Fourier global modeling modules.
Building on this foundation, we further investigate how to integrate frequency-domain information into SSMs. Most existing approaches- such as dual-branch frequency-done domaan structures (Luan et al., 2025; Tan et al., 2024; Bo et al., 2025), complex parallel architectures like FreqMamba (Zou et al., 2024), newly designed frequency mixers (Yun et al., 2023), or multi-band adapters (Shi et al., 2025a) 20hha)-enhance glohal perception through post-hoe fusion or external block-level modu- lation. While such external adaptations are effective, the frequency-domain information merely serves as supplementary signal to spatial-domain features and cannot influence the underlying modeling mechanism. In contrast, our GSSM is grounded in the proposed theoretical framework of deqqeecy-modulltee
SSMs. We introduce rreuenncydomail information before the modeling process and allow it to directly participate in the state-update dynamics of the SSM itself. This en- ables the model to acquire global perspective during the core modeling stage, rather than simply enriching the final feature representation.
C DERIVATION OF DISCRETE-TIME SSM FREQUENCY-DOMANN TRANSFER FUNCTION
We provide a detailed derivation of the frequency-domain transfer function for discrete-time SSMs. Consider discrete-time state-space model defined by: Ft = A + Bug
(19)
yt Cr.,
(20)
where A= = cA is the discrete-time state transition matrix, B = A- - I)B is the discrete- time input matrix, C is the output matrix, and the system causal and stable with p(A) <
Our objective is to derive the loqquency-domain transfer function:
H(w) C( - A)-1B
(21)
C.1 DERIVATION
Taking the Z-transform of Eq. 19 with zero initial conditions (2o = 0):
=x(x)) = AX(=) A (U)))
(22)
Rearranging terms:
(2l - A)x(a) = (B)
(23)
Solving for X()):
X(x) = (zl - BU()))
(24)
Taking the Z-transform of Eq. 20:
((2) = CX(2)
(25)
Substituting Eq. 24:
(()) = C(2l A BU)))
(26)
The Z-domain transfer function is defined as:
( Y())
C(2l - A)
(27)
U(z)
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By applying cهع to Eq. 27, obtain the trequency-domit transfer function:
H(w) = H())
= --
(28)
C.2 STABILITY ANALYSIS
The stability condition p(A) < ensures that the transfer function (w) is well-defined for all [-M, n, x|.
((A) < 1, then the matrix (I- Ae Ae- is invertible for all w E R. Let be any eigenvalue of A with [^] < 1. For any E R. have le |e 1, so aT jwl [t] < 1. This implies that Je-je # for any eigenvalue of Therefore, the matrix (7 Ae-Jw) has no zero eigenvalues and is invertible.
C.3 FINAL RESULT
The requency-domaile transfer function for a causal and stable discrete- -icerete-timeeeeee SSM is:
((w) = C(e) B.
(29)
D COMPLETE PROOF OF THE GLOBAL PROPERTIES OF THE DFT
To intuitively demonstrate the global properties of the DFT, we visualize the global perception of DFT as illustrated in Fig. 3: when a minor local perturbation is applied to time-domain signal, its frequency spectrum undergoes extensive global changes; conversely, local modifications in the frequency domain also induce holistic fluctuations throughout the time-domain signal.
[[:] N Σ 1
DFT
IDFT
Global Perception
Global Perception
Time Domain Signal
Frequency Spectrum
Reconstructed Signal
Figure 3: small perturbation in the time-domain signal leads global changes the frequency spectrum, and vice versa, illustrating the global sensitivity of both the DFT and its inverse.
Moreover, we provide a rigorous mathematical proof demonstrating that the DFT possesses a global property: local perturbation in domain (time frequency) induces non-zero responses at all indices in the dual domain.
Let [[n] CN be discrete signal length N. The DFT and its inverse are defined follows:
Flk]
Σ
k= I...,....,NN N-1
(30)
N-1
f|n]
F[k]
kn n ==0,1 I.
(31)
D.1 LOCAL PERTURBATION IN TIME AFFECTS ALL FREQUENCIES
We introduce small additive perturbation Af E C at time index no.
The perturbed signal becomes:
[[]]] + AS, n2p [[m])
f'
(32)
otherwise
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The DFT of the perturbed signal is:
N-1
F
[[n] e km
(33)
n=0
N-1
f|n] -it + Af e k5
(34)
= F[K] + e kg
(35)
Thus, the frequency-domain difference is:
AF = F" F(k] = Aʃ - kno
(36)
Since e- 3 kmo # O holds for all k, we conclude that a perturbation A at a single time index affects
all frequency components, i.e., A + 0 for all k. This proves the global property of the DFT to changes in the time domain.
D.2 LOCAL PERTURBATION IN FREQUENCY AFFECTS ALL TIME INDICES
Now consider a perturbation Af introduced at frequency index kg. The perturbed spectrum is:
[[
+ Af,
h = ko
F'[
(37)
F[
otherwise
The inverse DFT the perturbed spectrum becomes:
N-
f'm]]
=
F'[
(38)
N
k=0
1
N-1
F(K]
e
kn
Af
e
3 kon
(39)
N
N
k=0
AS
=
fmm]
+
kon
(40)
N
The corresponding time-domain difference is:
Af N
Afin| ['[m] fin]
.e Kon
(41)
Since the exponential term remains non-zero for all n, it follows that local perturbation A at single frequency index affects all time-domain components, i.e., Af * 0 for all n. This confirms the global property of the inverse DFT to changes in the frequency domain.
D.3 CONCLUSION
We have rigorously proven that the Discrete Fourier Transform and its inverse are inherently global in nature: any local modification in one domain (time frequency) induces non-zero changes across all indices in the dual domain. This global property enables SSMs to achieve global receptive fields, precisely regulating the state update and modeling processes of SSMs, thereby resulting in superior performance of SSMs in vision tasks.
E PROOF THAT THE 2D-DFT SATISFIES THE PROPOSED DEFINITION
We prove that both the 2D-DFT (forward) and its inverse satisfy the proposed definition.
For image X E HxH the forward and inverse 2D-DFT are defined follows:
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W-I
X Σ
Σ
Xije 2ml 2m #+W)
u= o..,..., H 1, v ....., W -
(42)
i=0 j=0
X,y=
1
Σ a=0
Σ
2x (x(
i= i......, - J, j= 0 W -1
(43)
HW
ueu
E. FORWARD 2D-DFT SATISFIES GLOBAL GRADIENT DEPENDENCY
Function Definition: For image X RR consider the forward transform as the modeling function:
H- 1 W-1
forword X) Dup
Σ
Σ
X
2m 2+(
=- 0,
1, v -= o,..., W -1 (44)
1=0 1=
Gradient Computation:
The gradient with respect to input pixel Xm, is:
df forward X),
=e
-2rri( up 1P
(45)
x mmn
The Frobenius norm over all frequency components:
0S f X
#-1 W
Σ
2nd 4 4 )
HW
(46)
2Xmmm
N=
#=
Define the global influence function:
I forward (m, n) = HWW >
(47)
Conclusion for Forward Transform:
0f forwardd( 0 mn
VHW Ifowward n)
(48)
F
E.2 INVERSE 2D-DFT SATISFIES GLOBAL GRADIENT DEPENDENCY
Function Definition: Consider the inverse transform as the modeling function for frequency domain input X E C.wW
#-1 W-1
(anverse(81s)) HW
u c (mi
i= H-1, j = 0...., W-1 (49)
Gradient Computation:
The gradient with respect to frequency component Xp.9 is:
Sinverse X)ss
2mi 2mi($ 84
(50)
0x p.g
HW
The Frobenius all spatial positions:
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finverse (X)
W-1
Σ
1
2
37
(8)
2
1
(51)
0Xp. P.r
HW
VWW
F
Define the global influence function:
(p.vers((P9))
(52)
VHW
Conclusion for Inverse Transform:
Öf Oiiverse
X)
(p,
(53)
0X p.
VHW
E.3 CONSTRAINT ANALYSIS
The 2D-DFT inherently avoids imposing strict order-dependent constraints, both the forward and inverse transforms treat spatial positions and frequency components uniformly, without relying on any specific ordering of the input pixels. As result, the global gradient dependency property holds regardless of the input arrangement, ensuring that exhibits the desired order-invariant global modeling behavior.
E.4 CONCLUSION
Based on the above analysis, we have rigorously demonstrated that both the forward and inverse 2D-DFT satisfy our proposed mathematical definition of global image modeling. Specifically, for any spatial pixel (i,j) or frequency component (W1,w2), the Frobenius norm of the corresponding gradient is strictly positive and bounded below by a constant:
II(i,)
inf I(i,)) 0, (FJ)
(54)
ax.,j
with Iorwaadd = v HW for the forward transform and Iimeerse = 1/v HW for the inverse trans- form.
F ALGORITHM FLOW OF THE GSSM MODULE
We provide the detailed procedure of GSSM in Algorithm 1. The input feature X is first linearly mapped into two branches, x and X1, and preliminary features are extracted through one-dimensional convolution and SiLU activation. If the frequency domain module is enabled (usefreq = True), a 2D DFT is applied to x to extract high and low frequency components, which then weighted and reconstructed. The modulation coefficients a₃ and 02 used to guide the fusion of frequency-dome -omaann information with the original features. The fused features are then fed into the SSM. where Long-range dependencies are modeled via selective scanning. Finally, the result concatenated with X, and projected to obtain the output X
G GMAMBA BLOCK EFFICIENCY ANALYSIS
We follow the computational complexity analysis methodology Vim (Zhu al., 2024a), where the input sequence is defined as L. Mx with M H x W denoting the sequence length and D representing the hidden dimension. The computational complexities of Self-Attention (Shaw
et al., 2018 1)), Mamba (Gu & Dao, 2023), VMamba (Liu et al., 2024b), and Vim (Zhu et al., 2024a) are given by:
(Self-AAtennton)) = 4MD² + 2M"D, ?(Mamba) = 8MDDN 2(Vim) 16MDN, 2(VMamba) 32MDN
(55)
(56)
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Algorithm GSSM Module Process
Input: Hidden states X & RBxLxD, feature dimension
Parameter: Frequency flag fre. learnable weights (8low, thigh, Oratio
Output: Global-aware representation oout E Bx
I: x, xixI Linear(X)
x < (es((Cooll((()))..... <- SiLU((onvId((xi))
3: if uss__frqq = True then
4: 1 Frequency Encoding Module */
5: X /vee DFFT2D x B, D', D'H,WW)
Xiows Xhigh freq. wwt.cddccooeee....mm freg)
7:
Flow + o((tow) - IDFT2D( (iow)
8:
Fhigh + a(0high) IDFT2D(X (Xiigt
9:
F gllobal & Concaa(( [xc, F Fow Fhigh), dim -1)
10:
1t Frequency- Guidee Modulation */
on 02 +- (igmoid(ConvBleee
globba))
12:
x e1 x x 02 F global
13: end if
14: /" State Space Modeling */
15: At, C SSM PaMMMPParsss
16: Discretize: At + softplus( At), A exp((Ato))
17: &- SelectiveScan(x: At, A, B)C)
18: Xone <- Linear Lineea(coonca((x) x1)))
19: return Xout
where is the state dimension (typically 16).
In our proposed GMamba, the FEM introduces an additional complexity of O(M log M). There- fore, the overall computational complexity GMamba is:
2(GMamba) = MN + M log M.
(57)
Notably, the complexity of GMamba scales in a linear-lggaittmiic manner with respect to the sequence length M, which is significantly more efficient than the quadratic complexity ((2 of conventional self-attention mechanisms.
H DATASETS AND EXPERIMENTAL DETAILS
H.1 DETAILED DESCRIPTION THE DATASET
Vaihingen. This dataset consists of 33 orthophoto images with 2500x2000 resolution and cm GSD, covering urban areas in Germany. We use only RGB images and exclude DSM data. The dataset includes six semantic categories: impervious surfaces, buildings, low vegetation, trees, cars, and clutter/background. Following standard protocol (Wang et al., 2022), we use 16 images for training and 17 for testing.
Potsdam.
This dataset contains 38 high-quality tiles with 6000 x 6000 resolution and cm GSD. We use only RGB bands and exclude image 7_10 due annotation errors. The semantic categories are consistent with Vaihingen. Following common practice (Wang et al., 2022), 23 images are used for training and 14 for testing.
LoveDA. This large-scale dataset covers urban and rural areas with 5987 images of 1024 x 1024 resolution and 0.3 GSD across three Chinese cities. includes seven categories: buildings, roads, water, vegetation, vehicles, clutter, and background. The standard split contains 2522/1669/1796 images for rrain/valiattion/eest.
UAVid. This UAV-based video semantic segmentation dataset contains 42 sequences with 4K reso- lution (3840x2160) captured from low altitudes. It covers diverse urban scenes including residential areas, commercial districts, and industrial zones. The dataset provides annotations for eight seman- tic classes: building, road, tree, low vegetation, moving car, static car, human, and clutter. Following the official split, we use 20 sequences for training, 7 for validation, and 15 for testing.
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Backhone
Output Image
Input Image
Upsampling
Upsampling pling
Upsampling ling
Seg Head
Stage 1
Stage
Stage 1
Stage
[Mambax
GMambax
GMumbax
[Mamba
Gitamba
GMammaxX
x
Encoder
Decoder
UNet
Figure 4: The GMamba module inserted after each CNN stage to inject global information into the feature representation.
Backbone
Outpul Image
Input Image
Stage 1
Stage 1
Stage
Stage
Faster RCNN
FPN
Mask RCNN
Glamba
G
Figure 5: Inserting GMamba modules into the first three stages of the backbone inject global information into feature representations.
H.2 EXPERIMENTAL DETAILS
Experimental Details on Vaihingen. We conduct experiments on the Vaihingen dataset using the popular GeoSeg (Wang et al., 2022) framework. To highlight the effectiveness of global modeling, we select the simple UNet network as the baseline and employ pre-trained ResNet34, Swin Transformer-Ting and Con-NeXt-Small as UNet backbones. For fair comparison, adopt GeoSeg's unified training configuration: batch size of 8, weight decay of 2.5e-4, initial learning rate of 6e-4, and training for 100 epochs. As shown in Fig. 4. insert modules into each output stage of the encoder and decoder via residual connections to provide global information, with a total of 7 modules insertable in the UNet network. All comparison modules (Swin Transformer (Liu al., 2021), Swin Transformer V2 (Liu et al., 2022), Vim (Zhu et al., 2024a), VMamba (Liu et al., 2024b), and Tiny Vim (Ma et al., 2024)) are inserted using the same strategy, maintaining identical training configurations, parameter settings, and module counts. Due to the high complexity of the ConvNeXt backbone and Swin Transformer V2, it is not feasible to train the full model single RTX 4090 (24GB) GPU. Therefore, we insert only 6 Swin Transformer V2 modules, leaving the last stage unchanged. All experiments are conducted using PyTorch on single NVIDIA RTX 4090 (24GB) GPU. We follow the official dataset split and cropping strategy, resizing all images to 1024x 1024, and report mean Intersection over Union (mloU), mean score (mF1), and Overall Accuracy (OA) metrics the test set.
Experimental details for Potsdam, LoveDA, and UAVid. Similar to the Vaihingen dataset, we conduct experiments Potsdam, LoveDA, and UAVid datasets using the GeoSeg framework. The experimental configurations follow GeoSeg's 's default settings: training for 100 epochs on Potsdam, 30 epochs LoveDA, and 40 epochs UAVid, with batch sizes set to 4, 8, and 2. respectively. All datasets are preprocessed using GeoSeg's tool and cropped to 1024 1024 size, with consistent experimental configurations maintained across all comparison modules.
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Experimental details MS-COCO. We conduct experiments the MS-COCO dataset (Lin et al., 2014) using the popular MMDetection (Chen et al., 2019) framework. Pre-trained ResNet50 (He et al., 2016) and Swin Transformer-Tin Tiny (Liu et al., 2021) are adopted the backbone net- works, with the Feature Pyramid Network (FPN) (Lin et al., 2017) serving as the neck architecture. For object detection, we employ Faster R-CNN (Ren al., 2016) and Mask R-CNN (He et al., 2017) as the detection heads. For instance segmentation, we use Mask R-CNN. To ensure fair com- parisons, we follow the default data processing pipeline and hyperparameter configurations provided by MMDetection. Our module is inserted into the first three stages of the backbone in residual manner to provide global information, as illustrated Fig. 5. For all comparison modules (Swin Transformer, Swin Transformer V2, VMamba, and Vimy, we adopt the same data preparation and parameter settings. All experiments are conducted on server equipped with 8 NVIDIA RTX 4090 GPUs (24GB), with each GPU processing 2 images. The models are trained for 12 epochs following the schedule.J. _lll training policy, where the learning rate is decayed by a factor of 10 at the 8th and 11th epochs. We evaluate the average precision (AP) over IoU thresholds ranging from 0.5 to 0.95 with a step size of 0.05. Additionally, we report AP metrics for small, medium, and large objects to provide comprehensive assessment of model performance.
I ADDITIONAL EXPERIMENTS ON SEMANTIC SEGMENTATION
1.1 COMPLEXITY ANALYSIS
To analyze the efficiency of GMamba, Table 8 demonstrates the comprehensive performance eval- uation of GMamba across different backbone architectures on the Vaihingen dataset. Our method consistently outperforms existing state-of-the-art approaches while maintaining computational ef- ficiency. Specifically, GMamba achieves competitive superior mloU scores compared to tablished methods: U-ResNet34 + GMamba reaches 84.74% mloU, surpassing DeepLaby3+ by 4.01% with significantly fewer parameters (30.96M vs. 59.30M) and reduced computational cost (36.30G vs. 181.20G Fi.OPs). When integrated with more powerful backbones, GMMmmba demon- strates scalable performance gains, with U-ConvNext(S) + GMamba achieving the highest mloU of 86.00% outperforming recent methods like XNet and SparseFormer. The consistent improvements across all three backbone Rechiectures-RReNee444 (+3.09%), Swin Transformer- Tinn (+2.39%) and ConvNeXt-Small (+2.89%) validate GMamba's 's universal applicability and hou-annd-play na- ture. While GMamba introduces moderate computational overhead (approximately 22% increase in parameters and 20% in FLOPs), this trade-off is justified by substantial accuracy gains, demonstrat- ing an effective balance between performance and efficiency for practical deployment scenarios.
Table Performance comparison of semantic segmentation methods on Vaihingen dataset and com- prehensive ablation study of GMamba enbancement. Evaluation metrics include parameters (M), FLOPs (G), model size (MB), and mean Intersection over Union (mloU).
Category
Model
Params (M)
FLOPS (G)
Model Size (MB)
minU (%)
DeepLabv3+ (Chen et al., 2018)
59.30
181.20
226.20
80.73
Existing Methods
FT-UNetFormer (Wang al., 2022)
96.00
128.40
366.30
84,10
OGGLNet (Ni et al., 2024)
34,83
605.00
132,90
83.89
SparseFormer (Chen et ul., 2024c)
42.52
41.95
162.17
84.12
XNet (/hou al., 2023)
41.42
115.09
158.03
84,43
UNet- NNNeeRRssNee34
25,33
30.32
96.85
81.65
Baseline
Backbones
UNet-Swintf
36.48
44.46
139.56
82.44
UNet-Con-NeeutSS
58.42
68.88
223.12
UNet ResNeRes GManba
30.96
36,30
118.45
84.74
GMamba
(Ours)
SWiet-Swn(TT--e GMamba
49.13
57.81
187.89
84.83
UNet- N + GMamba
71.06
85.66
271.39
86.00
I.2 ABLATION STUDY ON GMAMBA ENCODER-DECODER INTEGRATION
To validate the effectiveness of GMamba modules in providing global information at different net- work stages, we conduct detailed analysis of GMamba insertion positions and quantities across
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different backbone networks on the Vaihingen dataset, with results shown in Tables 9, 10, and 11. In- tegrating GMamba in both encoder and decoder stages achieves optimal performance improvements across all three backbone networks (U-ConwNeXtt-Small U-Swin(T), and U-ResNet34), with mloU improvements of +2.89%, +2.39%, and +3.09% respectively. The analysis reveals that GMamba integration in the encoder typically provides more significant performance gains than decoder-only integration, particularly evident in D--ConNNett-Smiee (+1.73% vs +1.59% mloU), indicating that early-stage global context modeling in the encoder plays crucial role in effective feature representation. Notably, the joint encoder-decode integration demonstrates significant synergistic effects, with performance substantially exceeding the simple summation of individual contributions, proving GMamba's complementary roles in global context capture and feature refinement. From computational efficiency perspective, all architectures main- tain reasonable computational overhead, with parameter increases of 22%-35% and FL.O increases of 17%-30%, while achieving accuracy improvements exceeding 2% mloU.
(+1.59% vs +1.02% mloU) and U-ResNet34
Table 9; Ablation study of GMamba integration in Encoder and Decoder based on U-Con VNext- Small.
Model Variant
Encoder
Decoder
Params (M)
FLOPs (G)
mloU (%)
Fl (%)
OA (%)
Baseline CUNet-ConVNext-Snee
58.42
68.88
83.11
90.19
92.30
GMamba in Encoder
X V
68.55
76.87
84,70
91.52
93,59
GMamba in Decoder
V x
60.93
74.24
84.13
91.16
93.35
GMamba in Both
x
x
71.06
85.66
86.00
92.31
93.99
Table 10: Ablation study of GMamba integration in Encoder and Decoder based on U-Swin(T).
Model Variant
Encoder
Decoder
Params (M)
FLOPs (G)
mloU (%)
FI (%)
OA (%)
Baseline (UNet-Swin(T))
36.48
44.46
82.44
89.75
92.18
GMamba in Encoder
x
46.62
52.45
83.26
90.64
93.12
GMamba in Decoder
V x
39.00
49.82
83.46
90.76
93.07
GMamba in Both
x
V x
49.13
57.81
84.83
91.61
93.65
Table 11: Ablation study of GMamba integration in Encoder and Decoder based on U-ResNet34.
Model Variant
Encoder
Decoder
Params (M)
FL.PPs (G)
mloU (%)
Fl (%)
OA (%)
Baseline (UNet-ResNet34)
25.33
30.32
81.65
89.24
91.86
GMamba in Encoder
X
29,84
33.89
83,38
90.72
93.12
GMamba in Decoder
v x
26.45
32.73
83.24
90.63
93.13
GMamba in Both
x4
V x
30.96
36.30
84.74
91.56
93.72
1.3 VISUALIZATION AND ANALYSIS OF SEMANTIC SEGMENTATION RESULTS
We further visualized the segmentation results on four remote sensing datasets before and after integrating GMamba into different backbone networks, as shown in Figs. 6-9, The black boxes highlight the performance differences between models with and without GMamba. The results demonstrate that GMamba integration can consistently improve segmentation performance across datasets, exhibiting remarkable generalization capabilities and global modeling advantages.
As illustrated in Fig. 6 and Fig. 7, on the Vaihingen and Potsdam datasets, the incorporation of GMamba significantly enhances the segmentation performance complex-shaped objects such as buildings and vehicles, which typically exhibit spatial distribution characteristics throughout the entire scene. This performance improvement fully demonstrates that GMamba can effectively in- tegrate information from distant regions, thereby overcoming the inherent limitations of local ceptive fields. Similarly, in the LoveDA dataset experiments shown in Fig. 8, large-scale categories such buildings and agricultural land achieve higher segmentation accuracy, reflecting GMamba's
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capability maintain object boundary consistency and reduce misclassification rates in complex and heterogeneous geographical landscapes. The results in Fig. 9 show that GMamba enhances the model's 's ability to extract global information the UAVid dataset, enabling more accurate identifi- cation of spatially extended objects such as roads, rivers, and large buildings, which typically span multiple local patches. These observations collectively validate the effectiveness of GMamba in global feature modeling, as well as its superior generalization performance across different datasets and backbone architectures.
Impervious
Butldingg
vogetation
GroundTruth
UNet
UNit ResNecR4
UNet SwincT)
UNet Swin(T) 6Mantaa
UNit DunNNestE))
UNet Con -Mannh
RosNetti
OMamba
Figure 6: Segmentation results on the Vaihingen dataset with different backbones, before and after integrating GMamba. Black boxes highlight improvements in globally dependent classes such as Buildings and Cars.
Imperstons surface
Building
Lewvegetation
Tree
clutter
Groundlruth
UNet
UNet BosNett4
UNet Swint?)
UNet SwiaCT) Chuuma
UÑet ConveNestt5)
UNet CoosRoot))
Figure 7: Segmentation results on the Potsdam dataset with different backbones. before and after integrating GMamba. GMamba enhances global context modeling for classes like Buildings and Cars.
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Radigroand
Building
Read
Water
Barrea
Fecest
Agriculural
Image
UNrt SwierT)
-ResNec34
-OMamla
-Manna
CenNNestt))
-GManba
Figure 8: Segmentation results the LoveDA dataset with different backbones, before and after integrating GMamba. GMamba improves segmentation of large-scale classes such Buildings and Agriculture.
Building
Image
GroundTruth
Rood
Tree
Low vegetation
UNet ResNet34
UNet ResNet34 GMamba
Human
UNee Swin(T)
UNet Swin(T) GMamba
Bicycle
Clutter
UNet ConvNext(S)
UNet CCnnvNext)) GMamba
Figure 9: Segmentation results the UAVid dataset with different backbones. before and after integrating GMamba. GMamba strengthens global information extraction, enabling better recognition of spatially extended objects.
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J ADDITIONAL EXPERIMENTS ON OBJECT DETECTION AND INSTANCE SEGMENTATION
J.1 COMPLETE COMPARISON EXPERIMENTS ON OBJECT DETECTION
In Table 12, we present a complete comparison between GMamba and other global modeling mod- ules the MS-COCO dataset for object detection, across different backbones (ResNet-50 and Swin-T) as well as model architectures.
Table 12: Comparison of GMamba and other global modeling modules inserted into the first three stages of different backbones (ResNet-50/ Swin-T) on the MS-COCO object detection task with Faster R-CNN and Mask R-CNN.
Model Variasi
(9))
APL (R)
APra (56)
APy (R)
APu (99)
AP. (R3
Parami (M)
FLOP& (G)
Faster R-UWW
Boselin (ReaNes50))
40.5
43.80023.5)
207 207.07176.50
Swin (x3)
20.0
59.1
41.01
23.0
41.5
-18.4
26.36556-1 56-4)
210.57190.00
Swar22 (c))
57.2
56.7
40.9
21.5
41.3
46.5
76.90156.0 6)
210.37 80)
TeyVVM (x3)
37.
58.6
40.6
21.6
41.3
45.4
61.4041.111 11
208
VMaanaa Co-3g
41.4
65.0044.71
Manbe
403
64.304410)
27474
FregMannh (-3)
37.6
56.7
40.9
21.5
41.3
48.4
64.9044..6
209.3 07053779000
Group Maaiia 3)
37.5
5K.5
40.5
21.3
41.0
45.5
64.8064.35 51
200 00133778800 90)
GManha (Dunn))
42.2
42.11
49.9
61-4044111
(c))
46.7
45.9
6338500613
500800
SwaaV22 (x3)
42.4
65.1
46.3
25.5
43.9
55.9
63.05145.3 31
216.30009 400
Thy/VM (x
41.4
64.7
453
26.7
65.8
16.3
11.45677 X)
21499067 400
VMinha (o
462
45.4
15.1
06000 200
Mazshe (x3)
45.5
6327566611
210 216-50000
ProgMambs (x3)
-2.1
64.3
46.2
25.0
45.5
55.3
196 300000000000000
Group Mariia (X:3)
42.4
65.1
46.4
25.5
45.7
55.1
61 6..15215
1355009188 050
GMMamb Cn (Cuan))
42.9
65.6
4699
27.1
46.4
36.4
55.256316)
256.1 156.1599.22 255
R-C
Buaciie (ecaN)
37.5
40.9
66.4912355
200.14106.50 50
-Soin
24.4
19.
41.7
67.2
50 100 080
SwaaV' (x:))
11.3
19
41.7
33.3
41.9
49.6
Tie/V (x3)
36.2
58.5
41.6
23.5
41.6
49.9
260
300
VMaaha (o
14.4
41.9
41.8
494
07
100 2412 010
Manibe
41.8
03002280
FrogMambi
28.1
19.5
42.1
22.1
41.9
49.1
013552196
Grau Marrha O4.3)
25.3
59.0
41.8
21.6
41.4
50.1
900
GManbe (c3) (Doo))
29.1
60.1
43M4
23.3
42.5
58.3
1101611111
111
261
23R2100 005
(c3)
47.1
46.4
120 133000
SwanV22 (c))
43.3
47.
28.2
42.0
37.4
VManbe (x3)
Try/VM (x3)
4310
42.7
653
65.1
473
46.
28.5
21.3
46.0
46.5
15.1
36.6
260 11
700
000
Mambo Venson (x3)
65.1
455
46.7
631102501
ProgMmbo
67.5
475
66.6
16.9
100 9008
Group Mariia (X:3)
43.0
65.2
4700
21.3
46.6
56.5
63.94435)
168 9000000000000 000
GMimbe 2- (Cunn)
45.7
66.4
4U1
31.
47.3
17.0
$7.89177.0
369 11/00 145
J.2 ABLATION STUDY ON INSERTING GMAMBA INTO DIFFERENT STAGES
To evaluate the effectiveness of GMamba integration at different stages of the backbone, we duct ablation studies on both object detection and instance segmentation tasks using Faster R-CNN and Mask R-CNN with ResNet50 and Swin(T) backbones on the MS-COCO dataset. Tables 13 and 15 show the results for Faster R-CNN, while Tables 14, 16, and 17 present the results for Mask R-CNN for object detection and instance segmentation. Inserting GMamba modules progressively from Stage to Stage 3 consistently improves performance across all backbones and frameworks. For example, in Faster R-CNN with ResNet50 (Table 13), AP increases from 37.2% (baseline) to 38.5% when GMamba is applied to all stages, and in Mask R-CNN with Swin(T) for instance segmentation (Table 17), AP improves from 38.7% to 39.8%. Stage-wise analysis indicates that early-stage enhancement provides modest gains, while late-stage integration contributes most sig- nificantly, highlighting the benefit of enhancing high-level semantic features. The computational overhead introduced by GMamba is moderate, with parameters and FLOPs increasing reasonably relative to the performance gains. Consistent improvements across backbone types and tasks demon- strate the robustness and universality of GMamba.
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Table 13: Ablation study inserting GMamba modules into different stages (Stage 1/2/3) of the
ResNet50 backbone in Faster R-CNN for object detection on the MS-COC dataset.
Insorted Stages
AP (%)
AP5o (%)
APrs (%)
APs (%)
APar (%)
APr. (%)
Params (M)
FLOPs (G)
Baseline (No GMamba)
37.2
57.8
40.4
21.5
40.6
43.8(23.5)
207 307.07(76.50)
GMamba x1 (Stage
37.5
58.7
40.9
22.1
41.1
48.1
44.7(24.4)
207 207.22(76.65)
+ GMambu X2 (Sluges 1-2)
37.9
58.7
41.3
21.4
41.4
49.8
48.0(27.7)
207,83(77 (3.77377722))
GMamba x3 (Stages 1-3)
38.5
59.6
42.2
22.1
42.0
49,9
61.41411)
210.22(79.65)
Table 14: Ablation study on inserting GMamba modules into different stages (Stage 1/2/3) of the
ResNet50 backbone in Mask R-CNN for object detection on the MS-COCO dataset.
Insorted Stages
AP (%)
AP5o (%)
APrs (%)
APs (%)
AP (%)
AP,, (%)
Params (M)
FLOPs (G)
Baseline (No GMamba)
37.5
58.1
41.3
21.2
40.9
48.3
46.45(23.5)
260.14(76.50)
GMamba x1 (Stage
37.7
58.3
40.9
21.5
41.0
48.7
47.35(24.4)
260.29(76. 65)
+ GMamba X2 (Stuges 1-2)
38.1
59.2
41.3
21.6
41.4
49.7
50.65(27.7)
260,90(77 10000777.26 26)
GMamba x3 (Stages
39.1
60.1
42.8
23.3
42.5
50.3
64.05(41.1)
263,29(79.65)
Table 15: Ablation study on inserting GMamba modules into different stages (Stage 1/2/3) of the
Swin(T) backbone in Faster R-CNN for object detection on the MS-COCO dataset.
Inserted Stages
AP (%)
APso (%)
APys (%)
AP3 (%)
AP (%)
AP2, (%)
Parms (M)
FLOPs (G)
Baseline (No GMamba)
41.6
64.0
45.2
25.7
44.8
45.15(27.55
213.00886. 10)
GMamba x1 (Stage
41.9
64.7
45.7
27.0
45.3
54.9
45.65(28.0)
213.15(86.25
GMamba x2 (Stages 1-2)
42.2
64.8
45.7
26.5
45.5
55.7
47.65(30.0)
213.76(86.86
GMamba x3 (Stages 1-3)
42.9
65.6
46.9
27.1
46.4
56.4
56.25(37.6)
216.15(89.25)
Table 16: Ablation study on inserting GMamba modules into different stages (Stage 1/2/3) of the
Swin(T) backbone in Mask R-CNN for object detection on the MS-COCO dataset.
Inserted Stages
AP (%)
APso (%)
APys (%)
APs (%)
AP (%)
APt. (%)
Params (M)
FLOPs (G)
Baseline (No GMamba)
42.2
64.7
26.7
45.5
47.79(27.5)
00066. 10)
GMamba x1 (Stage
42.6
65.0
46.6
26.4
45.8
56.6
48.29(28.0)
266. 15(86.265)))
+ GMambu X2 (Stuges 1-2)
42.9
65.5
46.8
26.5
46.1
56.8
50.29(30.0)
266.76(86.86
GMamba x3 (Stages 1-3)
43.7
66.4
48.0
27.5
47.3
57.0
57.89(37.6)
269.15(89.25
Table 17: Ablation study on inserting GMamba modules into diffferent stages (Stage 1/2/3) of the Swin(T) backbone in Mask R-CNN for instance segmentation on the MS-COCO dataset.
Inserted Stages
AP (%)
APso (%)
APrs (%)
APs (%)
AP (%)
AP; (%)
Params (M)
FLOPs (G)
Baseline (No GMamba)
38.7
61.3
41.5
20.2
41.6
56.7
47.79(27.5)
266.00086.
GMamba x1 (Stage
39.0
61.8
42.2
19.7
41.9
57.0
48. 29(2800)
266. 15(66.
+ GMamba x2 (Stages 1-2)
39.5
62.2
42.7
20.0
42.4
57.7
50.29(30.0)
266.76(86.88
GMamba x3 (Stages
39,8
62.7
42.8
20.1
42.7
58.0
57.89(37.6)
269.15(89.25)
J.3 VISUALIZATION AND ANALYSIS OF OBJECT DETECTION AND INSTANCE SEGMENTATION RESULTS
As shown in Fig. 10, we visualize the object detection and instance segmentation results of Mask R- CNN and Faster R-CNN on the MS-COCO dataset with different backbone networks, enhanced by our GMamba module. It can be observed that for large objects requiring global contextual informa- tion, the integration of GMamba significantly improves segmentation accuracy, enabling more pre- cise delineation of object boundaries. Moreover, GMamba consistently maintains high segmentation performance across different object categories, demonstrating its strong global modeling capability well its plug-and-pla, versatility and efficiency.
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(NN(Swin(T))
Mask R (NN(ResN)450)
Mask CNN(Swin(T))
Figure 10: Visualization of object detection and instance segmentation results of Mask R-CNN and Faster
R-CNN MS-COCO dataset with different backhones.
GMamba(Ours)
VMamba
Swin TransFormer
TinyViM
Figure 11: Receptive field distributions of GMamba, Swin Transformer, VMamba, and Tiny ViM. ViM.
K ADDITIONAL ABLATION STUDIES ON THE GSSM MODULE
K.1 COMPARISON OF EXISTING GLOBAL MODELING METHODS
As shown in Table 18, existing heuristic global modeling methods, such Self-Attention, Vanilla SSM, and VMamba, either rely on token-wise attention or reurrive/mulli-ddrecttoot state propa- gation. While they provide certain levels of globality, they generally suffer from limited gradient sensitivity, weak positional consistency, and lack rigorous theoretical guarantees. In contrast, our proposed GSSM leverages DFT-guided state updates, which integrate frequency-domain global in- formation into the state modeling process. This design ensures gradient sensitivity, preserves posi- tional consistency, and is supported by strong theoretical foundations, distinguishing our approach from heuristic methods and providing a rigorous mathematical foundation for image global model- ing.
Table 18: Comparison of Global Modeling Methods with Respect Theoretical Properties
Method
Globality
Gradient Dependence
Positional Consistncyy
Theoreiical Guarantee
Selt- Attention
Full token-wise interaction
Partially satistied (depends on attention weights)
Yes
Weak
Vanilla SSM
Rocarsive eccusulatiin
No jexponencial docay)
No (depends on sequence order)
Weak
VMaaha
Multi-directioall seaminn
No (willl decays)
No
Welk
DFT
Frequency domain transfomm
Yes
Yes
Strong
DFT-guideed
Strong
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K.2 ANALYSIS OF RECEPTIVE FIELD CHARACTERISTICS
To compare the receptive field sizes of GMamba with other global modeling modules, we visualize the receptive field distributions of different modules in Fig. 11. GMamba, leveraging the DFT- based global modulation mechanism, achieves true global perception with uniform distribution. VMamba also realizes global perception through its four-directional scanning mechanism, but the sequential nature results in cross-shaped distribution and limits its practical applicability in image tasks. Swin Transformer achieves global perception as well, but exhibits higher attention in the center and lower attention toward the edges. TiM, as lightweight global modeling module, has a smaller receptive field coverage.
K.3 EFFECT OF FREQUENCY INFORMATION
Table 19: Ablation Study on Frequency-domain Information
Model Variant
mloU (%)
mF1 (%)
OA (%)
w/o Frequency (NoFreqq
84.01
91.01
93.38
+ High-Frrquenny Only (HF Only)
85.20
91.83
93.74
+ Low- Low-Frequency Only (LF Only)
85.36
91.94
93.78
+ HF + L.F (Simple Addition)
85.53
92.03
93.89
+ HF + I.F (Adaptive Modulation, Ours)
86.00
92.31
93.99
Teuge
Gru
(Mdaptie Modalaste Ours)
Figure 12: Visualization of ablation experiments on requency-domane information.
To validate the effectiveness of frequency decomposition and adaptive modulation in GSSM, we conduct a detailed ablation study investigate the contributions of different frequency components. As shown in Table 19, removing frequency-domaii information (NoFreq) leads to a noticeable per- formance drop (84.01% % mloU), suggesting that purely spatial modeling insufficient to capture comprehensive semantic cues. When incorporating singlefirequency components, low-frequency in- formation (85.36% mloU) slightly outperforms high-frequency information (85.20% mloU), which confirms that low-frequency components preserve richer global semanties and contextual structures that are critical for visual understanding. Conversely, high-frequency components, though slightly weaker in isolation, contribute fine-grained boundary delineation and local details, which remain indispensable for precise predictions.
When both high- and freefreyy signals are combined, the model with simple addition achieves 85.53% mloU, indicating that complementary interactions exist between global semantics and fine details. However, naive summation still underutilizes their distinct contributions, as it treats all fre- quency signals with equal importance regardless of spatial context. Our adaptive modulation strategy further improves performance to 86.00% mloU and 92.31 mF1, achieving a 0.47pp gain over sim- ple addition. This demonstrates the necessity of dynamically learning requency-domanl allowing the model to selectively emphasize semantic-rich low-frequency cues while adaptively details depending scene complexity. These results validate both the
weights,
tegrating high-frequenc, rationality of frequency decomposition and the effectiveness of our proposed adaptive modulation, highlighting its role in achieving a better balance between global consistency and local precision.
As shown in Fig. 12, the visualization different frequency components further validates our ob- servations. Without frequency information (NoFreq). the model struggles to capture global semantic structures, resulting in blurred boundaries and missing regions. Incorporating low- www-frquency compo- nents improves the consistency of large semantic regions, but local details remain underrepresented.
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Published as a conference paper at ICLR 2026
In contrast, high-frequency components enhance edge sharpness and fine- tineggrineed details, yet of- ten introduce internal noise. Simply summing low- and highffreuenncy signals partially mitigates these issues, but still fails to fully exploit their complementary strengths. Our adaptive modula- tion effectively integrates both global semantics and local details, producing predictions that are both spatially coherent and moundary-precisse demonstrating the necessity of dynamically learning frequency-doaain weights.
K.4 ROBUSTNESS AND DOMAIN GENERALIZATION ANALYSIS
To further evaluate the robustness and cross-domain generalization capability of the GMamba model under complex environments, we adopt CNee-CCovNNett (S) as the baseline and apply typical input perturbations including Gaussian noise (0.01), Gaussian blur (k=3), and partial occlusion (5%). As shown in Table 20, GMamba consistently achieves the best performance under all perturbation set- tings, with a 5.23% improvement under Gaussian noise and 5.35% gain under blur, highlighting its strong noise resistance and stability. In addition, to assess the model's 's adaptability to cross-domain scenarios, we conduct domain generalization experiments on the LoveDA dataset. As reported in Ta- ble 21, GMamba not only enhances semantic representation but also significantly alleviates domain shift, maintaining superior and stable segmentation performance across different domains.
Table 20: Robustness Evaluation under Typical Input Perturbations
Method
Clean (%)
Noise (0.01) (%)
Blur (k=3) (%)
Occlusion (5%) (%)
UNet-ConwNext(S)
83.11
77.55
79.15
77.00
+Swin
84.82
79.10
80.30
78.20
V2
84.36
79.25
80.45
78.35
+ViM
84.24
79.00
80.20
78.10
+VMamba
84.56
79.40
80.60
78.50
+ ViM
84,38
79.35
80.55
78.40
+ -Mamba Version
84.80
79.70
81.10
78.90
+ Spatial Mamba
84.50
79.45
80.85
78.60
FFeegMamaa
84.60
80.10
81.50
79.20
+GMamb (Ours)
86,00
82.78
84.50
81.00
Table 21:
Evaluation on LoveDA Dataset
Urban Rural
Rural
Urban
Method
mIoU (%)
mF1-scom 1-score (%)
mloU (%)
F-F--ccoee (%)
UNel-ConWNext(S)
39.13
53.48
52.15
68.12
+Swin
41.05
55.25
54.10
70.05
V2
41.18
55.40
54.22
70.12
ViM
40,50
54.90
53.70
69.80
+ViM
40.20
54.70
53.45
69.50
+VMamba
39,80
54.30
53.10
69.10
+Mamha Version
40.00
54.50
53.30
69.30
Spatial Mamba
40.40
54.85
53.55
69.60
FFregMamaa
41.00
55.10
54.00
69,95
+Gambb (Ours)
42.89
58.38
55.63
71.00
K.5 FAIR COMPARISON WITH PARAMETER-NN MRACHED BASELINES
To further verify the effectiveness of GMamba under fair comparison conditions, we adjust the channel widths of different backbone networks so that their parameter sizes are comparable those of the models with GMamba, and compare their performance with and without GMamba, as shown Table 22. The results indicate that, although scaling up the baseline models can slightly improve mloU and mF1, the performance gains brought by GMamba consistently surpass those achieved by merely increasing model capacity. This demonstrates that the advantages of GMamba are not solely due to the increase in parameters, but stem from its enhanced global modeling capability and frequency-guin -uuiedd state space mechanisms, thereby validating its efficiency and general applicability across different backbone architectures.
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Published as a conference paper at ICLR 2026
Table 22: Fair Comparison: Scaled Baselines Matching Params of +GMamba
Model Variant
Params (M)
mIoU (%)
mF1 (%)
ResNet34 (Baseline)
25.33
81.65
89.24
ResNet34 (Sealed, matched params)
31.06
83.18
90.59
ResNet34 GMamba (Ours, matched params)
30.96
84.74
91.56
Swin-T (Baseline)
36.48
82.44
89.75
Swin-T (Scaled, matched params)
49.50
83.76
90,95
Swin-T GMamba (Ours)
49.13
84.83
91.61
ConvNeXI-S (Baseline)
58.42
83.11
90.19
ConvNeXt-S (Scaled, matched params)
71.07
84.46
91.38
ConyNeXI-S + GMamba (Ours)
71.06
86.00
92.31
Table 23: Ablation of GMamba with Different Global Modeling Modules
Global Module
Latency (ms image)
GPU Memory (GB)
mloU (%)
Self-Attention (Transformer)
68.9
12.78
84.78
VSSM (Mamba)
51.6
8.71
84.01
GSSM (GMamba, Ours)
58.1
10.13
86.00
K.6 PERFORMANCE ANALYSIS AND EFFICIENCY OF GSSM
To evaluate the efficiency of GSSM, we replaced the GSSM module in GMamba with existing approaches (self-attention and VSSM). Table 23 presents the inference performance and accuracy of the GMamba model with different global modeling modules. All experiments the Vaihingen dataset using a single NVIDIA RTX 4090 (24GB) GPU with an input resolution of 1024x1024, and tested on the (N)t) backbone. We measured the average inference latency (ms per image) and peak GPU memory usage (GB) with batch size of 1. It can be observed that the Transformer-based self-attention module achieves relatively high mIoU (84.78%) but suffers from high latency (68.9 ms per image) and memory consumption (12.78 GB), indicating lower efficiency. The VSSM (Mamba) module exhibits the best inference speed and memory usage (51.6 ms / 8.71 GB), but its accuracy is slightly lower (84.01%) %). In contrast, our proposed GSSM module achieves a substantial improvement in mloU (86.00%) while maintaining low latency (58.1 ms) and moderate GPU memory usage (10.13 GB), demonstrating superior trade-off between efficiency and accuracy. Fig. 13 illustrates the inference performance of GSSM compared to other global modeling modules single NVIDIA RTX 4090 (24 GB) GPU across different image resolutions. During the evaluation, the model was set to evaluation mode and gradient computation was disabled. As the resolution increases, both the inference latency and peak GPU memory usage of GSSM exhibit approximately linear growth.
conducted on
Table 24: Comparison of Frequency Enhancement Strategies in GMamba
Method
Frequency Strategy
Position
Mechanism
mloU
Baseline (GMamba)
None
None
None
83.11
GMamba w/ Dual Branch Fusion
Dual Branch Fusion
After SSM
Post hoc feature fuusion
84.10
GMamba w/ Pre-Modulation
Frequency Pre- Red-Madlltion
Before SSM
Frequency- Prequency-guided state update
86.00
K.7 COMPARISON OF FREQUENCY ENHANCEMENT STRATEGIES
In Table 24, we compare the proposed frequency pre-modulation method with most existing frequency-enhancement strategies, such as dual-branch fusion. The baseline model without any frequency modulation achieves an mloU of 83.11%. Introducing dual-branch fusion strategy (post-hoc feature fusion) after the state space model increases the mloU to 84.10%. In contrast, our approach, which applies frequency pre-modulation prior to SSM to guide state updates, achieves the highest performance, with an mloU of 86.00%. These results indicate that incorporating frequency information via meddolulation validating the effectiveness and rationale of the proposed frequency-modulatee modulated SSM framework, which validates hypothesis.
more effectively enhance the state modeling process, further
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Published as a conference paper at ICLR 2026
Inference Latency
GPU Memory
1.2
VSSM
VSSM
7000
6000
Memory (MB)
0.0
0.4
3000
2000
256x256
512x512
1020x1024
2048x2040
250x256
512x512
1024x1024
2040x2048
Resolution
Resolution
Figure 13: Performance comparison of three global modeling modules under different input resolutions,
L FAILURE CASE ANALYSIS
We present some failure cases in Fig. 14. In the first three images, the scenes contain dense crowds. Our model fails to accurately identify individuals in the back rows, whose targets occupy only few pixels and are partially occluded. In the last image. the scene shows food items on supermarket shelves. These items are small, closely packed, and exhibit similar colors and textures, and were also not accurately recognized. The GSSM module primarily enhances the recursive state selection pro- cess under global frequency guidance. For tiny objects, local information is easily diluted through multiple downsampling and state transitions. Consequently, GMamba achieves limited performance improvement in small-object scenarios. Future work could explore integrating more powerful local feature enhancement mechanisms to improve performance on small object recognition.
Airlin
Airlin
Figure 14: Visualization of failure cases.
35


Reviews:
[{"review_id": "WnHUhHr0cC", "reviewer": "Reviewer_nc9h", "summary": "This paper introduces the Global-aware SSM (GSSM) module, which integrates frequency-domain modulation using Discrete Fourier Transform (DFT) to enable true global perception in State Space Models (SSMs). ​ The authors propose a mathematical definition for global image modeling and prove that GSSM satisfies this definition. ​ They design GMamba, a plug-and-play module that enhances global contextual understanding in Convolutional Neural Networks (CNNs) with linear-logarithmic complexity. Extensive experiments on semantic segmentation, object detection, and instance segmentation demonstrate GMamba’s superior performance and efficiency compared to existing methods. ​ The study highlights the importance of frequency-domain information and adaptive modulation for balancing global semantics and local precision.", "questions": "1. The paper claims to provide the first rigorous mathematical definition of global image modeling, which is a significant contribution. However, it does not compare this definition with existing heuristic approaches in detail, leaving room for further exploration of how it improves interpretability and theoretical support.\n\n2. How does the frequency-domain transfer function derived for SSMs compare to other global modeling techniques, such as attention mechanisms?\n\n3. How does GMamba's linear-logarithmic complexity compare to the linear complexity of other SSM-based methods like Vim, VMamba or spatial mamba?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. True Global Perception: GMamba, powered by the GSSM module, achieves true global perception by leveraging the Discrete Fourier Transform (DFT) for frequency-domain modulation. This enables the model to capture global semantic information efficiently. \n\n2. Efficiency: GMamba exhibits linear-logarithmic computational complexity, making it significantly more efficient than traditional self-attention mechanisms with quadratic complexity.\n\n3. Plug-and-Play Design: GMamba can be seamlessly integrated into various stages of CNNs and other backbone architectures, enhancing their global modeling capabilities without requiring major architectural changes. \n\n4. Scalability: GMamba demonstrates scalable performance gains when integrated with more powerful backbone architectures, such as ConvNeXt-Small and Swin Transformer-Tiny.\n\n5. Effective Frequency Decomposition: The use of both high-frequency and low-frequency components enhances global semantic modeling and local detail preservation, with adaptive modulation further optimizing their integration.", "weaknesses": "1. Limitation: The reliance on DFT-based frequency-domain modulation may introduce challenges in scenarios where frequency-domain information is less effective, such as highly noisy or irregular data.\n\n2. Impact: While the frequency-domain approach enhances global perception, it may struggle in cases where spatial features dominate or where frequency information is less relevant.\n\n3. Although GMamba is more efficient than self-attention mechanisms, it still introduces additional computational overhead compared to simpler SSM-based methods like Vim or TinyViM. \n\n4. While GMamba is described as \"plug-and-play,\" its integration requires careful tuning of parameters such as modulation coefficients and frequency-domain weights. This could increase the complexity of implementation and training.\n\n5. The robustness of GMamba in such challenging scenarios remains unclear, which could affect its reliability in real-world applications.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HjVduHII7p", "reviewer": "Reviewer_rPrr", "summary": "This paper tackles the efficiency-global perception trade-off in visual tasks by proposing a rigorous mathematical definition of global image modeling and a frequency-domain modulated framework. Leveraging 2D-DFT’s global properties, the authors design the GSSM module and plug-and-play GMamba block, which seamlessly integrate into CNNs/Transformers. Extensive experiments across semantic segmentation, object detection, and instance segmentation show GMamba outperforms existing modules with linear-logarithmic complexity.", "questions": "please refer to the weakness part.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- First rigorous mathematical definition of global image modeling with formal proofs.\n- DFT-based modulation overcomes SSMs’ local limitation without complex scanning.\n- Strong performance across tasks, backbones, and datasets with efficiency advantages.\n- Thorough ablations for validating key design choices (GSSM components, frequency contributions).", "weaknesses": "- Insufficient analysis of scaling to ultra-high-resolution images (e.g., 4K+) and inference speed (FPS).\n- Lack of explicit comparison with recent frequency-domain SSM variants (e.g., FreqMamba [1]).\n- No analysis of failure cases.\n- Lack experiments on the Imagenet benchmark.\n\n[1] Freqmamba: Viewing mamba from a frequency perspective for image deraining", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "dirW60HAYH", "reviewer": "Reviewer_PSzr", "summary": "This paper addresses the limited global perception of State Space Models (SSMs) in vision tasks by proposing a frequency-domain modulation approach. The proposed GSSM block applies DFT-based frequency decomposition to extract global semantic information and uses adaptive modulation coefficients to guide SSM's state updates before sequential processing, achieving linear-logarithmic complexity O(nlogn). The authors show that the proposed GMamba block is plug-and-play across different CNN architectures. Experiments on semantic segmentation (Vaihingen, Potsdam, LoveDA, UAVid), object detection, and instance segmentation (MS-COCO) demonstrate consistent improvements of 2-3% mIoU across ResNet, Swin Transformer, and ConvNeXt backbones. While the theoretical framework looks good, the practical gains are modest given the added complexity, and the core idea of frequency-domain processing for vision is well-established in prior work.", "questions": "- It is unclear whether the GMamba models used for object detection and instance segmentation are initialized with backbones pre-trained on ImageNet or not. If yes, what is the top-1 accuracy of GMamba on ImageNet?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The paper provides an interesting mathematical definition of global image modeling and establishes a complete theoretical framework showing how DFT-based modulation can enrich the SSMs with global perception capabilities. \n\n- The motivation is simple yet effective: SSMs rely on sequential state updates, which limit them to local rather than global modeling, and existing methods using different scanning strategies have not enhanced SSM's global modeling capability.\n\n- The authors did extensive experiments on multiple tasks (semantic segmentation, object detection, instance segmentation) across many datasets with different backbone architectures, demonstrating the generalization capability of GMamba models.", "weaknesses": "- While the theoretical framework is novel, the core idea of using frequency-domain information for computer vision is well-established. (i.e, ICCV'23 works like SPANet [1]) and recent methods FAD [2]. The paper doesn't sufficiently differentiate its approach from these existing frequency-based methods.\n\n- Existing work, such as Vim and VMamb, has demonstrated that SSMs can achieve global receptive fields through bidirectional processing and multi-directional scanning. The paper's claim that current SSMs lack global perception seems overstated.\n\n- The related work and the comparison are missing recent state-space models (i.e, GroupMamba[3] (CVPR'25), MambaVision[4] (CVPR'25). Also, the provided implementation of GMamba_Block.py in the supplementary material appears to be largely derived from the MambaVisionMixer module introduced in MambaVision [4]. The authors have added their frequency components on top of that code. However, they neither cite nor compare their results with MambaVision paper [4].\n\n- The reported improvements are relatively modest (around 2–3% mIoU) while introducing a significant parameter increase of 20–35%. It remains unclear whether these gains come from the added parameters or from the model’s inherent effectiveness. For example, in Table 2, the baseline UNet-ConvNeXt(S) has 58.42M parameters, whereas incorporating GMamba raises this to 71.06M, yielding 2.89% improvement in mIoU. A fair comparison would require scaling the baseline (e.g., by increasing the number of channels or blocks) to match 71.06M parameters, to determine if the gains are truly architectural rather than parameter-driven.\n\n[1] https://openaccess.thecvf.com/content/ICCV2023/papers/Yun_SPANet_Frequency-balancing_Token_Mixer_using_Spectral_Pooling_Aggregation_Modulation_ICCV_2023_paper.pdf\n\n[2] https://arxiv.org/pdf/2505.08349\n \n[3] https://openaccess.thecvf.com/content/CVPR2025/papers/Shaker_GroupMamba_Efficient_Group-Based_Visual_State_Space_Model_CVPR_2025_paper.pdf\n\n[4] https://openaccess.thecvf.com/content/CVPR2025/papers/Hatamizadeh_MambaVision_A_Hybrid_Mamba-Transformer_Vision_Backbone_CVPR_2025_paper.pdf", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "YVRWZ2OPxr", "reviewer": "Reviewer_YRTs", "summary": "The authors propose a novel module, Global-aware SSM (GSSM), which is the core of a plug-and-play block called GMamba. The key idea is to use a Discrete Fourier Transform (DFT)-based modulation mechanism to \"inject\" global information into the features before they are processed by the SSM. This frequency-domain pre-modulation guides the SSM's state updates with a true global perspective, enabling efficient global modeling with linear-logarithmic complexity", "questions": "Please check the weakness.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The proposed GMamba block shows consistent and significant performance improvements when added to various backbones (e.g., ResNet, Swin, ConvNeXt) . It outperforms existing global modeling methods, including Transformer and other Mamba variants, on several dense-prediction tasks (semantic segmentation, object detection, and instance segmentation) across multiple datasets.", "weaknesses": "1. The paper's theoretical claims rest heavily on its new definition of global perception—\"global gradient dependency\". This definition requires that the Frobenius norm of the gradient of the output with respect to any input pixel is bounded by a non-zero constant $\\tau$. This is a very low bar. A gradient that is infinitesimally small but non-zero would satisfy this definition, but this may not align with an intuitive or practical understanding of \"global influence.\" The claim of \"true\" global perception is therefore only as strong as the acceptance of this new, and debatable, definition.\n\n\n2. Although the authors claim that the proposed GSSM enables efficient global image modeling, there is no related experimental data on practical inference latency or GPU memory cost. Relying only on FLOPs may not accurately reflect the module's true efficiency, as operations like 2D-DFT can have different hardware utilization profiles than standard convolutions.\n\n3. The experimental validation is extensive on dense prediction tasks (segmentation and detection). However, a standard benchmark for vision backbones is ImageNet classification. The absence of this benchmark makes it slightly more difficult to assess the module's generalizability as a fundamental building block for all vision tasks.\n\n4. Some illustrations of previous work in this paper appear to be incorrect and may mislead readers. The authors show the ViM scanning routes in Figure 1(c), but this depiction seems to be wrong (as noted in other work, e.g., [1]). This potential misrepresentation of a key baseline method is a concern.\n\n[1]. Visual mamba: A survey and new outlooks, 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)