Spatial-Mamba: Effective Visual State Space Models via Structure-Aware State Fusion
Authors: Chaodong Xiao
Minghan Li
Zhengqiang ZHANG
Deyu Meng
Lei Zhang
Venue: ICLR 2025 Poster (2025)
Keywords: Representation learning
Visual state space models
Structure-aware state fusion
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Abstract: Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at \url{ https://github.com/EdwardChasel/Spatial-Mamba }.

Published as a conference paper at ICLR 2025
EFFECTIVE VISUAL STATE SPACE MODELS VIA STRUCTURE-AWARE STATE FUSION
Chaodong Xiao Minghan Li Zhengqiang Zhang': 13 Deyu Meng", Lei Zhang 122
'The Hong Kong Polytechnic University Harvard Medical School
OPPO Research Institute
4 Xi' an Jiaotong University
chaodong. xiao@ connect polyu.hke
csl csinhan@@comp polyu. edu.hk
"Equal contribution 'Corresponding author
ABSTRACT
Selective state space models (SSMs), such as Mamba (Gu & Dao, 2023). highly excel at capturing long-range dependencies in ID sequential data, while their appli- cations to 2D vision tasks still face challenges. Current visual SSMs often convert images into ID sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood con- nectivity directly in the state space. Instead of relying solely on sequential state transitions, introduce structure-awat state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation us- ing the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multi- plication framework, providing a deeper understanding of our method. Experi- mental results demonstrate that Spatial-Mamba even with a single scan, attains surpasses the sfate-of-the-art SSM-based models in image classification, de- tection and segmentation. Source codes and trained models can be found Mambal
https://giitann com wwt.///wwwwwaaeeee//eeeeeeaaaeee
INTRODUCTION
State space models (SSMs) are powerful tools for analyzing dynamic systems with hidden states, and they have long been utilized in fields like control theory, signal processing, and economics (Friston eet al. 20033 Hafner et al., 2019 Gu et al. 2020). SSMs have been recently introduced into deep learning (Gu al.) 2021a), especially in natural language processing (NLP) (Gu & Dao 2023), thanks to their use of specially parameterized matrices. A major advancement is the introduction of selective mechanisms and hardware-awand optimizations for parallel computing, as demonstrated by Mamba
(Gu & Dao 2023), which selectively retains or discards information based on the relevance of each element sequence, efficiently modeling long-distance dependencies with linear complexity.
The significant success of Mamba in NLP inspires researchers to investigate how SSMs can be applied to visual tasks. Unlike ID sequences, visual data are typically characterized by 2D spatial structures. Therefore, it is crucial to maintain the spatial dependencies within images while adapting the information selection and propagation mechanisms Mamba. Existing visual SSMs (Zhu et al.. 2024; Liu et al. 2024 Yang et al.) 2024: Huang et al.) 2024: He et al.) 2024a Xiao et al. 2024) often use some scanning strategies to flatten 2D visual data into several ID sequences from different directions, and then process the flattened ID sequences using the original Mamba. These scanning strategies can be broadly categorized into three types: sweeping scan, continuous scan and local scan, as shown in Figs.
[c). respectively.
Vim (huu et al,, 2024) and VMamba (Liu et al. 2024) employ sweeping bidirectional scan and four-way scan, which are illustrated in Fig. a). These strategies aim to reduce spatial direction

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(a) Sweeping Scan
(b) Continuous Scan
(c) Local Sean
(d) Structure
aanccure--wwre aware state fusion with unidirectional sean
Figure 1: Illustration of the scanning patterns of existing visual SSMs (from sub-figures (a) to (c)) and our proposed Spatial-Mand with structure-aware state fusion (sub-figure (d)).
sensitivity and adapt the network architecture for visual tasks. Yang et al. (2024) argued that sweeping
scans neglect the importance of spatial continuity, and they introduced continuous scanning order, as shown Fig. bb), to better integrate the inductive biases from visual data. Huang et al. (2024) argued that scanning the entire image may not effectively capture local spatial relationships. Instead, they presented LocalMamba by using several local scanning modes, as shown in Fig. [Tc). which divides an image into distinct windows capture local dependencies. Beyond the above mentioned scanning patterns, other scanning methods such as Hilbert scanning (He et al.) 2024a) and dynamic tree scanning (Xiao al. 20244 have also been proposed to adapt SSMs to visual tasks.
While the existing scanning strategies partially address the issue of aligning spatial structures with sequential SSMs, they limited in model effectiveness and efficiency. On one hand, directional scanning inevitably alters the spatial relationships between pixels, disrupting the inherent spatial context in an image. For example, in the sweeping scan (Fig. [a),, the distance between a pixel and its left or right neighbor is 1, while its distance to the top or bottom neighbor equals to the image width. This distortion can hinder the models to understand the spatial relationships in the original visual data. On the other hand, the fixed scanning paths, such as the commonly used four-directional scan (Figs. Πa) and [b)), are not effective enough capture the complex and varying spatial relationships in an image, while introducing more scanning directions would also result in excessive computations. Therefore, it is imperative to explore how to design more effective and structure-aware SSMs for visual tasks.
To achieve this goal, we make an important attempt in this paper and present Spatial-Mambe which designed to capture the spatial dependencies of neighboring features in the latent state space. The processing flow of Spatial-Mambe consists of three stages. First, as shown in the left of Fig. T d), visual data converted into sequential data using unidirectional sweeping scan. The state variables are computed based on the state transition equations of the original SSMs and then reshaped back into the visual format. Second, the state variables processed through a structure-aware state fusion (SASF) equation, which employs dilated convolutions to re-weight and merge nearby state variables, as shown the left of Fig. d). Finally, these sructurr-awarc state variables are fed into the observation equation to produce the final output variables. The SASF equation not only enables efficient skip connections between non-sequential elements in sequences but also enhances the model ability to capture spatial relationships, leading to more accurate representations of the underlying visual structure. Furthermore, we show that Spatial-Mamba, original Mamba and linear attention can all be represented under the same framework using structured matrices, which offers more coherent understanding of our proposed method. We validate the superiority of Spatial-Mambe across fundamental vision tasks such as image classification, detection, and segmentation. The results demonstrate that Spatial- Spatial-Mamba, Mamba, even with a single scan, achieves or surpasses the performance of recent state-of-tt mate-of-thhe-rte using different scanning strategies.
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2 RELATED WORK
State space models (SSMs). Gu et al. 2222 firstly introduced the linear state space layer (LSSL) into the HiPPO framework (Gu et al. 2020) to efficiently handle the long-range dependencies in long sequences. Gu et al. (2021a) a then significantly improved the efficiency of SSMs by representing the
parameters as diagonal plus low-rank matrix. The so-called S4 model triggers a wave of structured
SSMs (Smith et al. 2022, Fu et al. 2022 Gupta et al. [022]] Gu & Dao 2023). Smith et al. (2022) proposed S5 by introducing parallel scans S4 layer while maintaining the computational efficiency of S4. Recently, Gu & Dao (203) developed Mamba, which incorporates data-dependent selection mechanism into S4 layer and simplifies the computation and architecture in a hardware-friendee
way,
achieving Transformer-like modeling capability with linear complexity. Building on that, Dao & Gu (2024) presented Mamba2, which reveals the connections between SSMs and attention with specific structured matrix. This framework simplifies the parameter matrix to scalar representation, making it feasible to explore larger and more expressive state spaces without sacrificing efficiency.
Visual SSMs. Although traditional SSMs perform well in processing NLP sequential data and capturing temporal dependencies, they struggle in handling nulti-dimensional spatial structure inherent in visual data. This limitation poses a challenge for developing effective visual SSMs. S4ND (Nguyen et al. 2022) is among the first SSM-based models for multi-dimensional data, which separates each dimension with an independent 1D SSM. Baron al. (2023) generalized S4ND discrete multi-axial system and proposed the 2D-SSM spatial layer, successfully extending the ID SSMs 2D SSMs. More recent visual SSMs prefer design multiple scanning orders or patterns to maintain the spatial consistency. including bidirectional (Liu et al. 2024), four-way (Zhu et al. (Huang et aal.[202)). and topology-based scanning (He et al., 2024a Xiao et | [2024). These visual SSMs have been used in multimodal foundation models (Qiao al. 20044] Mo & Tian (024), image restoration (Guo
2024). continuous (Yang al.) 2024), zigzag (Hu al.] (024).
et al. [024] Shi et al. 2024), medical image asilysis Yue & Li,
2024 Ma et al.
2024 He et al.
2024b; Liao et al.) 2024) and other visual tasks (Chen et al.
a (2024
Li et al. 2024
Yao ct al. 2024).
demonstrating the potential of SSMs in visual data understanding.
3 PRELIMINARIES
SSMs are commonly used for analyzing sequential data and modeling continuous linear invarinn (LTI) systems (Williams & Lawrence 2007). An input sequence u(t) E transformed into an output sequence v(!) E IR. through state variable æ(() E C.V. Here, / > represents the time index, and N indicates the dimension of the state variable. This dynamic system can be described by the linear state transition and observation equations (Kalman 1960): x' (t) = Ar(t) + Bu(t), v(t) = Cx(()) + Du(t), where A E N X is the state transition matrix, B, C E CN and D E C control the dynamics of the system. The state transition and observation equations describe how the system evolves over time and how the state variables relate to the observed outputs.
To effectively integrate continuous-time SSMs into the deep learning framework, it is essential to discretize the continuous- time models. One commonly employed technique is the Zero-Order Hold (ZOH) discretization (Gu & Dao 2023). The ZOH method approximates the continuous-time system by holding the input constant over each discrete time interval. Specifically, given a timescale
A, which represents the interval between discrete time steps, and defining A and B as discrete A)AB
parameters, the ZOH rule is applied as A = AA and B AA
However, real-world processes often change over time and cannot be accurately described by a LTT system. As highlighted in Mamba (Gu & Dao 2023), vvreiia systems can focus more on relevant information and offer more accurate and realistic representation of dynamic systems. In Mamba, the parameters of the SSMs are made context-aware and adaptive through selective functions. This is achieved by modifying the parameters A, B, C as simple functions of the input sequence us, resulting in input-dependent parameters A = SA (u)), B, = sg()) and C, = sc()). Then the input-dependent discrete parameters A, and B, can be calculated accordingly. Consequently, the discrete state transition and observation equations
be calculated follows:
Zt = A B Vt C + Du
(1)
simplified illustration of the above process is shown in Fig. aa).
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A
X
x
A
Fusion
h j
B x. At
C
(1)
Br x. D
C.
(1)
(p)(t)
Ut (a) SSM Mamba
Ut
SSM Spatial-Man
Figure 2: Illustraiions of the SSM in (a) Mamba and (b) -patial-Mamba, where the residual term
D omitted. In (b), 'Fusion' refers to our proposed structure- aware state fusion (SASF) equation.
(a) Input
(b) Original state 2;; (c) Fused state he
(d) Original state 2;, (c) Fused state ha
Figure 3: Visualization state variables before and after applying the SASF equation. Sub-figures
(b) and (c) show the mean of state variables across all channels in the first layer of Spatial-Mambo
while sub-figures (d) and (e) display the state variables for a specific channel in the last layer.
SPATIAL-MAMBA
4.1
FORMULATION OF SPATIAL-MAMB.
Pratial-Mamba is designed to capture the spatial dependencies of neighboring features in the latent state space. To achieve this goal, different from previous methods (Zhu et al., 2024] Liu et al. 2024 Huang al. 2024) that commonly employ multiple scanning directions, structure-awand state fusion (SASF) equation into the original Mamba formulas (refer to Eq. (T). The entire process of Spatial-Mamin can be described by three equations: the state transition equation, the SASF and the observation equation, which are formulated as:
introduce new
A,2111 Bru, he Σ pu(tr kEn
Yr
Cih, + D
(2)
where is the original state variable, h2 is the structure-aware state variable, Ω2 is the neighbor set, 0g learnable weight, and (t( is the index of the k-th neighbor of position illustrates the SSM flow in the proposed Spatial-Mamba. Compared with the original Mamba in Fig. a)),, we can see that the original state variable w, directly influenced by its previous state Tt-1. while the structure-aware state variable h, incorporates additional neighboring state variables (t) (t) pa(t)....... (t) through a fusion mechanism, where = [22] denotes the size of neighbor set. By considering both the global long-range and the local spatial information, the fused state variable h1 gains a richer context, leading to improved adaptability and a more comprehensive understanding of the image.
Fig. (
The proposed Spatial-Mambhe can be implemented in three steps. As shown in Fig. [d), the input image first flattened into ID sequence we, with which the state x, is computed using the state transition equation I, AAT1-1 + B The computed states then reshaped back into the 2D format. To enable each state to aware of its neighboring states in the 2D space, we introduce the SASF equation h ExeO (t) For state variable st, apply linear weighting to its neighboring states P& (t) in the neighborhood Ω using weights ag that we effectively integrate local dependency information into a new state h4, resulting in a more contextually informative representation. Finally, the output is generated from this enriched state h, through the observation equation Yt = C.h, + Du, This SASF approach helps the model to incorporate the local structural information in visual learning while retaining the benefits of original Mamba.
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Downn Sampling
Down Sampling
Down Sampling ling
Spatial-Mamba Block La
Sparial-Mumba Block L2
Spatinl-Mamba Block
Spotial-Mamba Block
Stem
Ta
Linear
SAAST
Diuucture Mewcuur--aaas aware
N
Spatial-Mami Block
Simueture-aware SSM
Figure 4: Overall network architecture of Spatial-Mamin
In practice, we simply employ multi-scale dilated convolutions Yu 2015) to linearly weight adja- cent state variables, enhancing spatial relationship characterizations and enabling skip connections. Specifically, we use three x 3 depth-wise filters with dilation factors 1,3,5 to construct the neighbor set Ωu (, E {-d, 0,
The SASF equation in Eq. (2 can be rewritten
he Σ
E
ki Fitiitjs
d=1,8,5
where kiy represents the filter weight for dilation factor d at position (i,j), Fr+-im+ denotes the neighbor of the state 2e located the position (i,.)), and indicates the width of the image.
To gain an intuitive understanding of SASF, we visualize the original state variables and our proposed structure-awand state variables in Fig. 3 Additional visualizations are provided Appendix A One
can see that the original state Ie (Fig. 3(b)) struggles to differentiate the foreground from background. In contrast, the structure-an aware state h4 (Fig. Bj)),, which has been refined through SASF process, effectively separates these regions. Moreover, the original state variable in Fig. (3 only shows horizontal attenuation along the scanning direction (gradually darkening from brightest value in the upper left corner), while the fused state variable h, in Fig. e) demonstrates decay along the horizontal, vertical and diagonal directions. This improvement stems from its ability to leverage spatial relationships within the image, leading to more accurate and context-aware representation.
4.2 NETWORK ARCHITECTURE
The overall architecture of Spatial-Mamie depicted in Fig. 4 consists of four successive stages, resembling the structure of Swin-Transformer (Liu al. 2021) We introduce three variants of Spatial-Mamba model at different scales: Spatial-Mamba- (tiny). Spatial-Mamba-S (small), and Spatial-Mamba- (base). The detailed configurations are provided in Appendix B Specifically, an input image / E IR H W x3 is first processed by an overlapped stem layer to generate a 2D feature map with dimension of stage comprises multiple Spatial-Mambe blocks, followed by down-sampling layer with a factor of 2 (except for the last stage), resulting in hierarchical features. Finally, head layer is employed to process these features to produce corresponding image representations for specific downstream tasks.
C. This feature map is then fed into four successive stages. Each
The Spatial-Mamba block forms the fundamental building unit of our architecture, which consists of Structure-aware SSM and Feed-Forward Network (FFN) with skip connections, as illustrated in the bottom left of Fig. 4 Building upon the Mamba block design (Gu & Dao 2023), the Structure- aware SSM. illustrated in the bottom right of Fig. is implemented by substituting the original 1D causal convolution with a x 3 depth-wise wise convolution and replacing the original S6 module with proposed SASF module, achieving local neighborhood connectivity in state spaces with linear complexity. Moreover, a local perception unit (LPU) (Guo et al.) (022) is employed before the Spatial-Mamba block and FFN extract local information inside image patches.

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(a) Input
(b) Linear attention
(c) Mamba
(d) Spatial-Mambe
Figure 5: Visualizations of matrices M and the corresponding activation maps for linear attention, Mamba and Spatial-Mambn The red arrows indicate specific rows in matrices M, along with the corresponding image patches (marked with red star).
4.3 CONNECTION WITH ORIGINAL MAMBA AND LINEAR ATTENTION
We analyze in-depth the similarities and disparities among linear attention (Katharopoulos et al. 2020), original Mamba (Gu & Dao 2023) and our Spatial-Mambar providing a better understanding of the working mechanism of our proposed method. Detailed derivations are provided in Appendix C
Linear attention is an improved aeff-attention (SA) mechanism, reducing the computational com- plexity of SA to linear by using kernel function 6. For an input sequence u, the query 4. key k2, and value U, are computed by projecting u, with different weight matrices, In autoregressive models, to prevent the model from attending future tokens, the I-th query is restricted by the previous keys, i.e., k,, S. t. Thus, if the kernel function ø is an identity map, the calculation of single head linear attention without normalization can be formulated as: y/2 E.se (c(k" v.).
Letting Vt = Ense ki Us. then we have 2i = -z-1 + lif vr. The linear attention can be rewritten as y/ = Q.Tt. This reveals that linear attention is actually a special case of linear recursion. The hidden state variable i2 is updated by the outer-product 1.d Us. and the final output ye is observed by multiplying za with the query Ut- If define C₁ qt and B, ko the linear attention can be expressed in a form similar to that of SSM:
C. C.B.Uss
e
where u, is linear transformation of u, Le., U, Linear(u.).
Mamba is essentially defined in Eq. [ By setting the initial state variable un to zero, the state variables can be derived recursively 2; = E..e A B, Here, A II -+ A, denotes the product of the state transition matrices with indices from s + to / for < I, and its value is 1 when s = t. The final output of the observation equation without Du, can be rewritten as:
Σ
C.A
A
Br
(5)
S51
Spatial-Mamba. Based on Eq. 2 and Eq.
5 the structure-awarc state variables from our proposed
SASF equation can be expressed as he >xEe Exspett) A B.u,, By omitting Du, for simplicity of expression, the final output of Spatial-Mamba can be reformulated as follows:
yt Σ Σ ark C. A B.
(6)
kER (1)
Remarks. From the above analysis, we can see that all the three paradigms linear attention, Mamba, and Spatial-Mamba - can be modeled within a unified matrix multiplication framework, specifically y M The differences lie the structure of M. For both linear attention and Mamba, M takes the form of a lower triangular matrix, whereas for Spatial-Mamba M is an adjacency matrix. Fig. provides a visualization of these matrices. In linear attention, the positions of brighter values remain consistent along the vertical direction, which indicates that the SA mechanism puts its focus on a small set of image tokens. Mamba, on the other hand, shows a decaying pattern over time, which is attributed the influence its state transition matrix A, This dynamic transition allows Mamba to shift its focus among previous image tokens. Unlike linear attention and Mamba, our Spatial-Mant Mamba considers the weighted summation all states within a broader spatial neighborhood Ω, allowing for more comprehensive representation of spatial relationships. The activation maps on the right side of Fig. 5 further demonstrate that linear attention focuses on limited region, while Mamba captures a broader region due its pangrange context modeling. Our Spatial Spatial-Mamba not only largely extends the range of context modeling but also enables spatial structure modeling, effectively identifying relevant regions even when they distant from each other.

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5 EXPERIMENTAL RESULTS
In this section, conduct series of experiments to compare Spatial-Mamba -amba with leading benchmark models, including those based on Convolutional Neural Networks (CNNs) (Radosavovic et al.
2020
Liu et al. 2022 Yu & Wang 2024). Vision Transformers (Dosovitskiy al.
2020
Liu al.
2021
Wang et al. 2022
Hassani et al. [2023). and recent visual SSMs (Nguyen et al.
2022
Zhu et al.
2024
Liu et al.) 2024 Huang al. 2024). Following previous works (Liu et 2021
2024), train
three variants of Apatial-Mamt
namely Spatial-Mamba- Spatial-Mamba- Mamba-S S and Spatial-Mambl B.
The detailed configurations are provided in Appendix B The performance evaluation conducted on
fundamental visual tasks, including image classification, object detection, and semantic segmentation.
5.1 IMAGE CLASSIFICATION IMAGENET-IK
Settings. We first evaluate the representation learning capabilities of Spatial-Mamba Mamba in image
classification on ImageNet- 1 (Deng al., 2009). We adopted experimental configurations
used in previous works (Liu et al. 2021 2024). which are detailed in Appendix B We compare our
method with state-of-ther
approaches, including RegNetY (Radosavovic et al., 2020), ConvNeXt
(Liu et al. (2022). VIT (Dosovitskiy et al. 22200, DeiT (Touvron et al.| Swin (Liu et al. 2021
NAT (Hassani et al. 2023). S4ND (Nguyen al. 2022 Vim (Zhu et al. 2024). VMamba (Liu et al.
2024
and Local Mamba (Huang et al. 2024).
Table I: Comparison of classification performance on ImageNet-IK, where 'Throughput" is measured using an A100 GPU with an input resolution of 224 x 224.
Arch.
Method
Im. size
#Param. (M) FLOPs (G) Throughput Top-1 acc.
RegNetY-4G
224
21M
4.0G
80.0
RegNerY-8G
224
39M
8.0G
81.7
CNN
RegNetY-16G
224
84M
16.0G
82.9
Con-NeXt-T
2242
29M
4.5G
1189
82.
ConvNeXt-S
224
50M
8.7G
682
83.1
ConvNeXI-B
224
89M
15.4G
435
83.8
ViT-B/16
3842
86M
55.4G
77.9
ViT-L/16
384
307M
190.7G
76.5
Transformer
DeiT-S
2242
22M
4.6G
1759
79.8
DeîT-B
224
86M
17.5G
500
81.8
DeiT-B
384
86M
55.4G
498
83.1
Swin-T
224
28M
4.5G
1244
81.3
Swin-S
2242
50M
8.7G
718
83.0
Swin-B
2242
88M
15.4G
458
83.5
NAT-T
224
28M
4.3G
83.2
NAT-S
2242
5IM
7.8G
83.0
NAT-B
2242
90M
13.7G
84.3
S4ND-ConwNeXt-T
2242
30M
683
82.2
S4ND-ViT-B
2242
89M
397
80.4
ViM-S
224
26M
811
80.5
VMamba-T
2242
30M
4.9G
1686
82.6
SSM
VMamba-S
2242
50M
8.7G
877
83.6
VMamba-B
224
89M
15.4G
646
83,9
LocalVMamba-T
224
26M
5.7G
394
82.7
Local
224
50M
11.4G
227
83.7
Spatial-Mamba-T
2242
27M
4.5G
1438
83.5
Spatial-Mamin Mamba-S
2242
43M
7.1G
988
84.6
Spatial-Mamin Mamba-B
224²
96M
15.8G
665
85.3
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Table 2: Comparison of object detection and instance segmentation performance COCO with
Mask R-CNN He et al. 2017) detector. FLOPs are calculated with input resolution of 1280 x 800.
Mask R-CNN 1x schedule
Backbone
APb
AP
AP751
Apm
AP 50
AP75
#Param.
FLOPs
ResNet-50
38.2
58.8
41.4
34.7
55.7
37.2
44M
260G
Swin-T
42.7
65.2
46.8
39.3
62.2
42.2
48M
267G
ConvNeXt-T
44.2
66.6
48.3
40.1
63.3
42.8
48M
262G
PVTv2-B2
45.3
66.1
49.6
41.2
64.2
44.4
45M
309G
ViT-Adapter-S
44.7
65.8
48.3
39.9
62.5
42.8
48M
403G
MambaOut-T
45.1
67.3
49.6
41.0
64.1
44.1
43M
262G
VMamba-T
47.3
69.3
52.0
42.7
66.4
45.9
50M
271G
Local Mambba-T
46.7
68.7
50.8
42.2
65.7
45.5
45M
291G
Apatial-Mamber
47.6
69.6
52.3
42.9
66.5
46.2
46M
261G
ResNet-
38.2
58.8
41.4
34.7
55.7
37.2
63M
336G
Swin-S
44.8
68.6
49.4
40.9
65.3
44.2
69M
354G
ConvNeXt-S
45.4
67.9
50.0
41.8
65.2
45.1
70M
348G
PVTv2-B3
47.0
68.1
51.7
42.5
65.2
45.7
63M
397G
MambaOut-S
47.4
69.1
52.4
42.7
66.1
46.2
65M
354G
VMamba-S
48.7
70.0
53.4
43.7
67.3
47.0
70M
349G
Lamba-
48.4
69.9
52.7
43.2
66.7
46.5
69M
414G
Opatial-Mamin
49.2
70.8
54.2
44.0
67.9
47.5
63M
315G
Swin-B
46.9
42.3
66.3
46.0
88M
496G
ConvNeXt-B
47.0
69.4
51.7
42.7
66.3
46.0
107M
486G
PVTv2-B5
47.4
68.6
51.9
42.5
65.7
46.0
102M
557G
ViT-Adapter-B B
47.0
68.2
51.4
41.8
65.1
44.9
102M
557G
MambaQut-B
47.4
69.3
52.2
43.0
66.4
46.3
100M
495G
VMamba-B
49.2
71.4
54.0
44.1
68.3
47.7
108M
485G
Opatial-Mamba+
50.4
71.8
55.3
45.1
69.1
49.1
115M
494G
Mask R-CNN 3x MS schedule
Backbone
APh
APb
AP
APm
APm 1
APm
#Param.
FLOPs
Swin-T
46.0
68.1
50.3
41.6
65.1
44.9
48M
267G
ConvNeXI-T
46.2
67.9
50.8
41.7
65.0
44.9
48M
262G
NAT-T
47.7
69.0
52.6
42.6
66.1
45.9
48M
258G
VMamba-T
48.8
70.4
53.5
43.7
67.4
47.0
50M
271G
48.7
70.1
53.0
43.4
67.0
46.4
45M
291G
Spatial-Mamba--T
49.3
70.7
54.3
43.8
67.8
47.2
46M
261G
Swin-S
48.2
69.8
52.8
43.2
67.0
46.1
69M
354G
XonvNeXt-S
47.9
70.0
52.7
42.9
66.9
46.2
70M
348G
NAT-S
48.4
69.8
53.2
43.2
66.9
46.5
70M
330G
VMamba-S
49.9
70.9
54.7
44.2
68.2
47.7
70M
349G
LacalVMamba-S
49.9
70.5
54.4
44.1
67.8
47.4
69M
414G
Spatial-Mamba-
50.5
71.5
55.5
44.6
68.7
47.8
63M
315G
Results. Tab. presents a comprehensive comparison between Spatial-Mamba against state-of- the-art methods. Notably, Spatial-Mambir achieves a top-1 accuracy of 83.5%. outperforming the CNN-based ConvNext-T by 1.4% with similar amount of parameters and FLOPs. Compared to Transformer- methods, Spatial-Mamba--T exceeds Swin-T by 2.2% and NAT-T by 0.3%. In comparison with SSM-based methods. Spatial-Mamba--T outperforms VMamba-T by 1.0% and LocalVMamba-T by 0.8%. For other variants, Spatial- Mamba also shows advantages. Specifically, Spatial-Mamba-S and Spatial-Mamba--B achieve top-1 accuracies of 84.6% and 85.3%, respectively, surpassing NAT-S and NAT-B by margins 1.6% and 1.0%, and VMamba-S and VMamba-BB by 1.0% and 1.4%. While Spatial-Mambo differences, the Small and Base variants of Spatial- Maatial-aamaa are faster than their VMmmba counterparts. Moreover, both of them significantly faster than CNN and Transformer-based methods.
is slightly slower than VMamba-T T due to architectural
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Table 3: Comparison of semantic segmentation ADE20K with UPerNet Xiao al. 2018
segmentor. FLOPs are calculated with input resolution of 512 x 2048. 'SS' and "MS' represent single-scale and multi-scale testing, respectively.
Method
Crop size
mloU (SS)
mloU (MS) f #Param.
FLOPs
DeīT-S MLN
5122
43.1
43.8
58M
1217G
Swin-T
512²
44.4
45.8
60M
945G
ConvNeXt-T
5122
46.0
46.7
60M
939G
NAT-T
5122
47.1
48.4
58M
934G
MambaOut-T
512
47.4
48.6
54M
938G
VMamba-T
512²
48.0
48.8
62M
949G
LocalVMamba-1
5122
47.9
49.1
57M
970G
Spatial-Mamba-T
512
48.6
49.4
57M
936G
DeiT-B MIN
5122
45.5
47.2
144M
2007G
Swin-S
512
47.6
49.5
81M
1039G
ConvNeXt-S
512
48.7
49.6
82M
1027G
NAT-S
512
48.0
49.5
82M
1010G
MambaOut-S
512
49.5
50.6
76M
1032G
VMamba-S
5122
50.6
51.2
82M
1028G
LocalVMamba-S
5122
50.0
51.0
8IM
1095G
Spatial-Mamba-S
512
50.6
51.4
73M
992G
Swin-B
512a
48.1
49.7
121M
1888
ConvNeXt-B
512
49.1
49.9
122M
1170G
NAT-B
5122
48.5
49.7
123M
1137G
MambaOut-B
5122
49.6
51.0
112M
1178G
VMamba-B
512
51.0
51.6
122M
1170G
Spatial-Mambor 512
51.8
52.6
127M
1176G
5.2 OBJECT DETECTION AND INSTANCE SEGMENTATION ON COCO
Settings. We evaluate Mamba in object detection and instance segmentation tasks using COCO 2017 dataset (Lin et al. 2014) and MMDetection library (Chen et al. 2019). We adopt Mask (He al. 2017) and Cascade Mask R-CNN (Cai & Vasconcelos (018) detector heads, apply Spatial-Mamba--1 T/S/B pre-trained on ImageNet- as backbones. Following common practices (Liu al. 2021 2024), we fine-tune the pre-traines models for 12 epochs (1x schedule) and 36 epochs with multi-scale ippuss (3x schedule). During training, Adam W optimizer is adopted with an initial learning rate of 0.0001 and batch size of 16.
Results. The results on COCO with Mask R-CNN are reported in Tab. and the results with Cascade Mask R-CNN are provided in Appendix D can be seen that all variants of Spatial- Mamba outperform their competitors under different schedules. For 1 x schedule, Spatial-Manba-T achieves box mAP of 47.6 and a mask mAP 42.9, surpassing Swin-T//Vambbal by 4.9/0.3 in box mAP and 3.6/0.2 in mask mAP with fewer parameters and FLOPs, respectively. Similarly, Spatial-Mamba- S/B demonstrate superior performance to other methods under the same configuration. Furthermore, these trends of improved performance hold with the 3x multi-scale training schedule. Notably, Spatial-Mambor achieves the highest box mAP of 50.5 and mask mAP of 44.6, surpassing VMamba-S with considerable gain of 0.6 and 0.4, respectively.
5.3 SEMANTIC SEGMENTATION ADE20K
Settings. To assess the performance of Spatial-Mamba semantic segmentation task, we train our models with the widely used UPerNet segmentor (Xiao et al. 2018) and MMSegmenatiin toolkit
2021 2024), we pre-train on ImageNet- IK, and use as the backbone to train UPerNet on ADE20K dataset (Zhou et al.) 2019). This training process encompasses 160K iterations with batch size of 16. The Adam W is used as the optimizer with a weight decay of 0.01. The learning rate is set to 6 x 10-5 with linear learning rate decay. All the input images cropped into 512 512.
(Contributors) 2020 Consistent with previous work (Liu et al.
model

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Table 4: Ablation studies Spatial-Mamba- for neighbor set Q and other module designs.
Module design
#Param. (M)
FLOPs (G)
Throughput
Top- acc.1
Baseline
25M
4.4G
1706
82.0
Ω (3 x 3)
25M
4.4G
1557
82.3
Q {5 x 5
25M
4.5G
1461
82.5
Q [Rald = 1,3,5)
25M
4.5G
1209
82.7
+ Overlapped Stem
27M
4.5G
1158
82,9
LPU
27M
4.5G
1065
83.3
+ Re-Param
27M
4.5G
1438
83.3
MESA
27M
4.5G
1438
83.5
Results. The results on semantic segmentation are summarized in Tab. 3 Spatial-Mamba variants consistently achieve impressive performance. For instance, Spatial-Mamba-T attains single-scale mloU of 48,6 6 and a multi-scale mloU of 49.4. This signifies an improvement of 1.5 mloU over NAT-T and 0.6 mloU over VMamba-T in single-scale input. This advantage maintained with multi-scale input, where Spatial-Mamha-T is 1.0 mloU higher than NAT-T and 0.6 mloU higher than VMamba-T. Furthermore, Spatial-Mamba-B achieves the best performance with a multi-scale mloU of 52.6.
5.4 ABLATION STUDIES
In this section, ablate various key components of task in Tab. 4 Based on the configurations of Swin-T (Liu et al. 202I), we construct the baseline model as Spatial-Mante Mamba-T but without the SASF module. This baseline uses 4 4 convolution with stride of as stem layer and merges 2 x neighboring patches for down- down-sampling.
ImageNet- IK classification
Neighbor set. First, adjustments the neighbor set f reveal that increasing the size from 3 results a gradual improvement in accuracy, from 82.3% to 82.5%, albeit
neighborhood to with corresponding decrease in throughput. Furthermore, employing broader dilated neighbor set with factors = 1,3, 5 increases the accuracy to 82.7%, while reducing throughput to 1158. This suggests a trade-off between speed and larger neighbor set.
Local enhancement. We replace the original non-overlapped stem and down-sampling layer with overlapped convolutions (refer to 'Overlapped Stem' in Tab. 4). resulting in a gain of 0.2% in accuracy. We also incorporate the LPU (Guo et al. 2022). depth-wise convolution placed at the top of each block and FFN, further increasing the accuracy by 0.4%. These modifications enrich the local information available between image patches before processing by the SASF module, enabling to better capture structural dependencies.
Optimization. To further enhance the model efficiency, we implement the SASF module using re- e-parammeerizzaioonn techniques (Ding et al. 2022] and optimize the CUDA kernels. This accelerates the model by at least 30% and boosts the throughput from 1065 to 1438. Finally, integrating MESA
(Du et al. 2022 to mitigate overfitting provides an additional 0.2% accuracy improvement.
In addition, we provide some qualitative results in Appendix D. in-depth discussion about SASF in Appendix and comparative analysis of the Effective Receptive Fields (ERF) (Ding et al. 2022) of various models is provided in Appendix G
CONCLUSION
We presented in this paper Spatial- Mambia, a novel state space model designed for visual tasks. The key of Spatial-Mamba lied the proposed structure-ave aware state fusion (SASF) module, which effec- tively captured image spatial dependencies and hence improved the contextual modeling capability. We performed extensive experiments on fundamental vision tasks of image classification, detection and segmentation. The results showed that with SASF, Spatial-Mamba surpassed the state-of-the- art state space models with only one signal scan, demonstrating its strong visual feature learning capa- bility. We also analyzed in-depth the relationships of Spatial-Mamba with the original Mamba and linear attention, and unified them under the same matrix multiplication framework, offering deeper understanding of the self-artention mechanism for visual representation learning.
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REFERENCES
Ethan Baron, Itamar Zimerman, and Lior Wolf. A 2-dimensional state space layer for spatial inductive bias. In The Twelfth International Conference on Learning Representations, 2023.
Zhaowei Cai and Nuno Vasconcelos. Cascade r-cnn: Delving into high quality object detection, In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 6154-6162.
2018.
Guo Chen, Yifei Huang, Jilan Xu, Baoqi Pei. Zhe Chen, Zhiqi Li, Jiahao Wang, Kunchang Li, Tong Lu, and Limin Wang. Video mamba suite: State space model as a versatile alternative for video understanding. arXiv preprint arXiv:2403.0963
2024.
Kai Chen, Jiaqi Wang, Jiangmiao Pang. Yuhang Cao, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jiarui Xu, et al. Mmdetection: Open mmlab detection toolbox and benchmark. arXiv preprint arXiv: 0000001155, 2019.
Yinpeng Chen, Xiyang Dai, Mengchen Liu, Dongdong Chen, Lu Yuan, and Zicheng Liu. Dynamic convolution: Attention over convolution kernels. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 11000-11039, 2020.
MMSegmentation Contributors. Mmsegmentation Openmmlab semantic segmentation toolbox and benchmark, 2020.
Jifeng Dai, Haozhi Qi, Yuwen Xiong, Yi Li, Guodong Zhang, Han Hu, and Yichen Wei. Deformable convolutional networks. In Proceedings of the IEFE international conference on computer vision, pp. 764-773, 2017.
Tri Dao and Albert Gu. Transformers are ssms: Generalized models and efficient algorithms through structured state space duality. arXiv preprint arXiv:2405.2 1060, 2024.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference computer vision and pattern recognition, pp. 248-255, Icee, 2009.
Xiaohan Ding, Xiangyu Zhang. Jungong Han, and Guiguang Ding. Scaling up your kernels to 31x31: Revisiting large kernel design in enns. Proceedings of the IEEE/CVE conference on computer vision and pattern recognition, pp. 11963-11975. 2022.
Alexey Dosovitskiy. Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition scale. arXiv preprint arXiv:2010. /9929, 2020.
Jiawei Du, Daquan Zhou, Jiashi Feng, Vincent Tan, and Joey Tianyi Zhou. Sharpness-aware training for free. Advances in Neural Information Processing Systems, 35:23439-23451, 2022.
Karl J Friston, Lee Harrison, and Will Penny. Dynamic causal modelling. Neuroimage, 19(4): 1273-1302, 2003.
Daniel Y Fu, Tri Dao. Khaled K Saab, Armin W Thomas, Atri Rudra, and Christopher Ré. Hungry hungry hippos: Towards language modeling with state space models. arXiv preprint arXiv:2212.1400 14052, 2022.
Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces, arXiv preprint arXiv:2312.00752, 2023.
Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, and Christopher Ré. Hippo: Recurrent memory with optimal polynomial projections. Advances in neural information processing systems, 33: 1474-1487, 2020.
Albert Gu, Karan Goel, and Christopher Ré. Efficiently modeling long sequences with structured state spaces. arXiv preprint arXiv:2111.00399 2021a.

---

Published as a conference paper at ICLR 2025
Albert Gu, Isys Johnson, Karan Goel, Khaled Saab, Tri Dao, Atri Rudra, and Christopher Ré. Combining recurrent, convolutional, and continuous-time models with linear state space layers. Advances in neural information processing systems, 34:572-585, 2021b.
Hang Guo, Jinmin Li, Tao Dai, Zhihao Ouyang. Xudong Ren, and Shu-Tao Xia. Mambair: A simple baseline for image restoration with state-space model. arXiv preprint arXiv:2402. 15648, 2024.
Jianyuan Guo, Kai Han, Han Wu, Yehui Tang, Xinghao Chen, Yunhe Wang, and Chang Xu. Cmt: Convolutional neural networks meet vision transformers. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 12175-12185, 2022.
Ankit Gupta, Albert Gu, and Jonathan Berant. Diagonal state spaces are as effective as structured state spaces. Advances in Neural Information Processing Systems, 35:22982-22994, 2022.
Danijar Hafner, Timothy Lillicrap, Jimmy Ba, and Mohammad Norouzi. Dream to control: Learning behaviors by latent imagination. arXiv preprint arXiv: 2019.
Dongchen Han, Ziyi Wang, Zhuofan Xia, Yizeng Han, Yifan Pu, Chunjiang Ge. Jun Song, Shiji Song, Bo Zheng, and Gao Huang. Demystify mamba in vision: A linear attention perspective. arXiv preprint arXiv:2405. 16605, 2024.
Ali Hassani, Steven Walton, Jiachen Li, Shen Li, and Humphrey Shi. Neighborhood attention transformer. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pp. 6185-6194, 2023.
Haoyang He, Yuhu Bai, Jiangning Zhang, Qingdong He, Hongxu Chen, Zhenye Gan, Chengjie Wang, Xiangtai Li, Guanzhong Tian, and Lei Xie. Mambaad: Exploring state space models for multi-class unsupervised anomaly detection. arXiv preprint arXiv:2404.06564, 2024a.
Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross Girshick. Mask r-enn. In Proceedings of the IEEE international conference computer vision, pp. 2961-2969, 2017.
Wei He, Kai Han, Yehui Tang, Chengcheng Wang. Yujie Yang, Tianyu Guo, and Yunhe Wang. Densemamba: State space models with dense hidden connection for efficient large language models. arXiv preprint arXiv:2403.0000 008/8, 2024b.
Vincent Tao Hu, Stefan Andreas Baumann, Ming Gui, Olga Grebenkova, Pingchuan Ma, Johannes Fis- cher, and Bjorn Ommer. Zigma: Zigzag mamba diffusion model. arXiv preprint 2xXvv22403.13800 2024.
Tao Huang, Xiaohuan Pei, Shan You, Fei Wang, Chen Qian, and Chang Xu. Localmamba: Visual state space model with windowed selective sean, arXiv preprint arXiv:2403.09333, 2024.
Rudolph Emil Kalman. A new approach to linear filtering and prediction problems. 1960.
Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and François Fleuret. Transformers are mns: Fast autoregressive transformers with linear attention. In International conference on machine learning, pp. 5156-5165. PMLR, 2020.
Kunchang Li, Xinhao Li, Yi Wang, Yinan He, Yali Wang, Limin Wang, and Yu Qiao. Videomamba: State space model for efficient video understanding, arXiv preprint 46X77.2403.06977 2024.
Weibin Liao, Yinghao Zhu, Xinyuan Wang, Cehngwei Pan, Yasha Wang. and Liantao Ma. Lightm- unet: Mamba assists in lightweight unet for medical image segmentation. arXiv preprint arXiv:2403.05226, 2024.
Tsung-Yi Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In Computer Vision- ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings. Part V 13, pp. 740-755. Springer, 2014.
Yue Liu, Yunjie Tian, Yuzhong Zhao, Hongtian Yu, Lingxi Xie, Yaowei Wang, Qixiang Ye, and Yunfan Liu. Vmamba: Visual state space model. arXiv preprint arXiv:2401. 10/66, 2024.
12

---

Published as a conference paper at ICLR 2025
Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo. Swin transformer: Hierarchical vision transformer using shifted windows. In Proceedings of the IEEE/CVF international conference computer vision. pp. 10012-10022, 2021.
Zhuang Liu, Hanzi Mao, Chao- Yuan Wu, Christoph Feichtenhofer, Trevor Darrell, and Saining Xie. A convnet for the 2020s. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 11976-1186, 2022.
Jun Ma, Feifei Li, and Bo Wang. U-mamba: Enhancing long-range dependency for biomedical image segmentation. arXiv preprint arXiv:2401.04723 2024.
Shentong Mo and Yapeng Tian. Scaling diffusion mamba with bidirectional ssms for efficient image and video generation. arXiv preprint arXiv:2405. 15881, 2024.
Eric Nguyen, Karan Goel, Albert Gu, Gordon Downs, Preey Shah, Tri Dao, Stephen Baccus, and Christopher Ré. $4nd: Modeling images and videos as multidimensional signals with state spaces. Advances in neural information processing systems, 35:2846-2861. 2022.
Yanyuan Qiao, Zheng Yu, Longteng Guo, Sihan Chen, Zijia Zhao, Mingzhen Sun, Qi Wu, and Jing Liu. Vl-mamba: Exploring state space models for multimodal learning. arXiv preprint arXiv:2403. 13600, 2024.
Ilija Radosavovic, Raj Prateek Kosaraju, Ross Girshick, Kaiming He, and Piotr Dollár. Designing network design spaces. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 10428-10436, 2020.
Yuan Shi, Bin Xia, Xiaoyu Jin, Xing Wang, Tianyu Zhao, Xin Xia, Xuefeng Xiao, and Wenming Yang. Vmambair: Visual state space model for image restoration. arXiv preprint arXiv:2403.1 1423, 2024.
Jimmy TH Smith, Andrew Warrington, and Scott W Linderman. Simplified state space layers for sequence modeling. arXiv preprint arXiv:2208. 04933, 2022.
Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou. Training data-efficient image transformers & distillation through attention. In International conference on machine learning, pp. 10347-10357. PMLR, 2021.
Wenhai Wang, Enze Xie, Xiang Li. Deng- Ping Fan, Kaitao Song, Ding Liang, Tong Lu, Ping Luo, and Ling Shao. Pvt v2: Improved baselines with pyramid vision transformer. Computational Visual Media, 8(3):415 424, 2022.
Robert L. Williams and Douglas A. Lawrence, Linear state-space control systems observability. 1001002/97804701117777777
2007.
Tete Xiao, Yingcheng Liu, Bolei Zhou, Yuming Jiang, and Jian Sun. Unified perceptual parsing for scene understanding. In Proceedings of the European conference on computer vision (ECCV), pp- 418-434, 2018
Yicheng Xiao, Lin Song, Shaoli Huang, Jiangshan Wang, Siyu Song. Yixiao Ge, Xiu Li, and Ying Shan. Grootvl: Tree topology is all you need in state space model. arXiv preprint wwX.::222060029999 2024.
Chenhongyi Yang, Zehui Chen, Miguel Espinosa, Linus Ericsson, Zhenyu Wang, Jiaming Liu, and Elliot J Crowley. Plainmamba: Improving non-hierarchical mamba in visual recognition. arXiv preprint arXiv:2403. 17695, 2024.
Jing Yao, Danfeng Hong, Chenyu Li, and Jocelyn Chanussot. Spectralmamba: Efficient mamba for hyperspectral image classification. arXiv preprint 2XXi::444400488, 2024.
F Yu. Multi-scale context aggregation by dilated convolutions. arXiv preprint arXiv:1511.07122 2015.
Weihao Yu and Xinchao Wang. Mambaout: Do we really need mamba for vision? arXiv preprint arXiv:2405.07990 2024.
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Yubiao Yue and Zhenzhang Li. Medmamba: Vision mamba for medical image classification. arXiv preprint arXiv:2403.03889, 2024.
Bolei Zhou, Hang Zhao, Xavier Puig, Tete Xiao, Sanja Fidler, Adela Barriuso, and Antonio Torralba. Semantic understanding of scenes through the ade20k dataset. International Journal of Computer Vision, 127:302-321, 2019.
Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, and Xinggang Wang. Vision mamba: Efficient visual representation learning with bidirectional state space model. arXiv preprint arXiv:2401.09417, 2024.
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Appendix to "Spatial-Mamba: Effective Visual State Space Models via Structure-aware State Fusion"
In this appendix, we provide the following materials:
More visual results for SASF (referring to Sec. 4.1 in the main paper); B
Architecture details of Spatial-Mamba and experimental settings (referring to Sec. 4.2 and Sec. 5,1
in the main paper);
Derivations of the SSM formulas of Mamba and Spatial-Mambe (referring to Sec. 4.3 in the main paper):
Results of Cascade Mask R-CNN detector head (referring to Sec. 5.2 in the main paper);
Visual results and comparisons for detection and segmentation tasks (referring to Sec. 5.2 and Sec.
5.3 in the main paper);
Further discussions about SASF (referring to Sec. 5.4 in the main paper);
Comparisons of effective receptive field (referring to Sec. 5,4 in the main paper).
A
MORE VISUAL RESULTS
More visual comparisons between the original and fused structure-aware state variables are shown in Fig. 6
Due to spatial modeling capability of SASF, the fused state variables demonstrate more accurate context information and superior structural perception across different scenarios.
(a) Input
(b) Original state
(c) Fused state
(d) Input
(e) Original state
(f) Fused state
Figure 6: More visualizations of state variables before and after applying the SASF equation.
B MODEL ARCHITECTURES AND EXPERIMENT SETTINGS CLASSIFICATION
Network architecture. The detailed architectures of Spatial-Mamba models outlined in Tab. Following the common four-stage hierarchical framework (Liu et al. 2021 Han et al. 2024), we construct the Spatial-Mami Mambaa models by stacking our proposed Spatial- Mamba blocks at each stage. Specifically, an imput image with resolution of 224 x 224 is firstly processed by stem layer, which consists of Convolution (Conv), Batch Normalization (BN) and GELU activation function. The kernel size is 3 x 3 with stride of 2 at the first and last convolution layers, and stride of 1 for other layers. Each stage contains multiple Spatial-Mambe blocks, followed by a down-sampling layer except for the last block. The down-sampling layer consists of 3 3 convolution with a stride of and Layer Normalization (LN) layer. Each block incorporates structure- SSM layer and a Feed-Forward Network (FFN), both with residual connections. The structure- SSM contains a SASF branch with 2D depth-wise wise convolution and multiplicative gate branch with activation function, illustrated in Sec. 4.2 of the main paper. The expand ratio of SSM is set 2, doubling the
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Table 5: Architectures of Spatial-Mambe models, where Linear refers to a linear layer, DWConv represents depth- wise convolution layer, SASF module refers to Fig. 4 in Sec. 4.2 of the main paper, and FFN is a nerd-oo Network.
Layer
Output size
Spatial-Mamba-
Spatial-Mamba-S
Spatial-Mamba-BB
Stem
56 x 56
Conv 3 stride 2, BN, GELU; Conv 3 x 3 stride 1, BN; Conv 3 x 3 stride 2, BN
Spatial-Marnb -arbb Blocks
Spatial- MMaiial Blocks
Spatial- Opatial-Mamba Blocks
Lincar 64 + 128
Lincar 64 + 128
Lincar 96 - 192
DWConv 128
DWConv
DWConv 192
Stagel
SASF 128
x
SASF 128
X
SASF
x
Linear 128 64
Lineur 128
64
Linear 192 96
FFN 64
FFN 64
FFN 96
Down Samphing Conv x stride 2, LN
Martial-Maanbaaa Blocks
Spatial-Mamba Blocks
Spatial-Mambu Blocks
Linear 128 - 256
Lincar 128 - 256
Lineur 192 - 384
DWConv 256
DWCony
DWConv 384
Stage2
SASF 256
SASF
x
384
4
Lincar 256 128
Linear 256 - 128
Lincur 384 192
FFN 128
FFN 128
FFN 192
Down Sampling Conv 3 x stride 2, LN
Spatial-Marha Mambba Blocks
Spatial- Blocks
Spatial-Mamba Blocks
Lincar 256 - 512
Lincar 256 + 512
Lincar 384 - 768
DWConv 512
DWConv 512
DWConv 768
Stage3
x
SASF 512
SASF 512
21
SASF
X 21
Lineur 512 256
Linear 512 256
Linear 768 384
FFN 256
FFN 256
FFN 384
Down Sampling Conv 3 x stride 2, LNN
Spatial-Marnbu Marbbu Blocks Lincar 512 - 1024
Spatial-Mamba Blocks
Spatial-Mambu Blocks
Linear 512 - 1024
Linear 768 - 1536 DWConv 1536
DWCCon 1024
DWConv 1024
Stage4
7
SASF 1024
SASF 1024
SASF 1536
Linear 1024 512
Lincar 1024 512
Linear 1536 768
FFN 512
FFN 512
FFN 768
Head
1 1
Average pool, Lincar 1000, Softmax
number of channels. The SSM state dimension is set to I for better performance and efficiency. We modify the embedding dimension and number of blocks to build our Spatial-Mambe Ma--a-ammaaaSSS-- models.
Settings for ImageNet-1K 1K classification. The -patial-Mamba- T/S/B models trained from scratch for 300 epochs using Adam V optimizer with betas set to (0.9, 0.999), momentum set to 0.9, and batch size set 1024. The initial learning rate is set 0.001 with weight decay of 0.05. A cosine annealing learning rate schedule is adopted with a warm-up of 20 epochs. We adopt the common data augmentation strategies in previous works (Liu et al 2021 2024). Moreover, label smoothing (0.1), exponential moving average (EMA) and MESA (Du et al. (2022) are also applied. The drop path rate set to 0.2 for Spatial-Mamba-T Mamba-T, 0.3 for Mpatial- and 0.5 for Opatial-Mambae
Implementation details. The Spatial-Mamba models employ a hardware-aware selective scan algorithm adapted from the original Mamba framework, with modifications to the CUDA kernels for decoupling state transition and observation equations. The SASF module of Spatial-Mambl is implemented by the general matrix multiplication (GEMM) with optimized CUDA kernels.
C DERIVATION OF SSM FORMULAS
Based the Mamba formulation provided in Sec. 3 of the main paper, the state transition equation in the recursive form can be rewritten as follows:
A, + Buu
A, 16-134-22 (A.1101224 + B 11 + Bist
A, (A,-1 AA-23113 + 2 + Bi-14(-1) + Bew
- 22 A
+ A,B,- B,
1-1 1.-1Bu-111
B,u,
= = A 11 A.
-r A, Bu + ,, B, 1- + B
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Published as a conference paper at ICLR 2025
By defining the initial state zeto, To Eq. can be expressed as:
Ft =
B Sit
where A
[
-
8 8<6
(8)
1,
8 ==t
We omit the term Di for simplicity. According the observation equation, final output y/ = E. C₁ Ag B, Suppose the input vector is u = _ uz!" R² with length L, the corresponding output vector is E RR, Then the above calculation can be written in matrix multiplication form, i.e, y = Mu, where M a structured lower triangular matrix and Mij J. B.
derive the
Similarly, we can represent Spatial- Mambaa in the same matrix transformation form. Based on the definition of Spatial-Mamba in Sec. 4.1 and Eq. (8. the SASF equation can be rewritten as he Σken Enspa (1) Ogg A (::p(()) Bg By multiplying C., we can derive the final output of udg. It can also be concisely represented as matrix multiplication form Mu, where M is a structured adjacency matrix and M.j
Spatial- -patial-Mamba as = Eken (espe(t) ag CAA (t) Bg
En (p
D RESULTS OF CASCADE MASK R-CNN DETECTOR HEAD
Detailed results of object detection and instance segmentation on the COCO dataset with Cascade Mask R-CNN framework are reported in Tab. [6] We can see that Spatial-Mamba- achieves box mAP of 52. and a mask mAP of 44.9, surpassing Swin-T/NAT-T by 1.7/0.7 in box mAP and 1.2/0.4 in mask mAP with fewer parameters and FLOPs, respectively. Similarly, Spatial-Mamber demonstrates superior performance under the same configuration.
Table Results of object detection and instance segmentation on the COCO dataset using Cascade Mask R-CNN (Cai & Vasconcelos 2018) under 3 schedule. FLOPs are calculated with input resolution of 1280 800.
Backbone
APb f
AP
AP 75
Apm
APm
APm
#Param.
FLOPs
Swin-T
50.4
69.2
54.7
43.7
66.6
47.3
86M
745G
Con-NeXt-T
50.4
69.1
54.8
43.7
66.5
47.3
86M
741G
NAT-T
51.4
70.0
55.9
44.5
67.6
47.9
85M
737G
Spatial-Mor Spatial-Mamba-1
52.1
71.0
56.5
44.9
68.3
48.7
84M
740G
Swin-S
51.9
70.7
56.3
45.0
68.2
48.8
107M
838G
ConvNeXt-S
51.9
70.8
56.5
45.0
68.4
49.1
108M
827G
NAT-S
52.0
70.4
56.3
44.9
68.1
48.6
108M
809G
Pratial-Mamba-
53.3
71.9
57.9
45.8
69.4
49.7
101M
794G
E QUALITATIVE RESULTS
In this section, we present the visualization results of object detection and instance segmentation in Fig. and present the results of semantic segmentation Fig. Compared with VMamba, our Spatial-Mammi demonstrates superior performance in both tasks, producing more accurate detection boxes segmentation masks, particularly in areas where local structural information is crucial. For example, in the second row of Fig. 7 VMamba mistakenly identifies the shoes on a skateboard as person, probably because it observes the shoes from four directions independently and resembles them as human. Our method avoids this mistake by simultaneously perceiving the shoes and their surrounding context. Similarly, in the semantic segmentation task, as shown in the second and third precise structures of trees and doors. These results
of Fig. 8 our approach achieves highlight the eifectiveness of our proposed Spatial- Mamba leveraging local structural information for better visual understanding.
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Published as a conference paper at ICLR 2025
(a) Input
(b) VMamba
(c) Spatial-Mamba
(d) Ground Truth
Figure 7: Visualization examples of object detection and instance segmentation on COCO dataset with Mask R-CNN 1x schedule (He al. 2017) by VMamba and Spatial-Mamba
cellng
FOOS
B:B
8:S.
Tameo
DO00
cheet STINAER 1otte
shice 21p0
cheet SrOvert
(a) Input
(b) VMamba
(c) Spatial-Mamba
(d) Ground Truth
Figure 8: Visualization examples of semantic segmentation on ADE20K dataset with single-scale
inputs by VMamba and Spatial-Man -Mabba..
FURTHER DISCUSSIONS ABOUT SASF
SASF extension. To further explore and validate the spatial modeling capability of our proposed SASF, we adapt SASF into Vim and VMamba backbones, resulting in Vim+SASF (by replacing the middle class token with average pooling and setting state dimension to 1) and SAA (directly integrated with SASF). Under the same training settings, the classification results on ImageNet- IK are presented Tab. 7 It can be seen that by integrating with SASF, the bi-directional Vim model is improved 0.5% in top-1 accuracy and the cross-scan VMamba is improved by 0.3%. These findings verify that SASF can even enhance the performance of multi-directional models, which have already incorporated (yet in inefficient manner) spatial modeling operations.
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Published as a conference paper at ICLR 2025
Table 7: Comparison of classification performance on ImageNet- by integrating with SASF, where "Throughput" is measured using an A A100 GPU with an input resolution of 224 x 224.
Method
Im. size
#Param. (M) FLOPs (G)
Throughput
Top- acc.
Vim-Ti
2242
6M
1.4G
71.7
Vim- -i--TT-SAFF
224
7M
1,6G
72.2
VMamba-T
224
30M
4,9G
1686
82.6
VMamba-T+SASF
2242
31M
5.1G
1126
82.9
Fusion operators. There are also different choices of the operators that can used for fusing state variables in SASF. We opt for depth-wise convolution due its simplicity and computational efficiency. However, operators like dynamic convolution (Chen et al. 2020), deformable convolution (Dai et al.) 2017), and attention mechanisms have also demonstrated superior performance in com- puter vision tasks. Therefore, we anticipate that they can be used as alternatives to the depth-wise convolution in our Spatial-Mamba. We simply train Spatial-Mamba-TT network with dynamic convolution and the results are shown Tab. 8 We can see that dynamic convolution yields a 0.2% performance gain in accuracy but significantly reduces throughput from 1438 to 907. This result suggests the potential ad advantages of more flexible fusion operators for SASF, but also highlights the importance of considering computational cost.
Table Comparison of classification performance by Spatial-Mamba-T with depth-wise conv. and dynamic conv. on ImageNet- IK, where 'Throughput' is measured using an A100 GPU with input resolution of 224 224.
Method
Im. size #Param. (M)
FLOPs (G)
Throughputt
Top-1 acc.1
Depth-wise Conv.
224
27M
4.5G
1438
83.5
Dynamic Conv.
224
33M
4.8G
907
83.7
G EFFECTIVE RECEPTIVE FIELD (ERF)
We compare the Effective Receptive Field (ERF) (Ding et al. 2022) of the center pixel on popular backbone networks before and after training, as shown in Fig. 9 The ERF values represent the contributions of every pixel input space the central pixel in the final output feature maps. To visualization, we randomly select 50 images from the ImageNet- 1K validation set, resize them resolution of 1024 x 1024, and then calculate the ERF values with the auto-grad mechanism. initially exhibits a larger receptive field than other methods
Before training, our Opatial-Mambor except DeiT-S due neighborhood connectivity in the state space. After training, our method, along with DeiT-S, Vim-S, and VMamba-T. T, all demonstrate global ERF. In addition, both Vim-S and VMamba-T exhibit noticeable accumulation contributions along either horizontal or vertical directions, which can be attributed to their multi-directiona fusion mechanisms. In contrast, our unidirectional Spatial-Mand Mamba-TT effectively eliminates this directional bias.
Before Training
After Training
ResNet-50
ConyNeXt-T
Swin-T
DeiT-S
Vim-S
VMamba-T
Spatial-Mambe-
Figure 9: Comparison of Effective Receptive Field (ERF) among popular backbone networks.
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Reviews:
[{"review_id": "mhZO7JmW7P", "reviewer": "Reviewer_ZoEw", "summary": "Spatial-Mamba introduces a \"structure-aware state fusion\" (SASF) mechanism using dilated convolutions in the Mamba architecture. This mechanism claims to add neighborhood connectivity directly in the state-space of SSM. The method is benchmarked on common image benchmarks, i.e. segmentation, classification, and detection using common datasets.", "questions": "The results for Cascade Mask R-CNN seem to be missing...\nMinor: On line 204, it is mentioned \"considering both temporal and spatial information\", but what exactly is the temporal information here? Or is it a typo?  \n\nOverall, the paper is sound and presents a good idea for an existing problem. I am open to adjusting my evaluation should any significant concerns be raised by other reviewers that I may have overlooked.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "SSMs do have the problem of spatial sense. While the recent papers of ViM and VMamba try to solve them in their way, the solution feels rather underwhelming. The idea of introducing dilated convolutions as a means of capturing structural dependency in images is quite intriguing. I like the idea and the authors have done a good job of explaining most of the paper and related works. It is written clearly and concisely.", "weaknesses": "There are not many weaknesses in this paper. Apart from Figure 5 (and qualitative and erf figures in supp.), the paper could improve on convincing the reader with visuals if the resultant SSM with SASF mechanism extracts structural dependencies from the images. \nMinor mistakes exist in the paper; specifically, on lines 199 and 200, equation 2 lacks a definition for alpha_k. It is only on line 212 that the alpha_k is mentioned as weights. Also, it is not clear from the text how exactly is this linear weighting being applied/calculated (on line 99, it mentions dilated convolutions to re-weight and merge states but it will be nice to add some clarity after equation 2 is introduced).", "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": "F3y25660Dr", "reviewer": "Reviewer_Q4w4", "summary": "This paper introduces Spatial-Mamba, a  state space models visual backbone designed for 2D visual tasks. It mainly introduce a multi-scale depthwise conv layer after the mamba operators to fuse the contextual information from different spatial locations. The author conducts theoretical analysis. Extensive experiements like image classification, dense prediction tasks are conducted.  The results show it outperforms the baselines and achieve competitive resutls.", "questions": "Please see weakness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The motivation is reasonbal and good. The vision mamba models suffers from processing  2D visual data due to the complexity of spatial structures. It heavily relys  on the 1D scanning strategy to transform 2D format into 1D sequence. The author apply conv-based layers to fuse the contextual information  in spatial domain, which is complemenary to the Mamba based operator. \n\n2. The experimetanl results are good. The accuracy in imageNet shows the improvement. The speed is still competitive as the conv operators are optimized, thus bringing less latency. \n\n3. The overall method is simple and easy to understand. Applying conv layers as a compelmentary module to improve the spatial modeling capability of the mamba is simple and direct.", "weaknesses": "1. The method seems to be a combination of Mamba and a classical module (depthwise conv).  It is also mentioned in No.3 point in Strengths. I would recommned author to validate/explore the spatial modeling enhancement methods more throughly. For example, applying the multi-scale conv layer to the original bi-directional Mamba (Vim) and cross-scan mamba (VMamba) to see the improvements. THough the one-direction scan and conv layer can aggregate enough spatial contextual information. \n\n2. The analysis of linear attention, mamba and the proposed method in section 4.3 is good. But the method proposed is rather straightforward. It seems the method doesnot improve the weakness of Mamba from the in-depth analysis. It first uses the Selective scan in Mamba to calculate the hidden states (one direction), following a depthwise conv to fuse the hidden states, then calculate the output y. It is not known the improvements over the method that adding more direcitons into the selective scan and computing the output. \n\n3. The modules/operators to fuse the contextual information can have mutiple choices. The paper chooses depthwise conv. Conv operator may have inductive bias, which aggregate the spatial information by a fixed pattern. I would see more explorations, which could improve the paper.", "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": "RcEG3mAyz7", "reviewer": "Reviewer_CLPg", "summary": "This manuscript proposes to aggregate neighborhood features in state-space models for more efficient state-space modeling. The experiments are convincing, and the manuscript is well-organized.", "questions": "Please refer to weakness part where I have expressed my concerns.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 2, "strengths": "+ The proposed fusing operation seems to have a decent performance gain onto the baseline.\n+ The manuscript is well-organized.\n+ The ablation studies are clear and convincing.", "weaknesses": "+  Novelty. The proposed fusion seems to be a re-invention and re-introduce of convolution on the feature map of state-space modeling but is claimed as \"Structure-Aware State Fusion\". The LPU, overlapped stem,  re-parameterization  and MESA are all proposed in previous works. The technical contribution seems to be limited.\n+ Clearness. The fusion seems to be applied after scanning. However, in Eq(2), the $x_t$ is the same in scanning and fusion. The notation here is not clear. It would be better to use $x_t^{\\prime}$ in the fusion formula if my understanding is correct.", "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": "IbCKuPd1XA", "reviewer": "Reviewer_P6PW", "summary": "This paper introduces Spatial-Mamba, a novel state space model (SSM) designed for visual tasks, capable of effectively capturing spatial dependencies in images to enhance contextual modeling. Experimental results demonstrate that Spatial-Mamba outperforms existing SSMs and other mainstream models in areas such as image classification and semantic segmentation.", "questions": "1. Could you further explain how state variables are modeled in the state space to design the structure-aware state fusion?\n2. Please provide details on the number of hidden states in each SSM layer and include relevant ablation experiments.\n3. Is Spatial-Mamba implemented using the hardware scanning algorithm proposed by Mamba?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. Improved upon existing SSMs by directly integrating spatial neighborhood dependencies into the state transition process.\n\n2. Analyzed the connections between Spatial-Mamba, Mamba, and linear attention, unifying them under a matrix multiplication framework.", "weaknesses": "1. The paper does not mention the number of hidden states used in the SSM, and the ablation study lacks an analysis of the impact of different numbers of hidden states.\n\n2. While the authors analyze the relationship between Spatial-Mamba, Mamba, and linear attention, they do not clarify the framework used to implement Spatial-Mamba, such as Mamba's hardware scanning algorithm or Mamba2's SSD framework.\n\n3. In Mamba’s proposed SSM, hidden states do not inherently have spatial relationships. I suspect the authors intend to model the hidden states as 2D local observation points?", "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)