MobileODE: An Extra Lightweight Network
Authors: Le Yu
Jun Wu
Bo Gou
Xiangde Min
Lei Zhang
Zhang Yi
Tao He
Venue: NeurIPS 2025 poster ()
Keywords: depthwise-separable convolution
lightweight models
nmODE
Primary area: deep_learning
TL;DR: We optimize depthwise-separable convolution through a discrete ODE module for building lightweight models, achieving remarkable performances with less parameters.

Abstract: Depthwise-separable convolution has emerged as a significant milestone in the lightweight development of Convolutional Neural Networks (CNNs) over the past decade. This technique consists of two key components: depthwise convolution, which captures spatial information, and pointwise convolution, which enhances channel interactions. In this paper, we propose a novel method to lightweight CNNs through the discretization of Ordinary Differential Equations (ODEs). Specifically, we optimize depthwise-separable convolution by replacing the pointwise convolution with a discrete ODE module, termed the \emph{\textbf{C}hannelwise \textbf{O}DE \textbf{S}olver (COS)}. The COS module is constructed by a simple yet efficient direct differentiation Euler algorithm, using learnable increment parameters. This replacement reduces parameters by over $98.36$\% compared to conventional pointwise convolution. By integrating COS into MobileNet, we develop a new extra lightweight network called MobileODE. With carefully designed basic and inverse residual blocks, the resulting MobileODEV1 and MobileODEV2 reduce channel interaction parameters by $71.0$\% and $69.2$\%, respectively, compared to MobileNetV1, while achieving higher accuracy across various tasks, including image classification, object detection, and semantic segmentation. The code is available at {\url{https://github.com/cashily/MobileODE}}.

MobileODE: An Extra Lightweight Network
Le Yu', Yu',Jun Jun Wu', Bo Gou', Xiangde Min", Lei Zhang', Zhang Yi', Tao He Machine Intelligence Laboratory, Sichuan University TTongii Medical College, Huazhong University of Science and Technology (yule, junwu, goub7779tb77775 scu edu. en '(leizhang, zhangyi, tao__aa_haa hhe@@ssuu @scu. Rascu.edu cn 2 mmx mexianade@tih, timu. edu. cn
Abstract
Depthwise--spparbbe convolution has emerged as a significant milestone the lightweight development of Convolutional Neural Networks (CNNs) over the past decade. This technique consists of two key components: depthwise convolution, which captures spatial information, and pointwise convolution, which enhances channel interactions. In this paper, we propose novel method to lightweight CNNs through the discretization of Ordinary Differential Equations (ODEs). Specifi- cally, we optimize depthwise-separable convolution by replacing the pointwise convolution with discrete ODE module, termed the Channelwise ODE Solver (COS). The COS module is constructed by a simple yet efficient direct differen- tiation Euler algorithm, using learnable increment parameters. This replacement reduces parameters by over 98.36% compared to conventional pointwise convo- lution. By integrating COS into MobileNet, develop new extra lightweight network called MobileODE. With carefully designed basic and inverse residual blocks, the resulting MobileODEVI and MobileODEV2 reduce channel interac- tion parameters by 71.0% and 69.2%, respectively, compared to MobileNetVI, while achieving higher accuracy across various tasks, including image classifi- cation, object detection, and semantic segmentation. The code is available at https:///itthul com/cashhy//oobieddd
Introduction
The design of lightweight networks has become central focus in computer vision, aiming balance high performance with low computational costs. This is especially crucial for aesource-constraan devices like mobile devices, embedded systems, and edge computing platforms, which have limited computational power and storage capacity. As these devices face growing demands for efficient model deployment, recent advancements in lightweight Convolutional Neural Networks (CNNs) have led to the development of efficient architectures that provide practical solutions to these challenges. Currently, the development of lightweight networks has largely focused on optimizing the MobileNet series and integrating self-attention mechanisms. MobileNerVI (Howard, [017]] was the first to introduce lightweight network by employing depthwise-separable convolutions, marking a milestone in the lightweight evolution of CNNs over the past decade. MobileNetV2-ve v4 (Sandler et al. 2018
Howard et al. 2019 Qin et al. 2025 enhanced MobileNetVI I by incorporating inverted residuals and linear bottlenecks, network architecture search, and universal inverted bottlenecks, respectively. GhostNet [Han et al. 2020]. ShuffleNet [Zhang et al., 2018), and MobileOne [Vasu et al. 2023b)
optimized deptawisseseparablle convolutions while maintaining the core design of separating spatial and channel computations. More recently, self-attention mechanisms have been introduced to further improve MobileNet variants by enhancing global context. Models like FistViT (Vasu al. 2023a]. Mobile VIT [Mehta and Rastegari] 2021] FfficientFormerr22 [Li et al. 2023). and Rep [Wang et al.
*Corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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46
42
4/
41
yn
DDE
x
Figure Detailed Structure of the COS Module. We propose the Direct Differentiation Euler (DDE) algorithm as a highly efficient method for approximating solutions in high-dimensional spaces. Building on DDE, we develop the Channelwise ODE Solver (COS) module, which enhances inter- channel interactions by mapping the input to its global attractor.
2024a have transformed MobileNet-like architectures into Vision Transformers (ViTs), significantly exceed, the original designs.
boosting their performance. However, their parameter counts still remain comparable to, or even
The primary mechanism behind depthwise-separable convolution lies the separation of spatial and channel computations, where depthwise convolution is responsible for extracting spatial information and pointwise convolution enhances channel interaction. However, this separable design reduces the receptive field of channelwise computations due to the reduction in the number of parameters. Specifically, the 1 x convolution only performs a linear mapping on features the form of x x C, where C' represents the number of channels. Moreover, the computational cost of spatial operations is lower than that channelwise computations. To address this, we aim to enhance the global receptive field of channel computations by adopting a non-linear mapping approach, thereby introducing an extra lightweight network with parameters comparable to those used in spatial computations.
Recently, Neural Memory Ordinary Differential Equations (nmODEs) Yi 2023 have shown sig- nificant advancements in efficiently modeling non-linear mappings. This is primarily due to their unique characteristic of having single global attractor, which implies that all trajectories within the dynamical system defined by nmODEs will ultimately converge to this attractor [Wills et al. 2005). This property enables nmODEs establish robust connection between the input space and the memory space [Poucet and Save 2005). These advancements have been particularly impactful
in fields of computer vision, such medical image segmentation (He et al.) 2024 2023). video captioning [Artham and Shaikh, 2024). and image recognition [Niu et al.] 2024 Luo et al. 2024).
The discrete nmODEs have been employed design lightweight network architectures. [He et al.)
2024] introduced various techniques, including Euler's method, Heun's 's method, and linear multi-step method, reduce the complexity of the decoder in U-like networks. These methods have been demonstrated effective when integrated into state space models [Wang et al., 2024b). While discrete nmODEs have streamlined network architectures for semantic segmentation tasks, there remains need for research focused on developing generalized network structures applicable to diverse tasks.
To the best of our knowledge, this paper is the first work develop the discrete nmODEs to construct an extra lightweight MobileNet-like network. The main contributions of this paper are as follows:
We propose discrete nmODEs module, named Channelwise ODE Solver (COS), illustrated in Fig. [ which is structured by a novel Direct Differentiation Euler (DDE) algorithm. The DDE enables the time increments learnable during network training, verifying the gradient descent stability of the COS module.
We build novel extra lightweight network, named MobileODE, which incorporates the COS modules. Both the basic block (COS-base) and the inverse residual block (COS-inv) perform efficiently. The resulting MobileODEVI and MobileODEV2 reduce the parameters for channel interaction by 71.0% and 69.2%, respectively, compared to MobileNetV 1,, as shown in Tab. [

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Extensive experiments across various tasks, including image classification, object detection, and semantic segmentation, demonstrate the effectiveness of the proposed MobilcODEVI and MobileODEV2 architectures.
2
Related work
MobileNet Series MobileNet (Howard 2017] introduced the classic depthwise-separable convolu- tion, significantly reducing the model's parameter count and computational complexity. Since then, numerous improvements based this module have emerged. MobileNerV2 (Sandler et al. 2018) enhanced feature dimensions by adding a pointwise convolution before the depthwise-separable convo- lution and introduced the linear bottleneck stabilize network performance. MobileNetV3 (Howard et al. 2019] updated the inverted bottleneck block from MobileNetV2 by incorporating the Squeeze- Excittiitttion (SE) module (Hu et al.) 2018 and the Hard-Swishh activation function, as well as introducing Neural Architecture Search (NAS) to automatically discover optimal network architec- tures. MobileNext [Zhou al. [020] introduced the SandGlass module, which establishes shortcuts based on gigh-dimensional features. MobileNet [Qin et al.] 2025) advanced the series further by introducing the Universal Inverted Bottleneck (UIB) block, which incorporates depthwise con- volution before the inverted bottleneck module. MobileOne (Vasu et al.] 2023b) returned to the original separable convolution, introducing reparameterization to merge multiple branches into a single-branch structure. Despite these several iterations of improvement, the fundamental nature of depthwise-separable convolution remains unchanged: it uses depthwise convolution to extract spatial information and pointwise convolution to enhance channel interaction. This paper optimizes the channel interaction of depthwise-separable convolution through a discrete nmODEs method.
MobileNets with Self-Attentions The integration of Transformer architectures with depthwise- separable convolutional blocks to better learn global representations has become major research focus. FiT [Vasu et al. [023a], a hybrid vision transformer architecture, placed the computation- ally expensive self-attention mechanism in the later stages of the network, where the resolution is lower. It also used structural reparameterization to reduce memory access costs and improve network accuracy. Mobile ViT [Mehta and Rastegari, [021] seamlessly combined the ViT structure with convolutions by introducing the Mobile ViT block, which replaced some of the inverted bottleneck blocks in the MobileNetV2 model, achieving global receptive fields at lower computational cost. EfficientFormer22 [Li et al. 2023] proposed lineggrined joint search strategy that simultaneously optimized latency and parameter count to find efficient architectures, enabling high-speed execution of ViT. ViT [Wang et al. [2024a] improved upon the MobileNetV3 block by separating token mixers and channel mixers, employing structural reparameterization techniques to enhance learning. These models achieved balance between speed and accuracy by lightweighting the ViT architecture to avoid the expensive computational cost.
Lightweight Discrete ODE Models Ordinary Differential Equations (ODEs) provides a conceptual framework for neural networks and has been widely applied in mathematics and physics (Chen et al.)
2018 Shou et al. 2024). Neural memory Ordinary Differential Equations (nmODEs) Yi 2023 was designed fully utilize the memory capacity provided by dynamic systems. nmODES enhanced the non-linear representation of neural networks through implicit mapping and non-linear activation functions. Discrete nmODEs has demonstrated its versatility and effectiveness in treamlining network structures. For instance, He et al. 2024) employed explicit Fuler's method, Heun's method, and linear multi-step method for discretization and further introduced three plug-and-play decoders that reduce the number of parameters and FLOPs while maintaining performance when embedded into various U-shaped networks. Similarly, He al. [2023] followed the explicit Euler's method and applied it to liver tumor segmentation. |Wang et al. [2024b] leveraged the powerful non non-linear representation capability of nmODEs combined with state space models, incorporating residual connections to build medical image segmentation network, called nmSSM-UNet. Additionally, Niu jet al. 2024 utilized the discrete nmODEs as the inverse path a bi-directional network structure, and evaluated the possibility of the bi-directional feedforward network architecture. These methods demonstrate that nmODEs possess strong learning capabilities across various tasks while facilitating lightweight networks, leveraging their inherent advantages in non-li nonelincar mappings.
3

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3 Method
3.1
Direct Differentiation Euler Algorithm
The basic method of discretizing nmODEs is to split the time step t into smaller intervals. The Euler method (Fuler 1845) is one of the simplest and most widely used techniques for solving ODEs numerically. Given an initial state y(to) and the basic nmODEs:
i(t) = v(t) + f(v(t)
(())((()))))
(I)
where, y(t) denotes the internal state, xtt) is the external input, g(-) denotes linear mapping of æ, and the f(-) is the non-lineas activation function. The discretization of the nmODEs is as follows:
y(t + At) y(t) At (()),
(2)
where, A/ represents the time increment, and y + At) is an approximate solution time t + At.
In previous related work [He et al. 2023 Wang et al., 2024b, Niu et al.] [2024] He et al. [024]]
the explicit Euler method employed for discrete nmODEs integrate information with minimal
parameters, where At is typically initialized as fixed constant. Combine Eq. (I) and (2) for each layer < L, we can derive that
+1 (1 At) y + AL J(y' g(x', ,0)))
He et al. 2024 and Niu al. 2024 initialized At as L. where I. is the number of discretization layers. However, every ODE sol solver's s discretization introduces approximation errors, which increase with larger time increments. Thus, using a constant to initialize At can harm the dynamies of nmODEs. This approach not only limits accuracy but also risks making the system uncontrollable.
To address this limitation, propose the Direct Differentiation Euler (DDE) algorithm, which introduces learnable time increments At to guide the model's computation, where At = {At', At? ..... )t initialized using Normal distribution. These increments are then passed through a ReLU6 activation function to ensure they remain non-negative and to limit their output range. For each layer 1 <, T., obtain:
(t) - + fly' + tg(z",0))). w''-= + Adl (1).
(4)
Instead of relying on a fixed At, the DDE method dynamically adjusts At during training through gradient descent. This allows the model to refine its temporal resolution adaptively, enabling the effects of time increments to accumulate across multiple layers.
The DDE method differs from previous ap- proaches, as shown Fig. First, prior meth- ods use Eq. (3) as gating operation that reg- ulates contributions from previous and current layers. In contrast, DDE computes specific par- tial derivatives layer by layer, solving them di- rectly as intermediate variables to reduce errors. Second, DDE employs sequenced time incre- ments for layer-wise adjustments at each step. In steeper gradient regions, At' learns smaller values, while in smoother areas, it can learn larger increments, as shown in Appendix [6.3] Previous gating methods are fixed and lack this flexibility. In Sec. 44.4, we investigate how At affects the learning process. We find that I. increases, fixed At can impair accuracy, whereas DDE consistently enhances it. Additionally, with deeper layers, the accuracy of features from each layer's outputs progressively improves, demonstrating strong learning capability.
Jr yd1
113
yd1
(b)
Figure 2: The distinction between the explicit Euler algorithm (a) and the proposed DDE algorithm (b).
3.2 Channelwise ODE Solver
Inspired by the unique global attractor of nmODEs, which allows every input to converge to a unified memory representation, we leverage this characteristic to introduce the COS module. Based on the

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DDE algorithm, COS is a lightweight inter-channel computation technique that integrates features with minimal computational cost. It decomposes inter-channel computation into two key steps: inter-channel linear transformation and unified channelwise mapping using DDE.
Inter-channel linear transformation. We define a feature tensor x E Cx where C represents the number of channels, and H and W denote the height and width of the input feature map, respectively. As illustrated in Fig. | we perform an inter-channel linear transformation to facilitate channel interaction at each pixel of the feature map, which is formulated as follows:
g( = (b,)) 4;
where, + IR VRVC learnable matrix, Sii H. S W, and (.,)) RR IRVCxVCxIx
Traditional convolutions exhibit quadratic complexity, while our method utilizes compact & matrix work in tandem with the learnable time increments. This the direct reason for the significant reduction in computational cost, transforming a quadratic complexity into linear complexity.
Algorithm Channelwise ODE Solver (COS) with DDE
Input: The feature tensor æ, learnable weight matrices + E RVCxvext, learnable time increments At E R ", initial internal state y E RCCHXW
2: Output: Final output o.
3: for layer 0 to T, - do
4: for 1
to H, W do 5: Calculate the linear transformation ((.)) described in Eq.
6: Update the internal state (h,))* as shown in Eq. (4).
7: end for
8: Combine these internal states along the feature map obtain y
9: end for
Reture: -y + x.
Unified channelwise mapping using DDE. After obtaining the linear transformation g(x²) of the nmODEs, we employ the DDE algorithm build the COS internal structure. For an L-layer DDE, we first compute the partial derivatives directly and then use the learnable At' to calculate the final output of the channelwise mapping, nmODEs by mapping the input to its global attractor, linking input space with memory space. The DDE operator transforms each (o,)) refining feature representation converge towards the global attractor. This process, governed by learnable time increments, captures both local variations and global patterns. As a result, the model transcends local information and approximates solutions in
shown in Eq.
The DDE harnesses the advantages of
high-dimensional space. Specific details of the COS module are provided in Algorithm
(a) The COS- base block.
(b) The COS-inv block.
Figure 3: The illustrations of the COS-base block (a) and the COS-inv block (b). represents the pre-defined discrete layers for the implementation of nmODEs.
The basic and inverse residual blocks. As shown in Fig. 3 (a), we retain the depthwise convolution
and replace the pointwise convolution with our COS for inter-channel computation using DDE. Inspired by the inverted bottleneck block in MobileNetV2 [Sandler et al. 2018). we further design the COS-inv block in Fig. (b). The main difference is that COS-inv places the COS module before the depthwise convolution for channel expansion, enhancing high-dimensional spatial computation and non-linear transformations by nmODEs. then employs another COS to restore the channels, introducing upsampling downsampling process before the linear transformation. Specifically, bilinear interpolation applied each (( facilitating channel expansion or compression by considering surrounding pixels and maintaining image smoothness and detail.
5

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MoNNkNaVL//Bikk
Chanaclris
MobR:DEYYL/ Strske
Chunch
Chamacii
Chasndvic
SepuntiVi/dd
M2x66
SeganatioV /4
12.54
SepestieN Fel
37ud4
SeperbleVi:ng
/2
ScpuraleViistt
128:122
144
10: 144410
CDS
144
1DC14455 20 w-)
178-25))
SepanbloNi D0St
144
(46
SepratieN M /al
144
166
296
256-770
256
10 1007554110
CDS les
756
10x 10-1666-5-001111 u
SeperaMeVi
256.-11
Sepasslao Sir CUS buae
756
256 17a
SquestiVV /i 3x CDB arr
716
250
SeparsieVi/al
512
5x312x512
129
329
Sx. 140 1-4x)-121 m4)
Sepantleeiing
512
51241834
SeparasiV. 1 CUS-taaz
129
120% 1024
SenuratiV /i COS ape
529
52%%
SepenteeV1112
1004
1004 1024
1024
V0x H00es
1024
10 1D:0022:342000 (2
Ang Poot
1024
Nig Poct
1034
Aug Pool PC
1034
FC
1004
2024-200
PC
1034
1004 300
1024
1004x200
Parern
09736
148Mi,
Table I: Comparison of architectures and parameters for MobileNetV1, MobilcODEVI, and Mo- bilcODEV2 presented. The red- eed-highlighted numbers indicate the repeated use of the block.
Detailed structures. We have constructed MobileODEVi and MobileODEV2, as shown in Tab. SeparableV1 refers to the parrhwise-separbbbe convolution from MobileNetV1, where we retained certain pointwise convolutions for downsampling while maintaining linear computational capabilities. Both the COS-base and COS-inv blocks are followed by BatchNorm [loffe, [0155 and ReLU6 non-linearity. We made slight modifications the input channels of the these blocks to enable square root calculations. An ablation study on discrete layer numbers is detailed in Sec. Sec. leading us to set L 10 for balance between performance and speed. In MobileODEVI and MobilcODEV2, depthwise-separabe convolutions are replaced with the proposed COS-base and COS-inv blocks, respectively. The number of parameters for channelwise computation shown in Tab. T COS in MobileODEV1 has only 0.04M parameters (4 98.36%) compared to the 2.44M of the replaced point- wise convolutions, and COS-inv has 0.10M (L 95.90%). Compared to Mobile MobileODEVI reduces channelwise computational cost by 71.0%, while MobileODEV2 reduces it by 69.2%.
In COS-inv block, e denotes the channel expan- sion factor. For pointwise convolution, increasing raises the computational cost by a factor of e on top
Block
Formula
Parramieeg C 512,e 4)
Pointwise Conv
C² Xe
512" 1 576
of the quadratic complexity (Tab. ( In contrast, COS-inv has a linear increase in computational cost with respect to This feature enables COS-inv to scale to larger channel numbers without signifi- cantly increasing computational costs.
COS-iav
CxexL+L
10+
Table 2: Comparison of computational over-
head between pointwise convolution and COS- inv with channel expansion factor = 4.
Experimental Results
In this section, evaluate Mo- bilcODEVI and MobilcODEV2 incorporating self-attention mecha- nisms. We replace the final COS and COS-inv components with Mobile blocks [Mehta and Rastegari] (021], resulting in MobileODEVI+ViT and MobileODEV2+vit. The VibileViT block integrates convolutional and transformer operations at low resolution,
#Puram.
CIFAR-10
CIEAR-100
IN-liny
GhostNet
4.16M
83.32
52.32
42,45
52.71
FasIViT-T8
3.4M
86.48
56.57
42.92
43,03
ShufeeNet22 1.0x
1.46
92.31
71.54
46.72
59.97
ShaffleNetV2 1.5x
2.69M
92.80
72.39
47.24
60.63
ShuflleNetV1 1.0x
1.10M
70.55
45.49
59.21
ShuflleNetV1
2.29M
61.39
MobileNaV3--Lare
4.4IM
93.55
73.72
44.72
60.93
MobileNetV4
2.75M
92.43
74.14
44.39
61.10
MobileOne-s0
4.47M
93,92
75.58
45.45
61.33
providing lightweight local and global perspective integration. our models achieving significant reductions in back- bone size while improving performance. All simulations use fixed seeds for repro- ducibility, and models are implemented in PyTorch on a single NVIDIA 4090 GPU. For fair comparison, we train all lightweight models from scratch without using pretrained parameters.
MobileNaVV
341M
93.17
74.77
42,23
60.78
MobileODEVI
1.4M
74.98
61.92
MohileNelV2
248M
93.77
74.73
43.01
63.53
MobileODEV2
1.52M
63.46
MobileVTT
5.58M
89.97
65.23
45.00
57.92
282M
94.13
75.56
47.35
62.98
MobileViTV2
18.45M
89.33
65.78
46.72
60.82
3.65M
94,26
75.89
48.08
63,56
Table 3: Comparison of classification performance across various methods and datasets, with values indicating top-1 accuracy (%). Bold entries highlight superior performance. The parameters of the presented models are evaluated on the IN-R dataset.

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4.1 Image Classification
Dataset and experiment settings. We validate our proposed methods on four different datasets, namely CIFAR-IO/CIFAR- 100 (Krizhevsky et al. 2009 ImageNet-R (IN-
R) [Hendrycks et al., 2021a] and Tiny Imagenet (IN-tiny) [Le and Yang. 2015] For CI/AR-10/100,
which are well-known for classification tasks, we use a resolution classes, and each class contains 500 training images, 50 validation images at resolution of 64 x 64. Additionally, we assess the robustness of our methods on IN-R dataset, which consists of 30K images from 200 ImageNet classes, rendered in diverse textures and styles (e.g.. paintings, embroidery, etc.). We divide IN-R into training and testing sets at 4 1 ratio, using a resolution of 256 x 256.
32 x 32. IN-tiny has 200
In our experiments, all networks are using identical training recipes to ensure fair comparisons. The batch size is set to 32 images for to 16 images. For CIFAR- CIFAR-IO/CIFAL 10/CIFAR- as suggested in Haase and Amthor (020], we remove the first and second pooling operations of MobileNets to obtain a final feature map of size 4. Our experimental setup is consistent with Mehta and Rastegari [2021]. Basic data augmentation techniques, including random resized cropping and horizontal flipping, are applied during training.
100, while for IN tiny and IN-R, it is set
For the comparative experiments, MobileODEVI and MobilcODEV2 are evaluated against their baselines, MobileNetV1 (Howard 2017 and MobileNetV2 (Sandler et al. 2018). Additionally, they are compared with other classic lightweight networks that have been improved based on MobileNet, including GhostNet [Han et al. 2020], ShuffleNetV1 [Zhang et al., 2018 ShuffleNetV2 [Ma et al. 2018). MobileNetV3 [Howard et al. 2019]. MobileNetV4 IQin et al. [2025], and MobileOne Vasu
al. 2023b]. Furthermore. with the integration of Mobile ViT blocks [Mehta and Rastegari, [202]
MobileNetV I+V and MobileNetV2++i are compared with Mobile ViT [Mehta and Rastegari
2021].
MobileViTV2 |Mehta and Rastegari 2021), and FastVYT--8 [Vasu al. 2023a].
Results. As shown in Tab. 3] MobileODEVI and MobileODEV2 show significant accuracy im- provements while keeping parameter counts low. MobileODEVI has 1.14M parameters, which is 66.57% fewer than MobileNetV1 (3.41M), and MobileODEV2 has 1.52M parameters, 38.7% fewer than MobileNetV2 (2.48M). On CIFAR-10, MobileODEVI outperforms MobileNetV1 I by 0.39%, and MobilcODEV2 surpasses MobileNetV2 by 0.24%. For CIFAR- 100, MobileODEVI improves over MobileNetV1 by 0.21%, while MobilcODEV2 achieves a 0.7% gain over MobileNetV2.. On IN-tiny and IN-R datasets, MobileODEV2++V exceeds the best results by 0.03% compared to MobileNetV2 and by 0.84% compared ShuffleNetV2 1.5x. Overall. MobilcODEV2 consistently outperforms MobileODEVI across all datasets, particularly in complex IN-R scenarios. This con- firms the practical applicability of our methods and the superior learning capability of COS-inv over COS. Integrating Mobile VIT blocks [Mehta and Rastegari (02T) enhances performance across all datasets. MobileODEV2+ consistently achieves the best results, highlighting the effectiveness of combining MobileODE with self-attention while minimizing computational overhead.
Model
#Param. PASCAL VOC2012
ADE20K
BUSI
FFE
Model
PParam.
MoblleNatV3-Large
6.69M
52,11
26.82
mAP
AP:.
AP::
mAP
AP:.
AP::
MobileNetV4
17.08M
50.85
26.64
MobaleNaV3-Large
3.07M
30.81
62.82
95.44
73.50
MobileOne-st
24.55M
53.27
27.21
MobileNetV4
1.99M
35.80
75.81 33.70 61.98
95:21
70.51
MobileNetV1
20.33M
49.39
25.96
Mobilenne-0t
5.09M
36.02
73.10
32.22
59.97
94,12
67.72
MobileODEVI
6.40M
51.73
26.88
MobileNetVV
3.90M
30.71
61.13
30.02
61.85
94.02
71.82
MobileODEVI
199M
32,50
61.73
28.94
61.88
91.35
73.13
MobilcNet22
8.09M
50.10
24.69
MobileNeV2
2.19M
58.51
33.62
62.84
95.82
72.11
MobilcODEV2
6.39M
51.82
27.12
MobileODEV2
144M
34.42
64.56
36.93
63.15
94.33
74.56
MobileViT
8.69M
50.86
24.73
MobileViT
5.14M
22.91
49,02
60.93
94.43 69.90
MobiLcODEVI-NTT
7.04M
52.13
26.98
MobI--DDEV-VIT
3.14M
3488
67.36 30.33
63.91
95.66 73.54
MobileVTTV2
35.38M
47,31
24.25
ViVV
18.55M
62.64 37.72 94.41 78.93
MobI 7.8MM
53.35
27.32
MobHeODEV2-VIT 6.15M
37.71 66.40 37.82 66.52 95.74 77.52
Table 4: Comparison of semantic segmenta- tion performance of DeepLab with differ- ent backbones across various datasets, evalu- ated using mIOU (%). Model parameters are assessed on the ADE20K dataset.
Table 5: Comparison of object detection perfor- mance of SSDLite with different backbones on
BUSI and FFE datasets. The parameters of the presented models are evaluated on the FFE dataset.
7

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4.2 Semantic Segmentation
Dataset and experiment settings. We integrate MobileODE with DeepLabV3 [Chen 2017] training Mo on PASCAL VOC 2012 [Everingham et al. 2015] dataset and ADE20K dataset [Zhou et al. 2019] from scratch, in accordance with standard training practices [Mehta and Rastegari 2021] J. All networks are trained for 200 epochs with a batch size of 16 images using a standard sampler. For the PASCAL VOC 2012 dataset, additional annotations from [Hariharan et al.) [011] are utilized. To substantially reduce the complexity of the segmentation head, we adjust the final output channels of MobileÔDEVI and MobileÔDEV2 to 576 and 256, respectively. and eliminate the classification layer. This modification facilitates a more accurate evaluation of MobileODE's performance as a lightweight backbone network.
Results. As shown in Tab. MobilcODEs significantly improve performance with much lower parameter count than other MobileNet variants. On PASCAL VOC 2012. MobilcODEVI improves over MobileNetV1 by 2.34%. MobileODEV2 surpasses MobileNetV2, achieving 1.72% higher ac- curacy. When integrated with the ViT block [Mehta and Rastegari| 2021]. I. IVVi improves Mobile ViT by 1.27%, while MobileODEV2+ ViT exceeds MobileViTVV by 6.04%. On the ADE20K dataset, MobileODEVI improves upon MobileNetV1 by 0.92%, using just 6.40M parameters versus MobileNetVI'ss 20.33M. MobileODEV2 surpasses MobileNetV2 by 2.43%. Mo- ViT achieves the highest accuracy just below MobileOne, recording 0.08% higher on PASCAL VOC 2012 and 0.11% higher on ADE20K, all while having 69.53% fewer parameters.
4.3 Object Detection
Dataset and experiment settings. We integrate MobileODE with the single-shot object detection (SSD) backbone [Liu et al. 2016) to develop an efficient object detection framework. We replace standard convolutions in the SSD head with separable convolutions, resulting in a lightweight model referred to as SSDLite [Mehta and Rastegari 2021]. We train and validate our model's detection performance on the publicly available BUSI dataset AAl-Dhayyani et al. 2020 and Facial Feature Extraction (FFE) dataset (kag) 2025). The BUSI dataset contains 437 images with benign lesions, 210 images with malignant lesions, and 133 normal images without lesions. The FFE dataset is a labeled dataset designed for the detection of various facial features, including eyebrows, eyes, nose, lips, and cestache-beard regions, with 457 images allocated for training and 126 images designated for validation. Model performance is evaluated using the mAP metric across IoU thresholds ranging from 0.50 to 0.95 (mAP@ loU 0.50 : 0.05 0.95). Additionally, we report performance at specific IoU thresholds, including AP50 and APTs, to provide more detailed evaluation.
Results. As shown in Tab. S on the BUSI dataset, MobileODEVI outperforms MobileNetV achieving a 1.79% increase AP and 3.6% increase in AP MobileODEV2 surpasses Mo- bileNetV2 across all evaluation metrics. particularly in AP50 ( 6.05%). The performance of MobileODEV VIT and MobileODEVV+ViT significantly exceeds that of the original MobileViT model. For instance, MobileODEV improves by 11.91% % in AP and 18.3% in AP50. while Mo- bileODEV2+VIT surpasses MobileViTV2 by 1.8% in AP. For the FFE dataset, MobileODEV2+ViT outperforms MobileViTVV with fewer parameters (6.15M vs. 18.55M). Overall, MobileODEVI and MobilcODEV2 perform exceptionally well as lightweight backbones for detection tasks, with the introduction of self attentio mechanisms providing a further boost in detection performance.
4.4 Ablation Study
Impact of I.. We apply both learnable time increments At and fixed time increments A (Ai= D) to MobilcODEVI and MobilcODEV2. As shown in Fig. 4 (a) and (b), it is evident that as the number of discrete layers increases, fixed At leads to unstable accuracy improvements, and even decline in performance. This aligns with our expectation in a non-linear environment. In contrast, for the learnable At, the model accuracy exhibits an increasing trend. However, when L is set to 10, the rate of improvement slowed. Additionally, by leveraging COS-inv blocks, MobileODEV2 demonstrates a more pronounced improvement in accuracy, following similar trend.
Impact of learnable At. We explore the learning process of the learnable At settings in Mo- bileODEV2. In Fig. (c), we present scatter plots of accuracy across all 200 categories of IN-R for each discrete layer the final COS-inv module, with the initial setting of T, = 30. The black points indicate the accuracy of the first discrete layer's output for each class, while the red points represent
8

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545
Mis UIGENT
$1.-
Accuray (%
Accousaty
51.0
62.0
Discrono Layees
Discret Lagres
Category
(a)
(b)
(c)
(d)
Figure 4: Study of the L setting in MobilcODEVI(a) and MobileODEV2(0) with learnable At versus fixed At on the CIFAR- 10 dataset. (c) Accuracy across each category at each discrete layer. (d) Accuracy with respect to learnable time increments for 30-layer DDF.
the accuracy of the last discrete layer's output. A clear upward trend in accuracy is observed for each category with the increase in discrete layers, indicating that the COS design exhibits fine- grained perception. In Fig. (d), we plot the values of the learnable At. with the spacing between the triangle markers proportional the time increment. becomes more pronounced, highlighting the impact of the time increments accumulating across multiple layers effectively.
evident that the trend of accuracy improvement
#Param. ACC
Model
FLOPs(M) Latency(ms)
1
0.61M
93.57
MobileNetV1
MobilcODEVI
7.09
24.54
4
1.27M
94.01
MobileODEVI w/Rungo-Kutta
18.49
50.12
9
1.77M
91.04
MobileViT
7.10
46.22
16
2.46M
89.57
MobileODEVI-ViT
7.32
30.64
25
3.35M
88.02
MobileODEV1 w/Runge-Kutu
18.27
43.16
Table 6: Study of e settings.
Table 7: Comparison of MobileODEVi and Mo-
bilcODEV V+T in terms of latency and FLOPs.
Impact of e. Tab. presents the number of parameters and Top-1 accuracy (%) for models under different expansion factor e settings, all evaluated the CIFAR-10 dataset. Overall, the analysis reveals notable fluctuations in model performance as increases. Specifically, model performance significantly declines, highlighting the limitations of using bilinear interpolation for parameter-free channel expansion and contraction concerning the value of e.
Computing efficiency. In Tab. 7 MobileODEVI exhibits significantly lower latency of 24.54 (batch size = 16) compared to the baseline models, despite a moderate increase in FLOPs to 7.09 million. This reduction in latency indicates enhanced efficiency in processing. Although the increase in FLOOPs is a common characteristic of ODE methods, such as those using the Runge- Kutta approach, proposed methods have effectively addressed this challenge. Moreover, MobileODEVI maintains competitive FLOOP count of 7.32 million while achieving a latency of 30.64 ms, further demonstrating the effectiveness of approach.
Conclusion
In this paper, we introduce MobileODE, an ultra-lightweight network based on the discrete nmODEs method, designed for various tasks. Our findings indicate a clear trend of improved performance as the number of discrete layers increases, emphasizing the potential for achieving state-of of-the----h--rn results. However, COS's sequential computation limits parallel processing, making indiscriminate increases L detrimental to inference speed. Therefore, a more balanced approach between performance and speed is essential. In future work, we plan integrate Neural Architecture Search (NAS) from MobileNerV3-Va into MobileODE to create more efficient structure and further explore L. settings. We hope this research inspires advancements in lightweight network models.

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Acknowledgements
This work is supported in part by the National Natural Science Foundation of China (Grant No. 62495064 and 62206189).
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Appendix
6.1
Training details for classification task
The loss function used cross-entropy with label smoothing (smoothing 0.1), and optimization was performed with AdamW W [Loshchilov 2017], and a weight decay of 0.01. The learning rate started 0.0002, increased to 0.002 for the first 2k iterations, and then decayed to 0.0002 using cosine schedule [Loshchilov and Hutter 2016]. The model was trained for a maximum of 200 epochs.
6.2 Training details for SSDLite and deeplabv3
Our experimental setup is consistent with Mehta and Rastegari [2021] The hyperparameter settings for semantic segmentation task PASCAL VOC 2012 dataset and object detection task are consistent. The AdamW optimizer with a weight decay of 0.01 is employed. The learning rate is first increased from 0.00009 to 0.0009 over the first 500 iterations. then annealed 1e 6 using a cosine scheduler. For the ADF20K dataset, training uses the SGD optimizer with momentum of 0.9 and a weight decay of 0.0001. A cosine annealing schedule applied, reducing the learning rate from 0.02 to 0.0001.
6.3 How DDE adaptively modify each At'.
Let the objective function be L(0). where 0 represents the model parameters. The learnable step size At' in DDE is optimized through backpropagation, and its gradient can be expressed as:
ØL
OL
0y
(6)
DAF
dy
dAd
where y/ = 3/ + Arl. .'. Expanding this gives:
0L
aL
(7)
By
Steep Regions: When ||: is large (high eurvature), the absolute value of the gradient d5r forcing At' to decrease to reduce loss. Flat Regions: When | is small (low curvature), the absolute aL is small, allowing At' to increase to accelerate convergence. value of the gradient dAr
8L is large,
6.4 Accuracy vs parameters on classification task
Tab. complements Tab. by providing additional details on parameter counts for CIFAR-10 and CIFAR- 100, along with two sets of comparative experiments conducted using ResNet- 100 and ResNet-353. Moreover, we add another challenging dataset ImageNet-A (IN-A) [Hendrycks et al.) 2021b), which contains 7.5K images across 200, featuring natural adversarial examples designed to challenge existing models.
94.5
94.0
Medi-opi
Ascuracy (%)
Accuracy (16)
93.0
Vertetioos 152
92.5
44
92.0
1.0
2.5
40
1.0
2,0
3.0
Parameters (M)
Parometers (M)
(a)
(b)
Figure 5: Visualization of accuracy results on the CIFAR-10 (a) and IN-R (b) datasets. The x-axis represents the number of parameters (lower is better), while the y-axis indicates accuracy (higher is better).
13

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Fig. 5 visualizes the accuracy results the CIFAR-10 10 and IN-R datasets. Our proposed models, MobicOODEV and MobilcODEV2, achieve impressive performance with a minimal number of parameters. Moreover, integrating self-attention mechanisms further enhances the results, leading to the best overall performance.
6.5 Licenses and copyrights across assets
1. CIFAR-10/100
Citation: Krizhevsky et al. 2009
Asset Link: hhttps://wwy
2. Tiny ImageNet (IN-tiny)
Citation: Le and Yang 2013
Asset Link: [https: htnggig.......ooaaaata///////aan
3. ImageNet-R (IN-R)
Citation: Hendrycks et al. 202
Asset Link: [https: wit.h..hh...oo
License htap://///shhhooooo////d/yy////r
MIT-1-ov-file]
4. PASCAL VOC2012
Citation: Everingham al. 2015
Asset Link:
5. ADE20K
Citation: Zhou al. 2019
Asset Link:
License:
6. BUSI
Citation: Al-Dhabyani al. 2020
Asset
Link httpp::/ www.
breast-ultrasounc -iw.uuddd-iaimss-dataaaae
7. FFE
Citation: kag 2025
Asset
facial-feature-eeee aaata
License:
(https://wwr) mit. htttpp://aw..mit.eed///aa htt///mmmmiiiiiIIeae
6.6 Demo in edge computing platform
We have developed a breast screening demo to effectively apply the proposed lightweight MobileODE models. This framework consists of three stages. In the first stage, binary classification distinguishes nodules from non-nodules (e.g., vessels, fat, muscle, etc.). Data identified as nodules are then passed to the second stage for detection. Images containing detected nodules, along with mask images generated from the detection boxes, are subsequently processed in the third stage to perform BIR ADS grading at the nodule level (as opposed to the image level). This framework has been successfully deployed on an edge computing platform, illustrated in Fig. 6 Since MobileODE is part of the components for BIRADS classification, we did not claborate on this demo in the main text. To date, have conducted screening trials across 1I hospitals (names withheld for anonymity policies), totaling 12,643 cases. With the assistance six ultrasound physicians for secondary verification, we calculated a consistency accuracy of 94.4%.
For hardware, We use the Lenovo Legion R9000P laptop, equipped with an NVIDIA GeForce RTX 4060 GPU (8 GB VRAM), AMD Ryzen 9 7945HX CPU, 15.3 GiB DDR5 memory. It runs Ubuntu 20.04.4 LTS (Linux 5.15 kernel). During the running, GPU memory usage was 1708/81 188 MiB, with utilization of 19%, indicating steady but low resource usage.
14

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Model
#Param.
CIFAR-10
#Faram.
CIFAR-100
IN-A
GhostNet
3.91
83.32
4.03M
52.32
7.02
FastVI1-18
3.27M
86.48
3.33M
56.57
9.13
ShuffleNetV2 10x
1.27M
92.31
1.36M
71.54
9.48
ShuffleNetV2 1.5x
2.49
92.80
2.59M
72.39
9.56
ShuffeNetV1 1.0%
0.93M
92.29
1.IM
70.55
9.41
ShufflNNetV 1.5%
2.03M
93.11
2.00M
72.16
8.84
MoblleNet33-Laree
4.17M
93.55
4,29M
73.72
10.07
MobileNett4
2.1M
92.43
74.14
8.33
MobileOne-so
3.56M
75.58
ResNet-110
LISM
93.78
1.17M
73.83
ResNet-353
3.65M
93.85
3.67M
72.11
MobileNetV1
3.20M
91.17
3.29M
74.77
8.42
MobilcODEVI
93.56
74.98
10.12
MobileNetV2
2.24M
93.77
2.35M
74.73
8.90
MobilcODEV2
1.27M
94.01
1.36M
75.43
10.72
MobileViT
4,94M
89.97
5.00M
65.25
9.46
MobileODEVI +VTT
2.65M
94.13
2.75M
75.56
10.94
VobileViTV2
17.44M
89.33
17.53M
65.78
9.11
MobileODEV2 + VIT
3.28M
94.26
3 3.40M
75.89
10.95
Table 8: As complement to Tab.
we provide the parameter counts for various models the
CIFAR- 10 and CIFAR-100 100 datasets, respectively. We also present new challenging benchmark IN-A prove the generalizability of our method
Browe Nadial Serweiig
Goeerate Repert
Ead Screming
Figure 6: The applications in edge computing platform.
6.7 The difference between Separable V1 and Separable
We incorporated the depthwise-separable convolution and inverted residual structure proposed in MobileNetV1 I and MobilcNetV2,, naming them Separable and Separable respectively. Sep- arableV consists of two separate layers: a lightweight depthwise convolution for spatial filtering and heavier 1 pointwise convolutions for feature generation. MobileNetV2 (Sandler al. 2018 introduced the linear bottleneck and inverted residual structure, creating more efficient layer designs by leveraging the low-rank nature of the problem. Separable is defined by a convolution, followed by depthwise convolutions and a x projection layer. A residual connec- tion applied only when the input and output have same number of channels. This structure maintains a compact representation at both the input and output while expanding internally to higher-dimensional feature space, thereby enhancing the expressiveness nonlinear per-channel transformations.
expansion
15

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(a)
(b)
Figure 7: (a) SeparableV1: MobileNetV1 layer (depthwise-sepaaable convolution). (b) Separable MobileNetV2 layer (Inverted Residual and Linear Bottleneck). Each block consists of narrow input and output (bottleneck) without nonlinearity, followed by an expansion to a much higher-dimensiona space and projection to the output. The residual connection links the bottleneck rather than the expanded representation.
6.8 Broader Impacts
This work advances the development of lightweight convolutional neural networks (CNNs) through the discretization Ordinary Differential Equations (ODEs), showcasing significant potential for positive societal impact. The proposed MobileODEs enable the execution of complex visual tasks on loourre-limited devices, such as smartphones and edge computing platforms (described in Sec. 666). Despite the improved accuracy of the model in various tasks, lightweight networks may generate inaccurate results in some cases, which, if rigorously validated, could lead the spread of misinformation. In critical areas like healthcare and law, such misinformation could have serious consequences. Therefore, while the technology shows great promise, responsible deployment and further research into alignment and safety remain crucial.
6.9 Qualitative results on the task of object detection
Fig and Fig.9 showcase the performance of SSDLite equipped with MobileODEVI and Mo- bilcODEV2, demonstrating successful detection of a diverse range of objects, including facial features and breast tumors. These results underscore the strong generalization capabilities of our proposed models across various mobile network variants. Furthermore, the integration of MobileODE enhances the model's 's ability adapt complex tasks, making it suitable for real- wolld applications that demand both accuracy and efficiency.
6.10 Qualitative results on the task of semantic segmentation
Fig and Fig present the visualizations of semantic segmentation results obtained using SrepLabww-MobbloDDEEA
on the PASCAL VOC 2012 and ADE20K datasets, respectively. The left column displays the input RGB images, the middle column shows the predicted segmentation masks, and the right column overlays the segmentation masks onto the RGB images. The qualitative results demonstrate strong understanding of scene semantics, highlighting the effectiveness and robustness of our proposed method across different datasets and complex scenarios.
16

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AMM
Figure 8: The object detection results of SSDLite SSDLite- MoVi (first row) and SSDLite-
MobileODEV2 (second row) on the Facial Feature Extraction Dataset validation set.
Figure 9: The object detection results of SSDDite-MobileODDD on benign tumors (first row) and malignant tumors (sccond row) demonstrate the performance the BUSI dataset.
17

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Figure 10: The semantic segmentation results of SIDLiee-MbhleDDEEVV-VIT on PASCAL VOC
2012 2 dataset.
18

---

Figure 11: The semantic segmentation results of SDDLic-NobbioDDEVV--VT ADE20K dataset.
19

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Question:
Answer:[ YYs]
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Answer: [Yes]
Justification: In Sec. || we discussed the limitations of the work in this paper.
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Reviews:
[{"review_id": "chmwDD6DET", "reviewer": "Reviewer_MTGp", "summary": "The paper introduces MobileODE, a novel and ultra-lightweight convolutional neural network (CNN) architecture designed to significantly reduce model size and computational cost while maintaining or improving accuracy. At its core, MobileODE revisits the standard depthwise-separable convolution architecture popularized by MobileNet, and replaces the pointwise (1×1) convolution — traditionally used for channel mixing — with a lightweight, learnable Channelwise ODE Solver (COS).\n\nThe COS module is built using a custom numerical solver called the Direct Differentiation Euler (DDE) algorithm. Unlike traditional discretization schemes that rely on fixed time steps, DDE introduces learnable time increments (∆t) that are optimized during training. This adaptive mechanism allows the model to fine-tune the temporal evolution of the feature transformations, enabling stronger inter-channel interactions with far fewer parameters. The result is a principled and trainable alternative to pointwise convolutions that operates at linear complexity with respect to the number of channels.\n\nTo showcase the versatility of the approach, the authors propose two variants:\n\nMobileODEV1: Replaces pointwise convolutions in MobileNetV1-style blocks with the COS module, preserving the basic block structure.\n\nMobileODEV2: Introduces the COS-inv block, inspired by MobileNetV2's inverted residual bottlenecks, and strategically applies COS before and after depthwise convolutions to enhance non-linear capacity and channel expressiveness.\n\nThe proposed models are evaluated across a diverse set of computer vision tasks, including image classification, semantic segmentation, and object detection, using datasets such as CIFAR-10/100, ImageNet-R, Tiny ImageNet, ADE20K, and PASCAL VOC. Experimental results show that MobileODEV1 and MobileODEV2 consistently outperform or match their MobileNet counterparts while achieving a ~70% reduction in parameters for channel interactions. Moreover, when paired with lightweight self-attention blocks (e.g., MobileViT), the models achieve state-of-the-art accuracy under strict efficiency constraints, all with lower inference latency and memory usage.", "questions": "** Typos & Formatting Issues\n- Algorithm 1 has a typo 'Reture' instead of Return. \n- small and overly compressed Figure 3.\n\n Q1: Why was standard ImageNet-1k training omitted from the experiments?\n\nWhile the proposed MobileODE variants show promising results on CIFAR, ImageNet-R, and Tiny ImageNet, it is unclear how well the method scales to full-resolution, large-scale datasets. Given that ImageNet-1k remains the standard benchmark for evaluating lightweight architectures (e.g., MobileNetV1–V4, MobileViT), could the authors clarify why ImageNet-1k training was not included? Are there challenges with scalability, convergence, or runtime that prevented this evaluation?\n\nQ2: Could the authors provide a detailed analysis of how increasing the number of DDE steps (L) affects inference latency, not just accuracy?\nWhile the ablation study in Section 4.4 explores the effect of L on accuracy, it would be helpful to see how this impacts latency and runtime. Since COS involves sequential updates, increasing L may introduce bottlenecks in real-time deployment.\n\nQ3: The use of ImageNet-R partially addresses robustness to distribution shift. Have the authors considered evaluating on additional robustness benchmarks such as ImageNet-C (corruptions), ImageNet-A (natural adversarial examples)?\nGiven the attractor-based design of COS and the dynamic evolution of features over discrete layers, it would be valuable to know whether the proposed method improves stability under noisy or corrupted inputs beyond stylized domains like ImageNet-R.\n\nQ4: While the paper introduces COS as a multi-step, attractor-based channel evolution module, it is not entirely clear how feature representations evolve across the L steps. Since the COS module is inspired by discrete ODE solvers and functions similarly to a recurrent update, it would be highly valuable to include visualizations or analyses that help interpret this process. For instance: \n- How different are the intermediate representations at each step, especially for small vs. large L?\n- Are later steps primarily refining the signal, or do earlier steps contribute more heavily to the final output?\n- How does the internal state y_l change over time across the L steps?\n\nSuch analysis could take the form of:\n- Activation similarity matrices across COS steps\n- t-SNE or PCA visualizations of intermediate outputs", "limitations": "While the paper briefly acknowledges some limitations in the conclusion (such as the sequential nature of the COS module limiting parallelism when L is large) and appendix, there is no dedicated Limitations section, and several important points are under-discussed. \n\n- The authors could explicitly discuss trade-offs between the number of discrete steps (L) and inference latency, memory usage, and deployment feasibility, particularly since the COS design introduces a recurrence-like structure (see Q2).\n\n- The method assumes that the number of channels C can be reshaped into a square matrix (i.e., C = k × k). This imposes structural constraints that may limit generalizability to arbitrary architectures or channel sizes (it would be specially difficult to combine with NAS where the channel size is learned and not fixed).", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "** Strengths\n* Novel Architectural Contribution\nThe paper proposes a new module, Channelwise ODE Solver (COS), which replaces traditional pointwise convolutions in depthwise-separable CNNs. COS is implemented via a novel Direct Differentiation Euler (DDE) algorithm, enabling learnable and adaptive time steps (∆t) during training. This introduces a principled, lightweight mechanism for inter-channel communication with strong theoretical and empirical justification.\n\n* Significant Parameter Reduction\nFor MobileODEV1 and MobileODEV2, the method reduces total channelwise parameters by 71.0% and 69.2%, respectively — a notable compression rate that doesn’t sacrifice accuracy. \n\n* Strong and Diverse Empirical Results\nImage classification (CIFAR-10/100, ImageNet-R, Tiny ImageNet)\nSemantic segmentation (PASCAL VOC 2012, ADE20K)\nObject detection (BUSI, FFE)\n\nResults hold across both general-purpose datasets and challenging domain-specific benchmarks, reinforcing the generalizability of the approach.\n\n\n** Weaknesses\n* No Evaluation on Full ImageNet-1k. The model is tested on ImageNet-R and Tiny ImageNet, but not on standard ImageNet-1k, which is the primary benchmark for mobile models. This makes it difficult to judge scalability and robustness on high-resolution, real-world tasks.\n* Limited Comparison to Competing ODE Frameworks. The authors briefly contrast COS with standard ODE solvers (e.g., Runge-Kutta) in latency/FLOP terms, but do not compare to existing ODE-inspired architectures like Neural ODEs, NODE-ResNets, or recent state-space models.\n* Scalability Constraints of COS. The paper notes that COS involves sequential computation across L discrete layers, which limits parallelism and may hinder scalability.", "was_revised": true, "final_justification": "After carefully considering the authors' rebuttal, I have decided to raise my score to Accept. The authors provided clear and technically detailed responses to all major concerns. In particular, they offered a well-reasoned explanation for the absence of full ImageNet-1k experiments, citing both computational resource constraints and specific optimization challenges encountered during training. While I still consider full ImageNet-1k evaluation an important benchmark for validating scalability and practical competitiveness, I understand the limitations faced and appreciate the authors’ transparency. Additionally, the inclusion of further robustness evaluations on ImageNet-A and ImageNet-R strengthens the empirical claims, and the authors' acknowledgment of the importance of feature evolution analysis, with corresponding visualizations added to the appendix, improves the interpretability of their method. Overall, the paper introduces a novel architectural module with strong empirical results across multiple tasks and demonstrates thoughtful engagement with reviewer feedback. These factors justify my recommendation to accept the paper, despite the remaining limitation regarding full-scale ImageNet validation.", "rebuttal": "First, we would like to thank the reviewer for carefully pointing out the writing issues. We have made the necessary corrections in the manuscript.\n\n## Q1: No Evaluation on Full ImageNet-1k.\n\nThank you for pointing out the lack of experiments on the full ImageNet-1k dataset. Due to computational resource constraints and the high cost of training ultra-lightweight models at scale, we focused our evaluation across diverse data domains on three popular tasks. In line with your concern about real scalability and robustness on high-resolution, real-world tasks, we conducted experiments on ImageNet-R (diverse textures and styles) and ImageNet-A (natural adversarial examples) at a resolution of 256 × 256, as detailed in Table 8 of the Appendix. Notably, MobileODEV1 and MobileODEV2 demonstrated substantial improvements over baseline models in the ImageNet-A experiments.\n\nNevertheless, we agree that a full ImageNet-1k evaluation would further strengthen our claims. In our study of MobileODEV1 on ImageNet-1k, we observed rapid learning progress in the initial stages, which subsequently decelerated as the model approached the performance of MobileNetV1. This phenomenon arose because the t value tended to approach zero in later iterations due to the ReLU6 activation function, thereby hindering learning performance. We hypothesize that large-scale data may excessively penalize the $t$ value, impeding the learning process. Based on these observed trends, we anticipate that MobileODE will maintain its strong efficiency-accuracy tradeoff on ImageNet-1k as well, particularly if an epoch-wise optimization strategy is adopted.\n\n---\n\n## Q2: Provide a detailed analysis of how increasing the number of DDE steps (L) affects inference latency.\n\nWe appreciate the reviewer's concern regarding potential bottlenecks in real-time deployment as $L$ increases. To provide a clearer analysis, we evaluated latency at larger step intervals (every 10 steps), as shown in the table below. Latency was measured on a single NVIDIA 4090 GPU with a batch size of 16. The results indicate that inference latency increases approximately linearly with $L$, allowing for flexible adjustment in practical deployments. Notably, compared to other higher-order derivative methods listed in Table Q1 of Reviewer Tqqz, our DDE algorithm demonstrates favorable computational efficiency.\n\n\n| Model                 | Discrete Layers    | FLOPs | Latency (bs=16) |\n|-----------------------|------------|:---------------:|:---------------:|\n| MobileODEV1 | $L=10$ |7.09M  | 24.54 ms |\n| MobileODEV1| $L=20$  | 23.75M| 42.63ms|\n| MobileODEV1| $L=30$ | 40.30M| 61.08ms|\n| MobileODEV1| $L=40$ | 56.85M| 68.42ms|\n| MobileODEV1| $L=50$ | 73.39M| 73.87ms|\n\n---\n\n## Q3: Consider evaluating on additional robustness benchmarks such as ImageNet-C (corruptions), ImageNet-A (natural adversarial examples).\n\nWe conducted experiments on ImageNet-A, as detailed in Table 8 of the Appendix. The results demonstrate that MobileODEs achieve substantial improvements over the baseline models.\n\n\n---\n\n## Q4: Visualizations or analyses of how feature representations evolve across the $L$ steps.\n\nWe fully agree that such visualizations and analyses (e.g., activation similarity matrices, t-SNE/PCA of intermediate outputs) would provide important insights into how feature representations change over discrete layers and the roles of different steps.\n\nHowever, according to this year's rebuttal guidelines, we are not permitted to include PDFs, links or visualizations directly in the response. Nevertheless, we recognize the value of such analyses and have included detailed feature visualizations and analyses in the Appendix of our revised manuscript. We hope these additions will help clarify how the internal representations and states evolve across the $L$ steps, and provide a deeper understanding of the COS module's dynamics. \n\n---\n\n## Q5: Why not compare to existing ODE-inspired architectures like Neural ODEs, NODE-ResNets, or recent state-space models?\n\nWe did not directly compare with existing ODE-inspired architectures for the following main reasons. We also acknowledge that the higher-order derivative methods listed in Table Q1 of Reviewer Tqqz are more appropriate baselines in our context.\n\n1. **Different Objectives:** Our work aims to develop ultra-lightweight, mobile-friendly models, whereas Neural ODEs, NODE-ResNets, and state-space models are typically designed for higher model capacity and are not optimized for extreme efficiency or deployment on resource-constrained devices.\n\n2. **Computational Cost:** Traditional ODE-based networks often rely on the odeint package, which can incur significant computational overhead and potential precision loss. By discretizing the computation process, our approach not only reduces computational costs but also increases transparency and controllability compared to the black-box nature of standard ODE solvers."}, {"review_id": "3FLb5b8qm5", "reviewer": "Reviewer_mANM", "summary": "This paper introduces MobileODE, a lightweight network architecture designed to improve the efficiency of depthwise-separable convolutions. The core idea is to replace the inefficient pointwise convolution component with a novel, parameter-efficient module named the Channelwise ODE Solver (COS). The COS is based on a simple yet efficient direct differentiation Euler algorithm. The paper introduces two variants of COS-based blocks (COS-base and COS-inv), and evaluates their performance on various tasks. The results show a significant reduction in parameters for channel interaction while achieving competitive or even improved accuracy.", "questions": "Please solve the questions in weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The paper addresses an important problem.\n- The proposed method is evaluated comprehensively across different tasks and datasets, which helps demonstrate its generality.\n- Experimental results are promising in terms of both model size reduction and accuracy. \n\n**Weaknesses:**\n- The experimental details for the latency benchmarks are insufficient. Since the proposed method increases FLOPs but is reported to be faster, it is important to clarify the evaluation setup (e.g., CPU/GPU model, memory) and understand if the reported latency improvements are specific to one type of hardware or if they generalize to other common accelerators like GPUs, NPUs, and TPUs, which are highly optimized for standard convolutions. \n- The motivation could be made stronger. For example, providing a breakdown of the computational cost or latency contribution for depthwise and pointwise convolutions would better highlight the inefficiency of pointwise convolution and justify the design choice. Similarly, showing the latency before and after replacing pointwise convolution would help quantify the benefit of the proposed method more clearly.", "was_revised": true, "final_justification": "The authors' rebuttal addressed my initial questions but also highlighted a key limitation. The new results show a performance degradation on TPUs, indicating the proposed efficiency gains are not universal across modern accelerators. This hardware dependency limits the overall impact and practical value of the contribution. Therefore, though the paper is technically sound, it has significant limitations in its general applicability, and I would keep my original score of \"Borderline accept\".", "rebuttal": "## Q1: On Latency Benchmark Details.\n\nWe appreciate the reviewer’s suggestion to provide a more detailed description of our latency benchmarks. As shown in the table, our model consistently outperforms MobileNetV1 in latency on both CPU and GPU. On the TPU, however, it is slightly slower, which we attribute to the sequential computation pattern of the COS module. We believe this overhead can be mitigated through hardware‑specific optimizations, especially as future accelerators become better optimized for directly differentiable models such as COS.\n\nTo address the reviewer’s concern, we will include additional details on the hardware configurations and the benchmarking protocol in the revised manuscript.\n\n| Model       | Hardware Platform              | Latency (bs=16) | Memory Usage (%) |\n| ----------- | ------------------------------ | :------------------: | :---------------: |\n| MobileNetV1 | Intel(R) Xeon(R) CPU @ 2.20GHz |              166.67 ms |              9.2 |\n| MobileODEV1 | Intel(R) Xeon(R) CPU @ 2.20GHz |              148.61 ms |              5.2 |\n| MobileNetV1 | NVIDIA GeForce RTX 4090        |               33.70 ms |              3.3 |\n| MobileODEV1 | NVIDIA GeForce RTX 4090        |               24.54 ms |              4.9 |\n| MobileNetV1 | TPU v2-8                       |                3.28 ms |              0.6 |\n| MobileODEV1 | TPU v2-8                       |                8.37 ms |              0.7 |\n\n## Q2: On Motivation and Ablation Studies.\n\nThank you for your insightful feedback. In response, we further investigate the latency of depthwise convolution (dw) and pointwise convolution (pw) on a single RTX 4090 GPU to provide a more detailed comparison. The following table, which aligns with Table 1 in our paper, clearly demonstrates that the original pointwise convolution consumes a significant portion of the computational resources, while our COS module accelerates this process.\n\nFurthermore, we explore the impact of replacing pointwise convolution with COS-based blocks, particularly in the context of other channel computing modules and higher-order solvers. As detailed in Table Q1 and Q4 of Reviewer Tqqz, the results highlight how the COS module enhances both accuracy and computational efficiency.\n\n| Layer             | MobileODEV1 Latency (ms, bs=16) | MobileNetV1 Latency (ms, bs=16) |\n| ----------------- | :-------------------------------: | :------------------------: |\n| SeparableV1/s1/dw | 0.023                           | 0.030                    |\n| SeparableV1/s1/pw | 0.049                           | 0.054                    |\n| SeparableV1/s2/dw | 0.023                           | 0.029                    |\n| SeparableV1/s2/pw | 0.045                           | 0.052                    |\n| SeparableV1/s1/dw | 0.021                           | 0.027                    |\n| SeparableV1/s1/pw | 0.044                           | 0.053                    |\n| SeparableV1/s2/dw | 0.022                           | 0.025                    |\n| SeparableV1/s2/pw | 0.044                           | 0.053                    |\n| SeparableV1/s1/dw | 0.021                           | 0.028                    |\n| SeparableV1/s1/pw | 0.044                           | 0.053                    |\n| SeparableV1/s2/dw | 0.021                           | 0.024                    |\n| SeparableV1/s2/pw | 0.042                           | 0.054                    |\n| SeparableV1/s1/dw | 0.021                           | 0.028                    |\n| SeparableV1/s1/pw | 0.043                           | 0.054                    |\n| SeparableV1/s1/dw | 0.023                           | 0.024                    |\n| SeparableV1/s1/pw | 0.043                           | 0.052                    |\n| SeparableV1/s1/dw | 0.021                           | 0.025                    |\n| SeparableV1/s1/pw | 0.042                           | 0.053                    |\n| SeparableV1/s1/dw | 0.021                           | 0.023                    |\n| SeparableV1/s1/pw | 0.043                           | 0.052                    |\n| SeparableV1/s1/dw | 0.021                           | 0.023                    |\n| SeparableV1/s1/pw | 0.043                           | 0.052                    |\n| SeparableV1/s2/dw | 0.021                           | 0.023                    |\n| SeparableV1/s2/pw | 0.043                           | 0.054                    |\n| SeparableV1/s1/dw | 0.022                           | 0.027                    |\n| SeparableV1/s1/pw | 0.041                           | 0.052                    |"}, {"review_id": "bgltkywaNE", "reviewer": "Reviewer_J9oG", "summary": "This paper proposes a method for making MobileNet CNNs more lightweight by using Ordinary Differential Equations as a replacement of the pointwise convolution in depthwise seperable convolutions. The authors apply their technique to MobileNetV1 and MobileNetV2 and provide experiments for classification tasks, semantic segmentation, and objects detection mainly using #Params besides Accuracy/mIOU/mAP to back up their claim.", "questions": "- Why did the authors provide ODEV variants for MobileNetV1 and V2, but not for the more recent versions, V3 and V4? Instead, they only used these for comparison in the experiments.\n\n- Minor question regarding an inconsistency between the paper and the provided source code: In lines 144 ff. of the paper, the authors explicitely state that \"These increments are then passed through a ReLU6 activation function to ensure they remain non-negative and to limit their output range.\" However, in the provided source code (cvnets/modules/mobilenetv2.py, line 259, CustomActivation class), something slightly different seems to be done (torch.maximum(torch.tensor(self.epsilon, device=x.device), x)), with the ReLU6 part being commented out above (line 258). While this implementation is basically a slightly modified version of ReLU and should still ensure that the values in x remain non-negative (given that the default value of epsilon is set to 1/num_layers), it does not enforce an upper limit on x, as ReLU6 does, but instead leaves the values in x unbounded.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The substantial experiments indicate that the proposed COS module significantly reduces model parameters while even outperforming the AI performance achieved by the respective baselines (MobileNetV1 and V2), as well as more recent MobileNet variants (e.g. MobileNetV3, V4 and ShuffleNet). The high quality of the method, the explanation of its mathematical background, the hyperparameter ablation study of $L$, $\\delta_t$ and $e$, and the provided source code make this a significant and novel contribution.\n\nThe part of the evaluation that focuses on computing efficiency is rather brief, especially since, as the authors also state, ODE methods have a high computational complexity. At the very least, the authors could specify the type of hardware on which the latency numbers were achieved and whether they represent averaged execution times. If so, they should also provide the standard deviation and clarify whether the measurements were taken per sample or per batch.\n\nFigure 2: The visual difference between (a) and (b) is very subtle. This could be improved by introducing a colour to guide the reader to the different delta t values.\n\nMinor inconsistency: in subfigure c, \"Accuracy (%)\" is defined between 0.0 and 1.0, but this should be between 0 and 100%, as in the rest of the paper.", "was_revised": true, "final_justification": "The rebuttal I received from the authors answered my remaining questions sufficiently. Considering the rebuttals received by the other reviewers, which in my opinion answered their concerns detailed and transparantly, I will remain with my inital score of acceptance. \n\nI want to add, that while I see the argument of reviewer mANM in that the performance degradation on TPUs might indicate that the proposed efficiency gains are not immediate and universal across all accelerators, I would personally argue that this is rarly the case for any algorithm since especially in high performance computing often extremly target specific adaptions are necessary to exploit different hardware architecture as best as possible, e.g., by explicitely using specific instruction set extensions which might not ne utilize automatically. So I would tend to agree with the response of the authors in that this insufficiency on TPUs could probably be improved by some target specific optimization and is not the result of a fundamental flaw in the proposed approach.", "rebuttal": "We thank the reviewer for these insightful questions, which will help guide our future research directions. We also appreciate the reviewer’s comments on our writing, which have improved the clarity and rigor of our paper.\n\n---\n\n## Q1: Why not provide ODEV variants for MobileNetV3 and V4?\n\nMobileNetV3 and V4 are fundamentally built upon the backbone architectures of MobileNetV1 and V2. Their improvements mainly involve incremental tricks and optimizations, rather than substantial structural changes to the core architecture. This is why our comparisons focus on V1 and V2, as they represent the foundational designs of the MobileNet series.\n\nImportantly, most of the tricks introduced in V3 and V4 can also be integrated into MobileODE. Exploring the incorporation of these enhancements, as well as further improving MobileODE with techniques such as NAS (Neural Architecture Search) and knowledge distillation, is an active area of our ongoing research.\n\n---\n\n## Q2: Inconsistency between the paper and the provided source code.\n\nWe thank the reviewer for carefully pointing out the discrepancy between the manuscript and the provided code regarding the activation function applied after the increment operation. In fact, we have implemented two versions of the activation: one using ReLU6, as described in the paper, and another using `torch.maximum(epsilon, x)`. We apologize for not clearly documenting this in the README file.\n\nDuring our ongoing experiments with large step sizes $L$, we observed that enforcing non-negativity with `torch.maximum(epsilon, x)` helps prevent invalid step sizes and achieves comparable, and in some cases slightly better, numerical stability compared to ReLU6. We will update our findings in the new appendix of the manuscript and revise the code documentation to clarify this point and ensure consistency.\n\n---\n# Concerns in the weakness.\n\n## W1: Hardware specifications for latency measurements.\n\nAll latency measurements were performed on a single NVIDIA RTX 4090 GPU. The reported latency represents the average inference time per batch, with a batch size of 16.\n\nAdditionally, we explore the impact of the hardware platform, as detailed in Table Q1 of Reviewer mANM. The results show that our model consistently outperforms MobileNetV1 in latency on both CPU and GPU. Furthermore, performance can be further optimized on TPU, while also revealing additional optimization potential in MobileODEs.\n\n---\n\n## W2: Writing issues\n\nIn the revised manuscript, we have updated Figure 2 by introducing distinct colors for different $\\Delta t$ values to improve clarity.\n\nAdditionally, we have corrected the axis in subfigure (c) of Figure 4 to range from 0 to 100% in the revised version."}, {"review_id": "KkRfBPbWSV", "reviewer": "Reviewer_Tqqz", "summary": "The paper introduces MobileODE, a novel lightweight CNN architecture that replaces pointwise convolution in depthwise-separable convolution with a Channelwise ODE Solver (COS) module based on discrete neural memory ODEs (nmODEs). By modeling channel interactions via a learnable time-increment Euler discretization (DDE), MobileODE achieves 98.36% parameter reduction compared to conventional pointwise convolution. Two variants, MobileODEV1 (0.97M parameters) and MobileODEV2 (1.03M), outperform MobileNetV1/V2 and other lightweight networks (e.g., GhostNet, ShuffleNet) on image classification, object detection, and segmentation tasks while maintaining low computational overhead.", "questions": "- What the performance difference between DDE and higher-order solvers like Runge-Kutta? Table 7 only shows FLOPs and latency.\n- It is possible to apply COS modules to NLP or speech?\n- Why omit MobileNetV3/V4, MobileOne? How does COS compare to dynamic convolution or attention-based channel mixers (e.g., in EfficientFormerV2)?\n- COS reduces parameters but increases FLOPs (Tab 7). Is this favorable on edge devices? Are there any energy consumption support on edge devices?\n- Why $\\sqrt{C}$ factorization for $\\Phi$? Ablate against linear (C×k) or low-rank (C×r×r) alternatives.\n- Why not test on full ImageNet-1K? Accuracy on IN-tiny (64×64) may not reflect real-world performance.\n\nI give a borderline score currently, may change my rating once the authors answered my concerns.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n+ Novel architecture: the Discrete Derivative Estimator (DDE) with learnable time-increments yields more stable gradients and higher accuracy than fixed-step ODE solvers, while the Channel-wise ODE Solver (COS) replaces 1 × 1 point-wise convolutions, dramatically cutting channel-interaction parameters relative to MobileNet V1/V2.\n+ Consistently strong empirical results across image classification, object detection, and segmentation.\n+ The ODE-based variants match or surpass MobileNet latency despite using far fewer parameters.\n\nWeaknesses\n- Performance gains taper off at large expansion factors (e ≥ 9 in Table 6), hinting that the bilinear interpolation used for channel reshaping may bottleneck scalability.\n- COS updates channels sequentially (Algorithm 1), which limits parallelism; for long ODE trajectories (large L) this can increase inference latency.\n- The “extra-lightweight” claim is overstated: ShuffleNet V1 (1.1 M parameters) is still smaller than MobileODE-V1 (1.14 M) as shown in Table 3.", "was_revised": true, "final_justification": "Increasing score from 3=>4 based on rebuttal, I think this paper is acceptable for the main conference.", "rebuttal": "We thank the reviewer for the valuable feedback and insightful questions. We appreciate the recognition of our contributions and the constructive suggestions, which have helped us further improve the quality and clarity of our work. Below, we address each concern in detail.\n\n---\n\n## Q1: What is the performance difference between DDE and higher-order solvers like Runge-Kutta?\n\nThe DDE algorithm is currently based on discretizing nmODE with the Euler method. Technically, it also supports all higher-order solvers. We conducted further experiments on MobileODEV1 with other higher-order solvers on CIFAR-10, as shown in the table below:\n\n| Method                            | ACC    | FLOPs  | Latency (bs=16)  |\n|------------------------------------|:------:|:----------:|:------------:|\n| MobileODEV1 | 93.56% | 7.09 M  | 24.54 ms  |\n| MobileODEV1 w/ Runge-Kutta | 91.20% | 21.51 M   | 241.46 ms |\n| MobileODEV1 w/ Adams Bashforth | 90.66% | 14.89 M  | 158.29 ms  |\n| MobileODEV1 w/ Adams-Moulton | 91.17%  | 8.27 M | 104.32 ms |\n| MobileODEV1 w/ Itô–Taylor | 87.00%  |  11.58 M | 130.44 ms |\n\nWhile higher-order solvers like Runge-Kutta can theoretically improve accuracy, our preliminary experiments show that, in the context of lightweight discrete ODE models, their additional computational overhead does not translate to significant accuracy gains compared to DDE. It is very important for us to include these results in Table 7 in the revision.\n\n---\n\n## Q2: Is it possible to apply COS modules to NLP or speech?\n\nExcellent question! The COS module is a general mechanism designed for modeling interactions among feature channels. At its core, it functions similarly to an RNN block, where $y^l$ can be interpreted as the hidden state at time step $l$. This design makes COS inherently adaptable to non-vision domains such as NLP and speech.\n\nFor instance, in Transformer-based models, COS could potentially be leveraged to capture token-wise or feature-wise dependencies, enhancing the model’s ability to represent complex relationships within sequences. We also encourage exploring the use of COS modules in various sequence modeling tasks beyond vision, as their flexible structure may offer benefits across a wide range of applications.\n\nAdapting COS to these domains would require redefining the dynamics over ODE or time steps, which we consider a promising direction for future work.\n\n---\n\n## Q3: Why omit MobileNetV3/V4, MobileOne?\n\nWe define MobileNetV3/V4 and MobileOne as our baselines across three tasks. For the reason why ODEV variants are not provided, please refer to Q1 of Reviewer J9oG.\n\n---\n\n## Q4: How does COS compare to dynamic convolution or attention-based channel mixers (e.g., in EfficientFormerV2)?\n\nWe compare COS to dynamic convolution and attention-based channel mixers in EfficientFormerV2 on CIFAR-10, as shown in the following table. DY-MobileNetV1 denotes replacing COS modules with dynamic convolutions, $K$ means convolution kernel number. SA-MobileNetV1 denotes replacing COS modules with the attention downsampling proposed in EfficientFormerV2 for mobile devices.\n\n| Method             | ACC    | Param. | FLOPs | Latency (bs=16) |\n|--------------------|:------:|:------:|:----------:|:------------:|\n| MobileODEV1        | 93.56% | 1.14 M   |7.09 M  | 24.54 ms |\n| DY-MobileNetV1 (K=2) | 90.63%  | 6.67 M    |  2.28M | 76.84 ms  |\n| DY-MobileNetV1 (K=4) | 90.29%  | 12.08 M    | 2.41M |  78.12 ms |\n| SA-MobileNetV1     | 93.52%  | 6.51 M    |  8.14G | 167.09 ms |\n\n---\n\n## Q5: COS reduces parameters but increases FLOPs (Tab 7). Is this favorable on edge devices? Are there any energy consumption measurements on edge devices?\n\nIn Appendix 6.7, our practical deployment shows that this trade-off is favorable for edge devices. We have implemented our lightweight MobileODE-based breast screening system on a Lenovo Legion R9000P laptop (NVIDIA GeForce RTX 4060 GPU with 8GB VRAM, AMD Ryzen 9 7945HX CPU, 15.3GiB DDR5 RAM), running Ubuntu 20.04.4 LTS. During operation, GPU memory usage was 1708/8188 MiB and GPU utilization was only 19%, indicating low and stable resource consumption.\n\nAlthough we have not directly measured energy consumption, the low hardware usage suggests that the increased FLOPs do not adversely affect deployment efficiency on edge platforms.\n\n---\n\n## Q6: Why $\\sqrt{C}$ factorization for $\\Phi$? Ablate against linear (C×k) or low-rank (C×r×r) alternatives.\n\nThank you for your question regarding the use of $\\sqrt{C} × \\sqrt{C}$ reshaping in our design. We would like to clarify that our approach does not involve matrix factorization or low-rank decomposition of a parameterized transformation matrix $\\Phi$. Specifically, we reshape the 1D channel feature vector of size $C$ into a 2D matrix of size $\\sqrt{C} × \\sqrt{C}$ solely for the channel-view of applying subsequent certain operations (such as batch normalization and bilinear interpolation in MobileODEv2).\n\nTherefore, the comparison with linear (C×k) or low-rank (C×r×r) alternatives is not directly applicable. We will clarify this design choice and its motivation in the revised manuscript to avoid confusion.\n\n---\n\n## Q7: Why not test on full ImageNet-1K? Accuracy on IN-tiny (64×64) may not reflect real-world performance.\n\nPlease refer to Q1 of Reviewer MTGp.\n\n---\n\n# Concerns in the weakness.\n\n## W1: The bilinear interpolation used for channel reshaping may bottleneck scalability.\n\nThank you for highlighting this issue. We agree that as the expansion factor $e$ increases, bilinear interpolation may lead to information loss between channels and diminishing performance gains. The ablation study on $e$ in our work is intended to demonstrate that simply increasing $e$ for performance improvement should not be the main focus of MobileODEV2, which aligns with the reviewer's observation.\n\n## W2: COS updates channels sequentially (Algorithm 1), which limits parallelism; for long ODE trajectories (large L) this can increase inference latency.\n\nThe sequential channel update in COS is motivated by the explicit Euler discretization in ODE solvers, which is designed to capture dependencies across channels. While this sequential nature can limit full parallelism—potentially increasing inference latency for long ODE trajectories (large $L$)—our experiments show that the relationship between $L$ and latency is approximately linear, as demonstrated in Table Q2 for Reviewer MTGp. Thanks to the lightweight design of our architecture and the significant reduction in overall model parameters, the actual increase in inference time remains modest in our benchmarks. Moreover, we anticipate that future advances in hardware and software (e.g., pipelined or block-parallel COS updates) could further mitigate this limitation, offering even greater efficiency.\n\n## W3: The \"extra-lightweight\" claim is overstated: ShuffleNet V1 (1.1 M parameters) is still smaller than MobileODE-V1 (1.14 M) as shown in Table 3.\n\nWe acknowledge that, as shown in Table 3, ShuffleNet V1 (1.1M parameters) has a slightly lower parameter count than MobileODE-V1 (1.14M). However, our “extra-lightweight” claim is primarily based on the **flexibility** of the MobileODE architecture with respect to the $L$ setting. As demonstrated in the table below, MobileODE can be scaled down to just 0.885M parameters when $L=3$, while achieving performance closely matching that of ShuffleNet V1 (1.0×) on CIFAR-10.\n\n| Model                 | Discrete Layers    | Param.| Top-1 Acc (%) |\n|-----------------------|:------------:|:---------------:|:---------------:|\n| ShuffleNet V1 |\\ | 0.93 M| 92.29|\n| MobileODEV1 | $L=3$ | 0.885 M |92.24 |\n| MobileODEV1| $L=5$ | 0.893 M| 92.52 |\n| MobileODEV1| $L=7$ |0.902 M| 93.16 |\n| MobileODEV1| $L=10$ |0.94 M |93.56 |\n\nTherefore, MobileODE offers not only competitive parameter efficiency but also **scalable flexibility**—allowing it to achieve even smaller sizes without significant performance loss. This adaptability makes MobileODE particularly suitable for resource-constrained scenarios and further supports our “extra-lightweight” claim."}]

Author rebuttal:

Meta-review: Summary of the Paper:
The paper introduces a lightweight network architecture aimed at improving the efficiency of depthwise-separable convolution by replacing the inefficient pointwise convolution component with a  parameter-efficient  Channelwise ODE Solver (COS). The paper proposed two variants of the model: MobileODE-V1 (0.97M parameters) and MobileODE-V2 (1.03M parameters).  These models outperform MobileNetV1/V2 and other lightweight networks (e.g., GhostNet, ShuffleNet) on image classification, object detection, and segmentation tasks, while maintaining low computational overhead.

The reviewers highlighted several strengths of the paper: 
1. Introduction of the novel Channelwise ODE Solver (COS) module to replace pointwise convolutions in depthwise-separable CNNs.
2. Significant parameter reduction without compromising accuracy.
3. Strong experimental results across image classification (CIFAR-10/100, ImageNet-R, Tiny ImageNet), semantic segmentation (PASCAL VOC 2012, ADE20K), and object detection.
4. The paper addresses an important problem in lightweight and mobile-friendly architectures.
5. Novel architecture with promising results in terms of both model size reduction and accuracy.
6. High technical quality, including mathematical formulation, hyperparameter ablation studies, and publicly available source code.
7. The rebuttal effectively addressed latency, memory usage, and additional ablation study concerns.


The following weaknesses were raised by the reviewers and are shared by the Area Chair:
1. Lack of evaluation on the full ImageNet-1k dataset.
2. Limited comparisons with other ODE-inspired frameworks and architectures (e.g., Neural ODEs, NODE-ResNets, or state-space models). It would be valuable to adapt and evaluate such models under similar lightweight network settings.
3. Performance degradation on TPUs, suggesting efficiency gains are hardware-dependent and may not generalize well across modern accelerators. This limits the practical impact.
4. COS updates channels sequentially (Algorithm 1), limiting parallelism. For long ODE trajectories (large L), inference latency can increase.
5. The claim of being “extra-lightweight” is overstated; for example, ShuffleNetV1 (1.1M parameters) remains smaller than MobileODE-V1 (1.14M) (Table 3).
5. Lack of clarity on why ODEV variants were proposed only for MobileNetV1/V2 and not for more recent MobileNet versions (V3/V4), which were only used as baselines.
6. Inconsistencies between the paper and the released source code. The authors have promised to resolve these issues in the final draft.

Decision: Reviewer Ratings and Discussions. 
Overall, the paper received two borderline accept and two accept ratings. The reviewers acknowledged that most of their concerns were addressed in the rebuttal. The Area Chair agrees with the reviewers and recommends acceptance. The authors are strongly encouraged to address the remaining concerns, particularly by incorporating ImageNet-1k results, resolving inconsistencies between the paper and source code, and providing ODE variants for more recent MobileNet architectures where appropriate. The authors are expected to include all additional experimental results and explanations provided in the rebuttal to the final draft. Additionally, it is expected that the authors will open-source their code, as indicated in their submission.
Decision: Accept (poster)