Meta-Exploiting Frequency Prior for Cross-Domain Few-Shot Learning
Authors: Fei Zhou
Peng Wang
Lei Zhang
Zhenghua Chen
Wei Wei
Chen Ding
Guosheng Lin
Yanning Zhang
Venue: NeurIPS 2024 poster (2024)
Keywords: Meta-learning Few-shot learning Cross-domain few-shot learning
Primary area: machine_vision
TL;DR: We introduce a novel framework, which is crafted to comprehensively exploit the cross-domain transferable image prior.

Abstract: Meta-learning offers a promising avenue for few-shot learning (FSL), enabling models to glean a generalizable feature embedding through episodic training on synthetic FSL tasks in a source domain. Yet, in practical scenarios where the target task diverges from that in the source domain, meta-learning based method is susceptible to over-fitting. To overcome this, we introduce a novel framework, Meta-Exploiting Frequency Prior for Cross-Domain Few-Shot Learning, which is crafted to comprehensively exploit the cross-domain transferable image prior that each image can be decomposed into complementary low-frequency content details and high-frequency robust structural characteristics. Motivated by this insight, we propose to decompose each query image into its high-frequency and low-frequency components, and parallel incorporate them into the feature embedding network to enhance the final category prediction. More importantly, we introduce a feature reconstruction prior and a prediction consistency prior to separately encourage the consistency of the intermediate feature as well as the final category prediction between the original query image and its decomposed frequency components. This allows for collectively guiding the network's meta-learning process with the aim of learning generalizable image feature embeddings, while not introducing any extra computational cost in the inference phase. Our framework establishes new state-of-the-art results on multiple cross-domain few-shot learning benchmarks.

Meta-Exploiting Frequency Prior for Cross-Domain Few-Shot Learning
Fei Zhou'
Peng Wang² Lei Zhang! Zhenghua Chen
Wei Wei!
Chen Ding' Guosheng Lin Yanning Zhang'
School of Computer Science, Northwestern Polytechnical University
2 School of Computer Science and Engineering, University of Electronic Science and Technology of China
Institute for Infocomm Research, and Centre for Frontier Al Research, A*STAR
School of Computer Science, Xi an University of Posts & Telecommunications
5 School of Computer Science and Engineering, Nanyang Technological University
zhoufei @mail wwwpaaii........mmem.. www.unueeea... en vangpeng86198gmai ccom
chen08320e.0 ntt.. edu. sg gelingntu. edu. dingchen@xupt. edu. edu.
hwwp:haangeii,eiiiiinnn (naiiieiiippyyyzzannnnn0mno ynzhang)Onupu www.gg.uu.uuuuuuuuu. edu.
Abstract
Meta-learning offers a promising avenue for few-shot learning (FSL), enabling models to glean a generalizable feature embedding through episodic training on synthetic FSL tasks in source domain. Yet, in practical scenarios where the target task diverges from that in the source domain, meta-learning based method is susceptible over-fitting To overcome this, we introduce novel framework, Mcta-Exploiting Frequency Prior for Coss--omminn Few-Shot Learning, which is crafted to comprehensively exploit the cross-domain transferable image prior that each image can be decomposed into complementary low-frequency content details and frebffrreyecyy robust structural characteristics. Motivated by this insight, we propose to decompose each query image into its high-frequeng and low-frequency components, and parallel incorporate them into feature embedding network enhance the final category prediction. More importantly, we introduce feature reconstruction prior and prediction consistency prior to separately encourage the consistency of the intermediate feature well the final category prediction between the original query image and its decomposed frequency components. This allows for collectively guiding the network's 's meta- meta-learning process with the aim learning generalizable image feature embeddings, while not introducing any extra computational cost in the inference phase. Our framework establishes new state-of- the-art art results on multiple cross-domain few-shot learning benchmarks.
Introduction
Meta-learning Finn et al. [2017] Lee et al. [2019], Rusu et al. [2019]. Zhmoginov et al. [022]]
Zhang al. (2033 Baik et al. 2020 represents potent paradigm within the domain of FSL Vinyals
et al. 2016 Snell et al. [2017] Huang et al. [202), Zhang and Huang 2022 Chen et al. [2021]
This paradigm harnesses feature embedding network to capture task agnostii meta-
facilitating generalization to novel tasks. To this end, meta-learning systematically samples sequence
of FSL episodes in the source domain supervisedly enforcing learn effective feature embedding network that assimilating cross-task transferable essentials and generalize well to novel target tasks.
Due to its exceptional learning-to-learn capabilities, meta-learning has established itself as the de facto approach for the development of effective few-shot solvers Vinyals et al. [2016), Snell et al.
Corresponding author.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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2017 Huang et al. [2022] Zhang and Huang 2022 Finn et al. 201 7 Lee et al. 2019 Rusu et al.
2019
Zhmoginov al. 2022]. Zhang et al. [002] Baik et al. 2020
However, in practical cross-domain scenarios where the target task exhibits a noticeable distribution discrepancy from that in the source domain, meta-learning based methods susceptible to over- fitting. This phenomenon can be attributed to two main reasons. Firstly, tasks randomly sampled in source domain often come from one or several fixed patterns, and thus the continual switching of episodes training may cause the model to over-fit on some task-specific priors. For instance, in tasks involving the discrimination between tigers and giraffes, meta-learning methods may compel the model to emphasize appearance outlines, while in tasks focused on finegrrined bird identification, models tend prioritize local discriminative textures. Yet, these task specific priors prove challenging to transfer across different tasks Lyu et al.] [202T] [hou et al. [2023]. Secondly, the iterative episodic training in the source domain can result the model over-fitting to semantic prior properties specific to that domain. For example, source domains comprised of natural scene images often exhibit obvious semantic priors, whereas specialized target domains like medical image analysis or remote sensing may lack clear semantic concepts. This overall domain bias also hampers the model's cross-domain generalization. For all these challenges, the underlying evil lies in the absence of cross-domain invariant priors to guide meta-learning in the source domain.
To address this challenge, we introduce a novel framework, Meta- Eett--xploi Frequency Prior for Few-Shot Learning. Inspired by classical image transform theories (Fourier Nuss baumer and Nussbaumer [1822] or wavelet Zhang and Zhang [2019], where each image can be decomposed into low-frequency content details and sighefrre structural characteristics, despite which domain it belongs to, we attempt to cast such a cross-domain invariant image property into appropriate frequency priors and utilize them to guide the meta-learning in source domain. Following this idea, we decompose each query image into a high-fr feehfrryyency and a low-frequency parts, and feed each into the feature embedding network for final category prediction, mirroring the process applied to the original query image. These allows for the independent feature learning in both spatial and frequency domains. In addition, the low- wwwfrequency and tighffrequency branch will separately exploit the complementary image content and structures for feature enhancement, which are often concealed in the spatial domain of original query image. More importantly, further develop two frequency priors, namely a feature reconstruction prior and a prediction consistency prior, which separately forces the original query image and its decomposed frequency components produce the consistent intermediate feature representation as well as the final category prediction. In a specific, the feature reconstruction prior requires to reconstruct the feature of original image through fusing the features of both decomposed frequency parts using a deep projection network. The prediction consistency prior aims to minimize the separate Kullback-Leibler divergence between the prediction scores produced by the original query image and its each frequency component. By doing these, meta-learning in the source domain can be appropriately regularized and produce the exceptional cross-domain generalizable feature embeddings. Moreover, such frequency priors only perform in the meta-learning phase without introducing any extra computational cost inference. Through series of rigorous experiments, our framework establishes itself as a front-runner, achieving statc-of-the-art results across multiple cross domain FSL. benchmarks. Additionally, our method exhibits significant efficiency advantages.
The primary contributions of this study can be summarized follows:
We present a novel insightful meta-learning framework that exploits cross-domain invariant frequency priors to alleviate the over-fitting problems of classic meta-learning in cross- domain FSL tasks.
We propose two frequency prior, namely prediction consistency prior and feature reconstruction prior, to collectively guide the meta-learning procedure.
We achieve state-of-the-art results multiple cross-domain FSL benchmarks.
2 Methodology
Problem formulation. Cross-Domain Few-Shot Learning (CD-FSL) aims to transfer the knowl- edge acquired by model in the source domain D, to perform few-shot tasks in the target domain D,, It is noteworthy that the categories in D, differ from those in the source domain. Each task T involves the random sampling of N categories, with K samples and M samples randomly selected

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Image D Decompositoon Module
Ptior Regui enzation Netwokk
Raw
Low www-freueency bmanch
Main branch
Hight figh-frequency branch
Caclent lask
Raw task
Structure
task
fg
EMA
Support
Query
FFT
Feature recostruct
Feature recossruut
Irequeacy
High frequeacy
CTO|S)
cr(O)s)
Support
Query
Support
Quety
Prediction
Prediction
Content taok
Structure lask
aiggmeent.
aligmment
Figure I: Framework of the proposed method. In this work, we present an insightful meta-learning framework that exploits cross dossin invariant frequency priors to alleviate the over-fitting problems of classic meta-learning in cross-domald FSL tasks. Our method consists of an Image Decomposition Module (IDM) and Prior Regularization Meta-Network (PRM-Net). Among them, IDM aim explicitly decomposing every image in few-shot task into low- and high-frequency components. PRM- Net develops prediction consistency prior and feature reconstruction prior to jointly regularize the feature embedding network during meta-learning aiming to learn generalizable image feature embeddings. Once the model trained, only the main branch is retained for meta-testing on target domains.
from each category to constitute the support set Ts and the query set To. respectively. The support set Ts is employed for constructing task-specific classifier, while the query TQ is used assess the classification accuracy for that specific task. To emulate the meta-testing process, methods based meta-learning typically sample series of few-shot tasks from the source domain for training.
Overview. In this study, we introduce sophisticated meta-learning framework that leverages cross-domain invariant frequency priors to mitigate the over-fitting problems of classic meta-learning in cross-domain FSL tasks. As illustrated in Fig. our method comprises two key components: the Image Decomposition Module (IDM) and the Prior Regularization Meta-Networkk (PRM-Net). The IDM is designed to explicitly decompose each image within a few-shot task into its low- and high-frequency components using Fast Fourier Transform (FFT) Nussbaumer and Nussbaumeri (1822) PRM-Net key component responsible for introducing prediction consistency prior and feature reconstruction prior. PRM-Net organized into three branches: the main branch, the low- wwwfrrquency content branch, and the high- frequencccc structure branch. In each branch, all images undergo feature extraction through the embedding network. Subsequently, a task-specific classifier is constructed predict the query set. Two frequency priors, namely the prediction
based the support consistency prior and the feature reconstruction prior, are proposed to collectively guide the network's meta-learning process with the aim of learning generalizable image feature embeddings. The IDM and PRM-Net work collaboratively to provide a robust meta-learning framework, aiming to enhance cross-domain generalization by explicitly considering image decomposition and introducing effective regularization during the meta-leannn meta-learning process. The subsequent sections will provide detailed description of each module.
2.1 Image Decomposition Module
In the realm of signal processing, classical image transform theory Nussbaumer and Nussbaumer (1822) [Zhang and Zhang (2019) posits that every image can decomposed into oreeueuyyncyy content and high-frequency structure, irrespective of its domain. Therefore, within the Image Decom-

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position Module, we adhere to this theory and employ Fast Fourier Transform (FFT) Nussbaumer and Nussbaumer [1982] to explicitly decompose each image from the few-shot task into low- frequency content image and high-frequency structure image. Specifically, for an image in T, the initial step involves decomposing it into the frequency domain:
(x))
where F. represents FFT, falm and fa represent the low-frequency and high-frequency compo- nents of in the frequency domain respectively. Following this decomposition, transform these components back into the image space using the inverse FFT:
Low F
(2)
high
where F-1 represents inverse transform FFT, nloo and high represent the decomposed low- frequency content image and high-freet freefrreyy structure image respectively. Similarly, apply the same decomposition process to each image in T to obtain the corresponding cow-frequency content task Tlow and high-frequency structure task Thigh.
2.2 Prior Regularization Meta-Network
The proposed Prior Regularization Meta-Network is designed to leverage cross-domain invariant frequency priors, addressing meta-learning over-fitting in the source domain. To achieve this objective, we introduce a three-branch, meta-learning network, dedicated to processing the raw few-shot task T, the low-frequu wwwfrreuency task Tlow, and the high-frequency task Thigh respectively. Significantly, propose prediction consistency prior and feature reconstruction prior to jointly regularize the feature embedding network during meta-learning. This approach empowers the learning process, facilitating the acquisition of a cross-domain generalizable feature embedding. Upon completing the meta-training the source domain, we discard the high-freyuency and low-frequency branches, retaining only the main branch for cross-domain validation.
The main branch. As depicted in Fig. 1 the main branch includes feature embedding network and a task-specific classifier. For a few-shot task T, the main branch first feeds each image into the feature embedding network to obtain features, and then utilizes the support set Ts to build prototype classifier Snell et al. 2017]:
1
Σ So (In,));
Gn = K
where Cn represents the prototype of the n-th category, Fn,k represents the k-th support sample of the n--hh category, fo represents the feature embedding network. Finally, we utilize the prototype classifier to make prediction on the query set:
exp (-d (fe (x)) Pay = Σ,, exp (-d (fo (zz) c)
n E [1,
where zy E To. Pz, represents the prediction scores of y. (-) represents the Euclidean distance. For the query image Ty. the category corresponding to the highest score in Pz, used as the predicted label Vz,- Subsequently, we calculate the cross-entropy loss between the predicted label üz, and the ground truth Vzy as:
C H0 Vaz)
where H (.) denotes the cross-entropy loss function.
The high- or low-frequency branch. As illustrated in Fig. 1 both the high-frequency branch and the lowffreyyency branch maintain consistency with the architecture of the main branch. In practice, we input the decomposed high-frequency task Thigh and low-frequency task Tlow into these two branches, respectively, to obtain the corresponding features and prediction scores for the query set. Mathematically, the prediction scores for the query image z; in the high- branch and the low- low-frequency branch are denoted plow and phishh respectively.

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Frequency prior regularization. In this work, we posit that the over-fitting problem is the core crux that limits the cross-domain generalization of meta-learning model. To this end, we resort to cross-domain invariant priors to regularize meta-learning in the source domain. Motivated by this perspective, we propose a prediction consistency prior and feature reconstruction prior to jointly regularize the feature embedding network during meta-learning using high-low frequency information obtained from image decomposition. Specifically, the prediction consistency prior aims to minimize the separate Kullback-Leible divergence between the prediction scores produced by the original query image and its each frequency component. Formally, for a query image Ij, we align its high-frequency prediction distribution phigh and low-frequency prediction distribution Plow with the original distribution Pa5 respectively:
Calign DKL (pIguI(Pa,) DKL.
(Phish [1P,,)
(6)
where DE (.) is the Kullback-Leible divergence loss function. The rationale behind this approach is twofold. Firstly, through explicit decomposition-alignneen
compel the model to attend to both low-frequency content and high-frequency structure. Despite their distinct nature, these two types of features synergistically contribute and complement each other in the challenge of cross-domain generalization. Secondly, establishing prediction consistency between high-low frequency and the original one is different domains.
This consistency aids the model in generalizing effectively across
The feature reconstruction prior aims at reconstructing the original features utilizing eyyfrrquency and high-frequenee information the latent space, which promotes the model learn comprehensive representations. Specifically, we first project embedding features into the low-dimensional latent space, and then utilize the information retained by high- and low-frequency to reconstruct the original features:
Fr; 9n (So (zi)),
2z. = In (fo (a!ow)) + In fro (2 (snhigh)
(8)
where fo and fo are the feature embedding network of the low-frequency branch and the high- frequency branch respectively, 9, is a projector composed of one layer full connected neural network (512x256), êz, is the reconstructed feature. Then, the reconstruction loss is calculated as:
precon
MSE (Ez4) Zx;))
where MSE (-) represents the mean square error loss function.
Meta-training. Based on the description provided above, for a few-shot task T, the total loss can be formulated as:
1 Σ 1EE, C = (Tal
MT (4%
Calign)
Σ
rrecon
(10)
ITi T:
Following this, we compute the gradient based the total loss L to update both the main branch 0 and the projector While one straightforward approach is to share parameters between the high-low frequency branches and the main branch, this might lead the feature embedding network to primarily focus on common features among the three, potentially causing distinctive features in the low-frequency branches to be overlooked. To address this concern and extract more distinctive features, we opt for an explicit design where three separate feature embedding networks are employed without parameter sharing. However, updating the high-frequency and uw-frequency branches through gradient a solution, we update the sighfrreuency branch ip and low-frequency branch @ as the Exponential Moving Average (EMA) of the main branch 0 during meta- meta-training:
can introduce additional computational overhead. As
+ miΦ + (1 m1) A & - m2p (1 m2)
(11)
where my and my are momentum hyper-parameters. We describe the entire meta-training process in detail in [
5

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Algorithm 1: Meta-training algorithm of the proposed method.
Input:
Source domain D,, main branch fo, low-frequency branch Sa, high-freyuency branch fip projector 4n
while not converged do
1. Sample a few-shot task = (Ts, To) from Da; for each image 2; in T do
Decompose vi to obtain high-frequency image xy high and low-frequency image a!ow:
3. Utilize fe. f and fo to extract feature for I; high and nlow respectively:
4. Calculate the reconstruction loss 22 Creeon according Eq. 7 Eq. and Eq. 9
5. Build prototype classifier for each branch separately based on the Ts in each branch; for each query image 2; in Tq do
6. Calculate the prediction scores Pay. Phiig and Pla according to Eq.
Calculate the cross-entropy loss Lay and alignment loss Laj according to Eq. and
Eq. [rrespcctivly
8. Calculate the total loss L according to Eq. 10 and update 0 and ny via gradient
backpropagation:
9. Update & and & according to Eq.
Output: The main branch fa.
Cross-domain evaluation. Once the model is trained, only the main branch fe is retained for meta-testing on target domains. The proposed method is designed to enable the model to learn cross-domain transferable knowledge during the training phase, achieving effective generalization without relying task-level feature extractor fine-tuning during meta-testing, Specifically, for each meta-testing task in the target domain, the main branch utilized to extract features. Subsequently, the support set Ts is employed to construct task-specific classifier for inference on the query set To- It's important to note that the proposed method does not require image decomposition during the meta-testing phase, thereby avoiding additional computational overhead.
3 Experimental Analysis
In this section, we begin by providing a detailed description of the experimental configuration, encompassing pre-training, meta-training, and meta-testing. Following that, we analyze the advan- tages of the proposed method in comparison with state-of-the-ar methods. Lastly, we delve into a comprehensive ablation study to further investigate the effectiveness of our approach. Due to space limitations, we put more experiments and analyses in the appendix.
3.1
Experimental details
Source domain and target domains. We focus the most challenging scenario of single-source domain Pross-Domain Few-Shot Learning (CD-FSL). Following the established setup Guo et al. Li et al. [2022] Zhou al. 2023). J, employ the base classes of the mini-ImageNet Vinyals et al. 2016 as the source domain dataset. Our model is evaluated across multiple target domains, encompassing natural image domains (CUB, Cars, Places, Plantae), remote sensing domain (Eu- roSAT), agricultural domain (CropDisease), and medical domains (ChestX, ISIC). These datasets are widely recognized in the field of cross- doos--domain few-shot learning. Additional details about each dataset can be found in Guo et al. 2020) Tseng et al. [2019].
2020
Pre-training and meta-training. In the context of CD-FSL, pre- preiiiain is common technique Li et al. (2022), Zhou et al. (2023). Hu and Ma [2022). Wang and Deng [2021] aiming to provide feature initialization for meta-training. Specifically. it involves supervised classification on the source domain through batch training. Following Li et al. 2202) Zhou et al. [2023). J. Hu and Ma (022), we utilize ResNet-10 as the feature embedding network and a one-layer fully connected neural network as the classifier. The total number of pre-training epochs is set to 400. After pre-training, only the feature embedding network is retained as the feature extractor for meta-training. During the meta mnta-training phase, employ Adam the optimizer and conduct meta-training for 50 epochs with

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Table 1: Comparison with state-of-the art methods 5-way 1-shot cross-domain FSL. Average classification accuracies (%) are provided. stands for exploiting the full data FSL task. means that the feature embedding network needs be fine-tuned (Ft) each target domain tasks. The best results are in bold.
Methods
Ft
CUB
Cars
Places
Plantae
Chest
ISIC
EuroSAT
CropDisease
Ave.
MatchingNel Net Vinyals el
2016
35.89
30.77
49.86
32.70
20.91
29.46
50.67
48.47
37.34
RelationNet Nest Sune et
2018
41.27
30.09
48.16
31.23
21.95
30.53
49.08
53.58
38.24
GNN Garcia and Bruna
2018
X
44.40
31.72
52.42
33.60
21.94
30.14
54,61
59.19
41.00
FWT Tseng
X
45.50
32.25
53.44
32.56
22.00
30.22
55.53
60.74
LRPiSun 2021
X
48.29
32.78
54.83
30.94
54,99
59.23
42.58
ATA Wanz Dens
2021
X
45,00
33.61
53.57
34.42
22.10
33.21
61.35
67.47
43.84
AFA Hu and Ma
M12
46.86
34.25
54.04
36,76
22.92
33.21
63.12
67.6 67.61
44.85
LDP net Zhou al.
2023
49.82
35.51
53.82
39.84
23.01
33.97
65.11
69.64
46.34
Ours
51.55
37.04
52.06
41.55
22.82
33,98
64.31
71.47
46.85
ATA
Wang and Deng
2021
X
50.26
34.18
$7.03
39.83
21.67
34.70
65,94
77.82
47.68
ARA
Huland Ma
2022
X
50.85
38.43
60.29
40.27
21.69
34.25
66.17
72.44
48.05
RDCT
X
47.77
38.74
32.29
GNNewave-
SAN
2022
X
50.25
33.55
57.75
40.71
22.93
33.35
69.64
47.37
LDP-net
Zhou al
2023
55.94
37.44
62.21
41.04
22.21
33,44
73.25
81.24
50.85
StyleAdv
Fu al.
2023
48.49
34.64
58.58
41.13
22.64
33.96
70.94
74.13
48.06
Ours!
39.48
38.86
62,90
44.06
22.48
34.28
69.56
84.01
$1.95
Fine Fineinuuing" Gin et al.
2020
43.53
35.12
50.57
38.77
22.13
34.60
66.17
73.43
45.54
ATA (Wane and Dens 2021
51.89
38.07
$7.26
40.75
22.45
35.55
70.84
82.47
49.91
RDC
50.09
36.28
70.51
learning rate of 0.001. In each epoch, we randomly sample 100 meta-tasks, where each meta-task consists of way 5-shot 15-query. Data augmentation techniques such as "Resize," "ImageJitter; and "RandomHorizontalFlin are applied during meta-traie meta-training. We set hyper-parameters m1=0.997 and m==0.999. All experiments were performed on 4090 GPU. Our experimental platform is 4090 GPU. Further details and verification of hyper-parameters can be found in the supplementary material.
Meta-testing. Upon completion meta-training, we directly employ the learned model for meta- testing across all target domains. Specifically, for each target domain, randomly sample 600 meta-tasks for testing. We consider two challenging meta-tasks: a 5-way 1-shot 15-query task and a 5-way 5-shot 15-query task. In each meta-task task, we learn Logistic Regression classifier using the support set and then conduct inference on the query set.
3.2 Comparison with state-of-the-an methods
Methods. In the realm of single-source domain CD-FSL, the state-of-the-at methods primarily include LDP-net Zhou et [2023]. AtyleAdv Fu et [2023), ENN+wave-SAAN Fu al. [2022 RDC et al. [2022]. AFA Hu and Ma [2022]. ATA Wang and Deng [201]) LRP et al. 2021] FWT Tseng al. 2019,, and Fine-tuning Guo al. [2020]. These methods can be categorized into three types: direct inference, using query samples to assist inference (marked with t), and fine-tuning-based inference (marked with *).
Among these methods, direct inference (e.g., I.P--nt, MatchingNet, AFA, ATA) is the most straight- forward manifestation of model generalization. It handles each test task without fine-tuning the feature embedding network, meeting practical application requirements. Using query samples to assist inference (c.g., RDC!, LDP-net AFAÍ, ATA!) also common experimental setting. is noteworthy that manner. The main reason is that both GNN+wave-SAn (GNN)Garcia and Bruna 2018 as a classifier. GNN treats each sample in the few-shot task as node of the graph, and the associations between different samples as edges for reasoning, akin to label propagationi_in et al. [2019]. This approach implicitly leverages unsupervised query samples when the number query samples in the few-shot task exceeds one. The original GNN paper Garcia and Bruna 2018 tested single query image for each few-shot task, avoiding this issue. For fair
wave-SANN and StyleAdv also leverage query samples in an unsupervised and StyleAdy use Graph Neural Network
7

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Table 2: Comparison with state-of-the-an methods on 5-way 5-shot cross-domain FSL. Average classification accuracies (%) are provided. stands for exploiting the full data of FSL task. means that the feature embedding network needs to be fine-tuned (Ft) on each target domain tasks. The best results are in bold.
Methods
CUB
Plantae
Chest
EuroSAT
CropDisease
MatchingNet Vinvals Vinyaal
2016
X
51.37
38.99
63.16
46.53
22.40
36.74
64.45
66.39
48.75
MAML
Finn Finn cl.
2017
X
23,48
40.13
71.70
78.05
RelationNen Sunk
201
56.77
40.46
64.25
42.71
24.07
38.60
65.56
72.86
50.66
MetaOpiNell Lee et
2019
22.53
36.28
64.44
68.41
Garcia
X
43.70
70.91
23.87
78.69
56.77
FWT sene 2019
X
64.97
46.19
70.70
49.66 66
24.28
40.87
78.02
87.07
57.72
I.RP
2021
X
64.44
46.20
74.45
54.46
24.53
44.14
77.14
86,
58.94
ATA Wang and Deng
2021
66.22
49.14
75.48
52.69
24.32
44.91
83.75
90.59
60.89
AFA Hu and Ma 2022
68.25
49.28
76.21
54.26
25 02
46.01
85.58
88.06
61.58
LDP-nct Zhou cta
2023
X
70.39
52.84
72.90
58.49
26.67
48.06
82.01
89.40
62.60
X
73.78
26.53
63.77
ATA Wane and Dong. 2021
X
65.31
46.95
72.12
55.08
23. 23.60
45.83
79.47
88.15
59.56
AFA
Hu and Ma Alra
65.86
47.89
72.81
55.67
23.47
46.29
80.12
85.69
59.73
RDC
Li et al. 2022
63.39
52.75
72.83
$5.30
25.10
42,10
79.12
88.03
59.83
GNN+
SAN
Io ml.
2022
70.31
46.11
76.88
57.72
25.63
44.93
85.22
89,70
62.06
LDD--net
73.34
53.06
75.47
26.88
84.05
64.10
StyloAdy
Fu
2023
68.72
50.13
77.73
61.52
26.07
45.77
86.58
93.65
63.77
Ours
76,68
55.44
76.98
63.08
26.45
49.07
83,22
93,09
65.50
Fine-tuning" Ga al. NSAE(CE-CE)
2020
63.76
51.21
70.68
56.45
25.37
49.51
81.59
89.84
61.05
Lione cl
2021
68.51
54,91
71.02
59.55
27.10
54.05
83.96
93.14
64.03
ConFeSS' Das et al.
2021
27.09
48.85
84.65
88.88
ATA Wang
2021
73.87
59,02
24.74
63.98
RDC
2022
67.23
53.49
74.91
57.47
25.00
49.91
84.29
93.30
63.21
comparison, we also implement a variant that uses query samples to assist inference. Specifically, we train classifier based on the support set to generate pseudo-labels for the query set, then filter samples from the query set based on these pseudo-labels to expand the support set, and finally retrain the classifier based on the expanded support set for the ultimate prediction on the query set.
Results. Tables D and present the experimental results under 5-way 1-shot and 5-way 5-shot settings, respectively. For easy comparison, the average performance across eight target domains is calculated as the metric. Our method achieves 46.85% (1-shot) and 73.77% (5-shot) under the direct inference setting. Compared to the second-highes method LDP- net Zhou et al. 2023 the proposed method improved by 0.51 % and 1. 1.17% on the 1 --shot and 5-shot tasks, respectively. In comparison to other methods like AFA Hu and Ma [022], ATA Wang and Deng 2021). LRP (un al. [202T]. and FWTgTseng et al. [019]. 9J. the proposed method demonstrates greater performance advantages. Moreover, the proposed method achieves the best results on five target domains, showcasing its robust generalization ability across diverse domains. When the proposed method further utilizes query samples to assist inference, the performance is further improved. Under the same comparison, the proposed method (1) improved by 1.10% (I-shot) and 1.40% (5-shot) compared to the second- best method LDP net Zhou al.
(023) In contrast to methods based on fine-tuning (e.g.. Fine-
Li et al. (2022)), the proposed method still achieves certain performance advantages without requiring additional fine-tuning. In summary, the proposed method has demonstrated the best cross-domain few-shot learning performance, indicating its ability to learn generalizable features in the source domain. Additionally, the method's independence from task- embedding network fine-tuning makes it suitable for potential industrial applications.
tuning" Guo et al. (2020). RDC
3.3 Ablation study
Comparison with baselines. We design two baselines: the "Pre-training baseline" and the "Meta- baseline." For the "Pre-traine Pre-trrining baseline", we directly use the pre-trained model for meta-testing. The proposed method performs meta-training on the basis of pre-training. When all components are removed from the proposed method, it is equivalent to the "Meta-baseline" "Chen et al. (2021). We take the Meta-bbaeeline" as the baseline of the proposed method. For fair comparison, during the meta-testing stage, these two basclines also use the same classifier the proposed method. The
8

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comparison results are shown in T Overall, compared with these two baselines, the proposed method has achieved greater performance advantages. Specifically, compared with the "Pre-training baseline", the performance of the proposed method is improved by 2.79% (1-shot) and 3.28% (5-shot) on average. Compared with the Meta-baseline"", the performance of the proposed method is improved by 2.26% (1 (1-shot) and 3. 5.10% (5-shot) average. These results show that the proposed method can improve the baselines and provide a novel meta-learning framework for CD-FSL.
Table 3: Ablation study. Average classification accuracies (%) are provided.
indicates that this
component used, vice versa. The best results are in bold.
CUB
Places
Plantae
CronDisease
Ave.
Meihod Pretraining baseline
I-sbot
5-shod
I-shot
5-shoo
1-shot
5-shot
1-shot
5-shot
5-eliod
46.90
68.05
50.24
71.43
38.47
57.08
69.89
89.80
51.37
71.59
Meta bascline Ouns
47.05
67.99
51.09
71.74
39.26
57.82
70.22
89.51
51,90
21.77
$1.55
73.61
$2.06
73.78
41.58
61.39
71.47
90.68
$4.16
74.87
Alignment
Recomstruction
I-shot
S-shot
1-shot
5-hhot
1-shot
5-shot
1-shot
5-shot
I-shot
5-chot
X
50.79
51.42
73.22
41.05
60.93
70,80
90.11
74.22
50.55
71.39
51,96
72.60
41.11
60.22
70.04
89.44
53.41
73.41
51.55
73.61
52.06
73.78
41.55
61.39
71.47
90.68
54,16
74.87
Effectiveness of the proposed frequency prior. In this work, we propose prediction consistency prior and a feature reconstruction prior to jointly regularize the embedding network during meta- learning. Among them, the prediction consistency prior encourages to align the predictions produced by the original query image and its each frequency component. The feature reconstruction prior aims at reconstructing the original features utilizing low- frequency and fregufrryeency information in the latent space, which promotes the model to learn comprehensive representations. We conduct ablation studies illustrate the contribution of these components. The results are shown in Table 3 As can be seen, compared to the "Meta-baseline" (meaning not using any components), the proposed method achieves average gains of 1.61 % (1-shot) and 2.45% (5-shot). The above experimental results show the proposed prediction consistency prior is effective. We can draw similar conclusions for feature reconstruction prior. In addition, the proposed method improves by nearly 0.65% under both I-shot and 5-shot tasks when the feature reconstruction module is added. In particular, for the CUB dataset, the proposed method can achieve nearly 1 % improvement on the 5-shot task. This indicates that the proposed feature reconstruction prior is beneficial to the entire method.
3.4 Visualization
Feature highlight. we adhere to established practices Zhou et al. [2023], utilizing the model trained on the source domain to extract features from target domain images. Subsequently, these features serve as attention scores to activate the original images. The results are presented in Fig Overall, our proposed method exhibits the capability to capture more nuanced representations compared to the baseline, a critical aspect for effective cross-domain generalization. As an illustrative example, consider image (d) in Fig 2] The baseline tends to concentrate solely on the neck of the bird, neglecting the broader characteristics of its entire shape. In contrast, our method not only hones in on local texture details, such the head, wings, and claws, but also encapsulates the entirety of the contour shape. This underscores the capacity of our method to learn comprehensive features, avoiding undue emphasis on local textures alone.
Domain gap. The t-SNE Van der Maaten and Hinton (2008) visual results are shown in Fig (a-b). The blue cluster represents the source domain distribution, while the other four colors denote distinct target domain distributions. Notably, the baseline exhibits substantial gap between target domains and the source domain. In contrast, our method effectively mitigates this domain gap. In addition, we conduct a quantitative assessment of the distribution distance between different target domains and the source domain. Specifically, we compute the first-order statistics based on the sampled samples in each domain, treating it as the statistical characteristic of that domain. Subsequently. we measure the Euclidean distance between the first-order statisties of different target domains and the source domain. The resulting quantitative metrics, comparing the proposed method and the baseline, are visualized in (c). (c). Evidently, the proposed method exhibits a smaller distribution distance between the source domain and the target domains, with particularly notable improvements in the medical domain (ISIC)

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(a) Raw image
(b) Baseline
(c) Ours
(d) Raw image
(e) Baseline
Ours
Raw image
(h) Baseline
(i) Ours
(j) Raw image
(k) Baseline
(l) Ours
Figure 2: Feature visualization for Baseline and the proposed method.
reld lost
Sualll
ISC
DaroGIT
CrepCheess
Chist
6.34
0.7
Creah seshireee
bundlt)
Cwet
(a) Baseline
(b) Ours
(c) Quantitative comparison
Figure 3: Visual observations in domain gap.
and the remote sensing domain (EuroSAT). This underscores the capability of our method to learn robust representations in the source domain, effectively mitigating domain shifts.
Conclusions
In this work, we propose an insightful meta-learning framework inspired by the cross-domain invariant frequency priors. Furthermore, we present prediction consistency prior and feature reconstruction prior to jointly regularize meta-learning on source domain, enabling learning cross- domain transferable features. This simple yet effective work achieves state-of-the-art experimental results as well as excellent inference efficiency.
Limitations. The limitation of the proposed method lies its robustness in some extremely challenging cross-domain tasks. For example, on the Chest dataset, the proposed method fails to outperforms all competitors. This indicates that the fixed image decomposition (e.g., Fast Fourier Transform or Wavelet Transform) strategy may be not the optimal solution for all unknown cases in terms of exploit frequency priors. In the future, decomposition strategy. In addition, the proposed method requires to decompose the query image before being fed into the network. While the Fast Fourier Transform for signal decomposition efficient, this does introduce a certain additional training time overhead. Notably, this work does not contain negative social impact.
will attempt exploit the learnable image
Acknowledge. This work was supported in part by the National Natural Science Foundation of China under Grand 62372379, Grant 62071387. Grant 62472350, Grant 62472359 and Grant 62101454; in part by the National Key R&D Program of China under Grand 2022ZD01 18700; in part by the Xi' an's Key Industrial Chain Core Technology Breakthrough Project: AI Core Technology Breakthrough under Grand 23ZDCCJSSGGOWS3-20 Dissertation of Northwestern Polytechnical University under Grant CX2024017; part by National Key Laboratory of Science and Technology on Space-Born Intelligent Information Processing fundation under Grant TJ-04-23-04.
in part by Innovation Foundation for Doctor
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A Related Work
Few-shot learning. Early investigations into model generalization with limited data primarily focused on few-shot learning (FSL), giving rise series of seminal meta-learning methods Vinyals
et al. [2016]. Snell et al. [2017] Huang et al. [2022]. Zhhag and Huang [202]] |Finn et al. [2017] Lee
et al. 2019] Rusu al. 2019]. Zhmoginov et al. 2022]. Baik et al. [2020]. Zhang et al. 2020 aimed
at addressing FSL challenges. In the realm of architecture, a typical meta-learning model comprises
a task-agnostic meta-learner and task-specific base-learner. Notably, ProtoNet[Snell et al. 2017]
and MatchingNet (Vinyals et al. (2016) construct the base-learner using non-oonnnaitt con--arametric distance measure, while Meta-opt [ee et al. [2119] and DeepEMD Zhang et al. [2020] employ a differentiable
linear classifier for this purpose. On the optimization front, meta- veeaa-lernnng methods Vinyals et al.
2016 Snell et al.
2017 Huang et al. [2022). Zhang and Huang [022]] Finn et al. 2017]. Lee et al.
2019]. Rusu et al. 2019] Zhmoginov et al. [2022] Baik et al. [020 typically employ two-stage
optimization strategy. Initially, they optimize the base-learner based on a limited set of labeled data,
followed by optimizing the meta-learner to minimize empirical risk unlabeled data. Despite the
progress made by these methods, they exhibit limited generalization capabilities when confronted
with cross-domain tasks Guo et al. [2020]
Cross-domen few-shot learning. Several recent advancements Zhou et al. [2023] Fu ct al. [2022] 2.23). Li et al.] [2022]. 1 WWang and Deng [022] J. Hu and Ma [002]]. Guo al. [2020], Liang et al. [02T] Das et al. 2222]] [. et al. [2021] Fu et al. [202T]. Sun ct al. [2021] have concentrated on few-shot learning (FSL) within cross-domain scenarios, where the target and source domains differ not only in category but also in domain distribution. Cross-domain few-shot learning (CD-FSL) presents significant challenges and opportunities, given that the distribution of target tasks in practical applications often deviates from that of the source domain. Moreover, acquiring data for extreme target domains, such as medical images Tschandl et al. (2018), , Wang et al. [2017). or annotating remote sensing scene images Helber et al. [2019]. is frequently arduous.
Zhou et al. Zhou et al. [023 consider that local features are robust to cross-domain tasks and propose an improved ProtoNet Snell et al. [2017) to help the model focus on local regions of the image to avoid the simplicity bias. Fu et Fu et al. [2022] employ style augmentation during model training as a strategy to mitigate the detrimental effects on generalization caused by style variations in the target domain. Building upon the ideas presented in their earlier work Fu et al. (2022). ,. Fu et al. Fu eet al. (2023) extend their approach by incorporating adversarial training. This additional step aims to assist the model in adapting domain shifts, enhancing its robustmess across different domains. Li et al. Li et al. [2022) utilize target task information to perform distance calibration on the embedding of the source domain model to promote generalization. Wang et al. Waan and Deng [021] and
Hu et al. Hu and Ma [2022] design adversarial training methods to simulate domain changes from the task-level and feature-level respectively. In this way, the model can obtain Nomain-invariaan representations. Guo et al. Guo et al. (2020) propose a cross-domain fine-tuning baseline, which fine-tunes the feature extraction model for each target domain task. Liang et al. Liang et al. [2021] further design a self-supervised reconstruction loss to fine-tune the model, which can help the model learn more comprehensive representations. Although fine-tuning based methods Guo et al. (2020).
Liang et al.) [2021] achieve good performance, they require a large number of iterative training for each target domain task. This paradigm brings additional computational and storage overhead. In
contrast, our proposed method prioritizes enabling the model to learn cross-domain generalization knowledge during the training phase, allowing for generalization across various target domains without relying on fine-tuning. Additionally, orthogonal to the aforementioned methods Zhou et al.
2003 Fu et al. [2023], Li et al. [2022]. Wang and Deng (2021), Hu and Ma [2022]. Guo et al.
2020 Liang et al. 2021 Das et al. [202]] Li et al. [2021] Fu et al. [2021], Sun et al. [2021]
approach centers on utilizing cross-domain invariant frequency priors to alleviate the over-fitting
problems of classic meta-learning, facilitating the acquisition of cross-domain transferable features.
Different image priors. In the realm of classical image processing. researchers historically devised effective pattern extractors based on diverse image priors such as texture Guo et al.) [2010), Pathak and Barooah| 2013) and shape Vincent et al. 2209), Ding and Goshtasby (001]. However, with the advent of deep learning, Convolutional Neural Networks (ConvNets) have demonstrated remarkable
proficiency in capturing texture features but have often struggled to encapsulate critical shape
priors Geirhos et al. (2018), Hermann et al. 2200 Ringer et al. [2019] Jain et al. (2022). To
15

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address this limitation, recent works Stojanov et al. [2021], Padmanabhan et al. [2023], Heo et al. 2023] have employed shape priors mitigate texture bias and enhance model generalization. For instance, Jain et Jain et al. [2022] advocate for incorporating both texture and shape priors to bolster model generalization and mitigate spurious correlations. In Few-Shot Learning (FSI.), Stojanov et al attoannoo et al. [221]] employ point clouds to explicitly derive shape priors, subsequently minimizing the distance between point cloud embeddings and image embeddings to alleviate texture bias. Similarly, Padmanabhan al Padmanabhan al. [2023] utilize the Sobel operatorVincent et al. 2009 to extract object shape priors and integrate shape-aware knowledge to enhance model
generalization.
On a different front, certain studies Yin et al., [2019]
al. (2022). Chen and Wang
(021), Zhao
it al.] [2022]. Cheng et al. [2023] have underscored the positive impact of frequency priors on model generalization. For instance, Yin et Yin er al. (019 observed distinct robustness levels of high-
frequency and low-frequency components to noise, inspiring researchers to employ frequency domain
data augmentation for enhanced model generalizatior/hhan et al. [2022]. Cheng et al.) [202).. FSL,
Chen et al Chen and Wang [021] concatenate frequency domain features with original image features to obtain comprehensive representations. Fu et au et al. [0022] propose exchanging high-frequency and low-frequency components between different images for image style augmentation. Cheng et al. Cheng et al. [202]] leverage gradient information to identify areas with higher activation levels in frequency domain images.
In contrast to methods relying on texture or shape priors, the proposed method starts from the princi- ples of image transformation theory, focusing on cross-domain invariant frequency priors to enhance the robustness of model. Additionally, our approach compels the model to simultaneously attend to both high-frequene structure and low-freat low-frequency content. This strategy enables our method to strike balance between the contributions of texture and shape to model generalization. Furthermore, unlike other methods grounded in frequency priors, our work's primary innovation lies in the seamless integration of fowufreyenccy and high-frequency features within a meta-learning framework. This integration provides elegant solution to the persistent challenges of cross-domain few-shot learning, allowing for the independent learning of features from these distinct segments, each excelling in capturing unique aspects of visual information.
Table 4: Ablation on different priors. Average classification accuracies (%) are provided. The best results are in bold.
CUB
Places
Plantae
CropDisease
Ave.
Method
1-shot
5-shot
1-shot
5-shot
1-shot
5-shot
1-shot
5-shot
1-shot
5-shot
Texture
48 68
70.31
51.12
72.66
39.41
58.72
70.09
89.80
52.32
72.87
Shape
45.02
67.14
49.95
71.15
36.27
56.97
65.81
87.18
49.26
70.61
Texpure+Shape
48.08
70.00
51.27
72.60
38.49
58.66
69.19
89.19
51.75
72.61
Low frequency
50.05
71.58
51.31
72.78
40.72
60.28
70.05
89,90
53.03
73.63
High frequency
49.89
71.61
51.14
72.84
40.65
60.49
70.04
89.95
52.93
73.72
Ours
51.55
73.61
52.06
73.78
41.55
61.39
71.47
90.68
54.16
74.87
B Further analysis
Why exploit frequency prior? As discussed in Sec.
A previous works Stojanov et al. 2021
2019] Chen and Wang 2021 Zhao al. 2022], Cheng et al. 2023 have explored the integration of various priors, including texture, shape, and frequency, among others. To highlight the advantages of our proposed method, we conducted comparative experiments with different variants. To ensure a fair comparison, we replaced different priors in our framework while maintaining other settings constant. Specificallyy, we adopted the approach of Jain et al. [2022) to model the texture prior. For the shape prior, similar to Stojanov al. [2021). Paadmanabhan et al. [2023), we employed the Canny operator Ding and Goshtasby [2001] to extract the shape prior. For high-frequency or low-frequenc, priors, we retained only the high-frequency branch or the low-frequency branch in our framework. The results are presented in Table Overall, our method outperforms the variants with different priors. The reasons behind this superiority are as follows. Firstly, the texture prior compels the model to excessively focus on local discriminative regions, leading to texture bias and impairing generalization. Secondly, the
Padmanabhan al. [003]_ Heo et al. (2023) Yin al.
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shape prior directs the model's attention to global shapes, which may cause the model to exhibit shape bias and overlook semantic information. Thirdly, compared texture or shape priors, the frequency prior provides more original information, expanding the model's search space and enabling a higher generalization upper bound. Fourthly, our method couples high-frequency and low-frequency information within unified framework, presenting an elegant solution to the persistent challenges of cross-domain few-shot learning. This approach allows for the simultaneous consideration of both types of information, harnessing their complementary aspects for improved generalization.
Why can our work alleviate overfitting? In this study, we subscribe the limited generalization capacity of exiting methods in cross-domain few-shot learning (CD-FSL) their over-fitting onto source domain. Since during the meta-training procedure, only tasks randomly sampled from source domain are utilized for model update, when the target domain shows obvious distribution discrepancy from the source domain, these existing methods are prone to over-fitting, in other words, fail to generalize well in the new target domain. Why can our work alleviate overfitting? To solve over- fitting, a direct solution is to introduce appropriate prior (e.g., regularization) during training on source domain. Inspired by this, we attempt to comprehensively exploit the cross-domain transferable image frequency prior that each image can be decomposed into complementary low-frequency content details and nigh-frequency robust structural characteristics. Following this idea, we first utilizes Fast Fourier Transform to explicitly decouple the high- frequunyy and low-frequency components of the image. Then, we feed each component and the query image into a three-branchs feature embedding network for category prediction. More importantly, we further establish feature reconstruction prior and a prediction consistency prior to collectively guiding the network's meta-learning process. The feature reconstruction prior requires to reconstruct the feature of original image through fusing the features of both decomposed frequency parts using a deep projection network, while the prediction consistency prior aims to minimize the separate Kullback-Leible divergence between the prediction scores produced by the original query image and its each frequency component. By doing these, both priors encourage exploit deep feature space where matter full-frequency band (original image), high-frequency component or low-frequee uwwfrreue component can lead to the unique and correct classification prediction, i.e., the idea semantic feature space which is transferable cross-domain Therefore, the proposed method is able to mitigate the over-fitting problems in CD-FSL. Our state- of-the-art performance on eight benchmark datasets well the ablation study also support this conclusion.
Whether this work is equivalent to data augmentation or self-supervised learning? In this work, our core idea is to utilize cross-domain invariant frequency priors to alleviate the over-fitting problem of classical meta-learning in cross-domain few-shot learning tasks. To this end, we propose two key components: the Image Decomposition Module (IDM) and the Prior Regularization Meta- Network (PRM-Net) Among them, IDM aims to use Fast Fourier Transform (FFT) to explicitly decompose each image from few-shot task into its low- and frequuryy components Nussbaumer and Nussbaumer [1982]. PRM-Net is a key component responsible for introducing a prediction consistency prior and a feature reconstruction prior. It is important to note that our method is fundamentally different from simple data augmentation methods and self-supervised learning methods. The insight behind our method is divide and conquer, that is, explicit decomposition and implicit coupling. First of all, the IDM is to explicitly obtain the frequency priors of the image rather than to simply perform data augmentation. IDM provides frequency prior for the subsequent PRM-Net, and its role is "divide". In addition, PRM-Net designs regular terms with the help of frequency priors, rather than simple self-supervised learning, and its role is "conquer". More importantly, this divide-and-conqque strategy enables IDM and PRM-Net to collaborate to provide a powerful meta-learning framework, aiming to enhance cross- -oos-dnoain generalization by explicitly considering image decomposition and introducing effective regularization during the meta- meea-lcerning process. We design some experiments compare the proposed method with other data augmentation methods and self-supervised learning methods. For the data augmentation method, we use random rotation to augment the image, and design the angular self eelf-supervieed loss as the regularization term Gidaris et al. 2018). For self-supervised learning methods, we choose the most representative SimCLR Chen et al. 2020) and YOL Grill et al. 2020). All compared methods keep the same backbone network and training data as the proposed method. The experimental results are shown in Table Overall, the proposed method can achieve better results compared to using simple data augmentation and self-supervised learning methods.
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Table 5: Comparison with other data augmentation methods and self-supervisedd learning methods. Average classification accuracies (%) are provided. The best results are in bold.
CUB
Places
Plantae
CropDisease
Ave.
Method
1-shot
5-shot
1-shot
5-shot
I-shot
5-shot
I-shot
5-shot
1-shot
5-shot
Rolation augmenlation
49.04
71.17
50.07
72.79
39.90
59.33
69.52
90.59
52.13
73.47
SimCLR
46.40
69.08
50.78
72.86
39.77
59.65
72.50
91.56
52.36
73.28
BYOL
47.96
70.13
49.48
71.88
40.38
59.73
71.91
91.15
52.43
73.22
Ours
51.55
73.61
52.06
73.78
41.55
61.39
71.47
90.68
54.16
74.87
Whether it is applicable to any image decomposition method? To answer this question, conducted comparative experiments using FFT-based Nussbaumer and Nussbaumer [982] decom- position and Wavelet-based Zhang and Zhang 2019 decomposition. The results are presented in T In comparison to the baseline, our method consistently demonstrates sigmificant performance advantages regardless of the decomposition method employed. This indicates the scalability and effectiveness of our method across different decomposition techniques. Additionally, the model trained with Wavelet decomposition exhibits further performance improvement the Places dataset.
Table 6: Comparison with different image decomposition methods. Average classification accuracies (%) are provided. The best results are in bold.
CUB
Places
Method
1-shot
5-shot
1-shot
5-shot
Baseline
47.05
67.99
51.09
71.74
Haar-wavelet
49.12
71.12
52.63
73.92
FFT
51.55
73.61
52.06
73.78
Plantae
CropDisease
Method
1-shot
5-shot
1-shot
5-shot
Baseline
39.26
57.82
70.22
89.54
Haar-wavelet
40.56
60.46
70.82
90.45
FFT
41.55
61.39
71.47
90.68
Does performance benefit from additional parameters? First of all, we clarify that our method does not introduce additional learnable parameters and the parameter amount is same as our baseline. This is because only the parameters in the main branch (e.g.. query image branch) are learnable, and the parameters of the high-frequency branch and low-frequency branch are updated through the exponential moving average of the main branch parameters. Moreover, after training, we only keep the main branch for prediction in the test phase, since the prediction consistency prior have foreed these three branches to produce the same prediction results when the training procedure converged. Therefore, our method does not introduce any additional inference costs compared with our baseline. We also supplemented experiments to answer whether the performance gain comes from additional parameters. Specifically, we triple the learnable parameters of the baseline method and then compare with our method. As shown Table 7 our method still outperforms the baseline when the parameters of the baseline are increased three times.
Efficiency. As mentioned previously, the proposed method focuses on obtaining generalizable model through meta-learning without relying on fine-tuning the embedding network on the target domain. This makes the proposed method very practical and efficient in handling target domain tasks. To verify the efficiency of the proposed method, we chose a classic fine-tuning based method Guo et al. [2020) for comparison. For the fine-tuning based method, we follow its original settings for experiments. We report the average classification accuracy across different target domains as well as the required inference time for each target domain task. Our experimental platform is single
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Table 7: Compared three times baseline with Average classification accuracies (%) provided.
The best results are in bold.
CUB
Places
Plantae
CropDisease
Ave.
Method
I-shot
5-shot
1-shot
5-shot
1-shot
5-shot
1-shot
5-shot
1-shot
5-shol
Baseline
47.05
67.99
51.09
71.74
39.26
57.82
70.22
89.54
$1.90
71.77
Baseline@
48.16
69.42
51.51
72.20
39.25
58.14
70.83
90.21
52.43
72.49
Ours
51.55
73.61
52.06
73.78
41.55
61.39
71.47
90.68
$4.16
74.87
3090 GPU. The results shown in T It can be seen that the proposed method only requires about 0.06 seconds to effectively handle a few-shot task in the target domain. Compared with the fine-tuning based method, the proposed method is nearly 100 times faster the 5-shot task. At the same time, the proposed method also has great advantages in performance. The above experiments show that the proposed method efficient and has the potential for practical applications.
Table 8: Comparison of efficiency between the proposed method and fine-tuning method. The average inference time on each task reported. The best results are in bold.
1-shot
5-shot
Method
Efficiency
Accuracy f
Efficiency
Accuracy
Fine-tuning Guo et al. 2020 Ours
2.21
45.54
7.67
61.05
0.06
46.85
0.07
63.77
Hyper-parameters validation. The syper-parameters of the proposed method encompass the momentum parameters my and m2, which are integral to the Exponential Moving Average (EMA) update strategy. In our approach, we employ the loss for calculating gradients and subsequently updating the network parameters of the main branch through back-propagation. Conversely, for the parameters in the fow-frequency and high-frequency branches, we update them using EMA. To validate the advantages of EMA, we conducted parameter sharing experiment for comparison, denoted as "none" in Table 9 The results indicate a substantial performance decrease when using parameter sharing opposed to EMA, underscoring the necessity of employing EMA. Additionally, we explored different values for the momentum parameters and observed that the model's performance not highly sensitive to the specific values of m. and m2. We have set my to 0.997 and m2 to 0.999 based on these findings.
Additional visualization. More feature highlight results are provided in Fig 4 and Fig In sum- mary. the baseline model tends to focus narrowly on specific local regions of the object. Conversely, method exhibits extensive focus the object, indicating ability capture more comprehensive semantic understanding and, consequently, achieve superior generalization.
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(a) Raw image
(h) Baseline
(c) Ours
(d) Raw image
(c) Baseline
(f) Ours
Raw image
(h) Baseline
(i) Ours
Raw image
(k) Baseline
(I) Ours
(m) Raw image
Baseline
(0) Ours
(p) Raw image
(q) Baseline
(r) Ours
Figure 4: Feature visualization for baseline and the proposed method.
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(a) Raw image
(b) Baseline
(c) Ours
(d) Raw image
(c) Baseline
(f) Ours
(g) Raw image
(h) Baseline
(i) Ours
Raw image
(k) Baseline
()) Ours
mm) Raw image
(n) Baseline
(0) Ours
Raw image
(q) Baseline
(r) Ours
Figure 5: Feature visualization for baseline and the proposed method.
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Table 9: Classification accuracy w.r. values of momentum. Average classification accuracies (%) are provided. The best results are in bold.
CUB
Places
Value
1-shot
5-shot
1-shot
5-shot
none
50.76
72.56
51.83
72.76
mi m0.99.999, m2=0.99955
51.28
73.33
52.10
73.75
mi (..99999..... m==0.99977
51.44
73.44
52.14
73.84
009997. m0290.9999
51.55
73.61
52.06
73.78
m71 =0.9999, m=2=0.9999
51.52
73.54
52.00
73.72
Plantae
CropDisease
Value
1-shot
5-shot
1-shot
5-shot
none
40.73
60.46
69.47
89.56
=0.9999, 0.99999
41.37
61.30
71.11
90.38
m/ #0.9999 m=290.9997
41.44
61.10
71.32
90.45
mi 0.9997 m2=9099999
41.55
61.39
71.47
90.68
mi =0.9999 m==0.9999
41.25
61.23
71.23
90.65
22

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Reviews:
[{"review_id": "PJtXYjllqP", "reviewer": "Reviewer_SF8W", "summary": "The paper introduces a novel framework called Meta-Exploiting Frequency Prior for Cross-Domain Few-Shot Learning, which aims to improve meta-learning's generalization by decomposing images into high- and low-frequency components. This method leverages these components to guide the feature embedding network, enhancing category prediction consistency and feature reconstruction. The framework achieves state-of-the-art results on various cross-domain few-shot learning benchmarks, demonstrating its effectiveness and efficiency.", "questions": "See weakness", "limitations": "yes", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper presents a novel approach by introducing the concept of exploiting cross-domain invariant frequency priors for few-shot learning. The idea of using cross-domain invariant frequency priors is interesting.\n\n2. The proposed framework is rigorously evaluated on multiple cross-domain few-shot learning benchmarks, demonstrating its effectiveness. \n\n3. Good writing and clear presentation.", "weaknesses": "1. The method relies heavily on the strong prior assumption that using low and high-frequency components can effectively mimic the distribution shift encountered during testing. However, this assumption may not hold true when the test and training datasets are entirely unrelated, as observed in the EuroSAT dataset where the performance of the method is not as impressive. The authors need to clarify and justify this assumption.\n\n2. The paper does not provide an evaluation of the method's performance on within-domain few-shot learning tasks. Understanding how the proposed framework performs in a scenario where the training and testing data come from the same domain could provide a more comprehensive view of its robustness and generalizability.\n\n3. The computational complexity of the proposed framework during the training phase is not thoroughly discussed. While the paper claims no additional inference cost, the added steps of image decomposition and feature reconstruction during training could introduce significant computational overhead. Detailed analysis and discussion on the computational requirements and efficiency would be beneficial.\n\n4. The impact of the choice of image decomposition method (e.g., Fast Fourier Transform) on the overall performance of the framework is not thoroughly explored. Alternative decomposition techniques may yield better results or be more computationally efficient. A comparison of different decomposition methods and their influence on the performance and efficiency of the framework would provide valuable insights and strengthen the paper's contributions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## To Reviewer SF8W:\n### Weaknesses 1\n### Response : \nWe compared the FFT decomposition results of natural images and EuroSAT images (please see Fig. 1 in Response.pdf). We observed that FFT decomposition of natural images can obtain clear low-frequency and high-frequency information. However, the high-frequency part of the image from EuroSAT is almost all noise. There may be two reasons for this. One is that during the imaging process of remote sensing scene images, due to the high spatial resolution of remote sensing scene images, the camera often compresses high-frequency information to improve imaging efficiency. Second, remote sensing scene images focus on containing low-frequency texture content and lack clear high-frequency structural information.\n\nWe will further clarify this weakness in the manuscript.\n\n\n\n### Weaknesses 2\n### Response : \nFollowing the suggestion, we have supplemented experiments for the proposed method in the in-domain setting. All in-domain experiments followed standard settings, the results as shown in Table 1. It can be seen that the proposed method achieved good results with both Resnet-10 and ViT-S backbones. \n\nWe will supplement these experimental results into the manuscript.\n\n\n**Table 1 : Performance on within-domain few-shot learning tasks under 5-way 5-shot setting.**\n|　Method　|　　Backbone　|　mini-ImageNet　|　CIFAR-FS　|\n|---|---|---|---|\n|　ProtoNet[1]　|　ResNet-12 　|　  80.53% 　|　 83.5%±0.5% 　| \n|　MetaOptNet[2]　|　ResNet-12 　|　 78.63%±0.46% 　|　84.3%±0.5% 　| \n|　SetFeat[3]　|　ResNet-12 　|　 82.71%±0.46% 　|　- 　|\n|　DiffKendall[4]　|　ResNet-12 　|　 80.79%±0.31% 　|　- 　|\n|　MetaDiff[5]　|　ResNet-12 　|　 81.21%±0.56% 　|　- 　|\n|　**Ours**　|　ResNet-10 　|　 83.30%±0.57% 　|　86.86%±0.63% 　| \n\n|　Method　|　　Backbone　|　mini-ImageNet　|　CIFAR-FS　|\n|---|---|---|---|\n|　P>M>F[6]　|　ViT-S (DINO pretrain) 　|　  98.0% 　|　92.5%   |　- 　|\n|　**Ours**　|　ViT-S (DINO pretrain)　|　 98.78%±0.12% 　|　93.75%± 0.10% 　| \n\n[1] Prototypical networks for few-shot learning， NIPS 2017.\n\n[2] Meta-learning with differentiable convex optimization，CVPR 2019.\n\n[3] Matching Feature Sets for Few-Shot Image Classification, CVPR 2022.\n\n[4] DiffKendall: A Novel Approach for Few-Shot Learning with Differentiable Kendall's Rank Correlation, NIPS 2023.\n\n[5] MetaDiff: Meta-Learning with Conditional Diffusion for Few-Shot Learning, AAAI 2024.\n\n[6] Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference, CVPR 2022.\n\n### Weaknesses 3\n### Response : \n\nFollowing the suggestion, we present the computational costs of the proposed method during the training and inference phases in Tables 2 and 3, respectively. We can draw the following conclusions.\n\n1) The backbone network and the feature reconstruction network in our method are lightweight, which to some extent mitigates the computational overhead.\n\n2) In addition, a portion of the computational overhead of our method comes from the FFT. In future work, we will explore the use of efficient, learnable image decomposition techniques, employing differentiable convolutional kernels to capture information from different frequency bands of the images.\n\n3) During the inference phase, the proposed method does not introduce additional computational overhead, resulting in efficient inference and good generalization.\n\nWe will supplement these analyses and discussion into the manuscript.\n\n**Table 2 : About  parameters (M), FLOPs (G), and Iteration time (S) during training phase. Take the 5-way 1-shot 15-query task as an example to calculate the floating point and training iteration time. N represents the number of pixels in each image.**\n|　Items　|　Decomposition　|　Backbone 　|　Reconstruction 　|\n|---|---|---|---|\n|　Parameters　|　0　|　4.9057　|　0.1313　|\n|　FLOPs　|　O(NlogN) |　71.6513　|　0.0105　|　\n|　Iteration time　|　0.6912 |　1.3859　|　0.1039　|\n\n\n**Table 3 : Performance and efficiency during target domain inference phase under 5-way 1-shot (5-way 5-shot ) setting.**\n|　Method　|　Inference time　|　Average performance 　|\n|---|---|---|\n|　Baseline　|　0.06 (0.07) 　|　51.90 (71.77)　|\n|　Ours　|　0.06 (0.07) |　54.16 (74.87)　|　\n\n### Weaknesses 4\n### Response : \n\nFollowing the suggestion, we compared the performance and efficiency under different decomposition methods. The results are shown in Tables 4 and 5. It can be seen that, compared to the baseline methods, the proposed method achieves better results across various decomposition methods. Additionally, using wavelet-based decomposition results in higher computational efficiency.\nWhen we prioritize efficiency, wavelet decomposition is the optimal choice. However, compared to FFT, the performance of wavelet decomposition is slightly lower. Therefore, overall, FFT remains a better choice.\n\nWe will supplement these analyses and discussion into the manuscript.\n\n**Table 4 : Performance on different image decomposition method under 5-way 1-shot (5-way 5-shot ) setting.**\n|　Method　|　CUB　|　Places　|　Plantae　|　CropDisease　|　Ave.　|\n|---|---|---|---|---|---|\n|　Baseline　|　47.05 (67.99) |　51.09 (71.74) 　|　39.26 (57.82) 　| 　 70.22 (89.54) 　|　 51.90 (71.77) 　|\n|　Haar-wavelet　|　49.12 (71.12 ) 　|　52.63 (73.92)|　40.56 (60.46)　| 　70.82 (90.45) 　|　53.28 (73.98)　|\n|　DB-wavelet　|　49.52 (71.59) 　|　52.74 (73.65)|　40.78 (60.60)　| 　70.87 (90.54) 　|　53.47 (74.09)　|\n|　FFT　|　51.55 (73.61 ) 　|　52.06 (73.78)|　41.55 (61.39)　| 　71.47 (90.68)|　54.16 (74.87)　|\n\n\n**Table 5 : Decomposition efficiency (sec).**\n|　Method　|　One image　|　All images in 5-way 1-shot 15-query task 　|\n|---|---|---|\n|　Haar-wavelet　|　0.0015　|　0.1200　|　\n|　DB4-wavelet　|　0.0016 |　0.1280　|　\n|　FFT　|　0.0086 |　0.6912　|", "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": "F98DqUAiVF", "reviewer": "Reviewer_mWuv", "summary": "The paper introduces an innovative framework that leverages the concept of frequency priors for cross-domain few-shot learning. The novel idea of decomposing images into high and low-frequency components and integrating these into the meta-learning process is a creative advancement in the field.\nBuilt upon established image transformation theories such as the Fourier Transform, the proposed method is grounded in a solid theoretical foundation, which enhances its credibility and applicability across various domains. The empirical validation through extensive experiments on multiple cross-domain benchmarks further substantiates the effectiveness of the framework, showcasing its superiority over state-of-the-art methods. And the experiment, along with the supplementary materials, has been very comprehensive, addressing most of my questions.", "questions": "(1) Is there a hyperparameter used during the FFT process to determine the high and low-frequency information? If so, how was the threshold for decoupling these frequencies determined, and how might it influence the experimental results?\n(2) How does the model perform over a longer period of training, and are there any signs of degradation or improvement in performance? Can the loss optimization curve and loss landscape be provided?\n(3) The content task and structure task are measured in a decoupled manner. Are these tasks entirely independent, and theoretically, could the low-frequency information be used as the query set to predict within the raw image support set, and vice versa for high-frequency information? And so on.\n(4) Besides the EMA (Exponential Moving Average) update method, what other update mechanisms have been considered or could be applicable to the model's training process?\n(5) There seems to be a limited ablation study regarding the choice of loss functions. Why was MSE chosen for the Feature Reconstruction Loss, and could cosine similarity loss be a viable alternative? Similarly, why was KL divergence chosen for the Prediction Loss, and was this decision based on empirical results or theoretical analysis?\n(6)The experiments were conducted using ResNet-10. Could the authors provide insights into whether the proposed method could be applied to larger models such as ResNet-101? Additionally, could the method be beneficial when applied to models like CLIP from OpenAI or the DINO model, and are there any explorations in this direction?\n(7) Some of the experimental content in the supplementary materials could be incorporated into the main text, such as the sections on 'low' and 'high' in Table 4. This is just a suggestion.", "limitations": "The authors have transparently addressed the limitations of their method, particularly its performance on the Chest dataset, and have responsibly considered the broader societal impacts, confirming no negative social effects. They also acknowledge the increased training time associated with their approach. Proactively, they suggest future improvements and responsibly guide how their work can contribute to the field's progression, aligning well with the checklist for addressing limitations and societal impacts.", "rating": 7, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The paper is commendably structured, with a clear and concise presentation of ideas, and it exhibits a high degree of reproducibility, further enhanced by the open sourcing of some of the code. The abstract and introduction effectively encapsulate the motivation and key contributions of the work, providing readers with a quick yet comprehensive understanding. The methodology is explained in a step-by-step fashion, making it accessible to readers who may not be intimately familiar with meta-learning or frequency domain analysis, thereby demonstrating the paper's strength in both clarity and comprehensiveness.", "weaknesses": "(1) While the paper highlights the efficiency advantages of the proposed method, it falls short of offering a detailed analysis of computational complexity. A critical evaluation extending beyond inference times to include the total floating-point operations (FLOPs) during both training and inference phases is essential. Understanding the complete computational costs provides insights into the method's practicality, scalability, and suitability for deployment across varying computational environments.\n(2) The paper could be improved by including more extensive ablation studies on the choice of backbone network and loss functions. The current presentation lacks a thorough exploration of why specific architectural decisions and loss formulations were made, which is crucial for understanding the contribution of these choices to the overall performance.\n(2) Although the paper demonstrates strong empirical results, there is a need for a more profound theoretical analysis underpinning the effectiveness of frequency priors in cross-domain generalization. A deeper theoretical understanding would bolster the paper's claims and offer insights into the broader applicability of the proposed method.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## To Reviewer mWuv :\n### Weaknesses (1) \n### Response : \n\nWe present the computational costs during the training and inference phases in Table 2 and 3 (Due to character limitations, please see \"To Reviewer SF8W\".), respectively. We can draw the following observations.\n\n1) During the training, the computational overhead of our method mainly comes from the backbone and image decomposition. As shown in Table 2 (please see \"To Reviewer SF8W\"), the backbone and the feature reconstruction network are lightweight, which to some extent mitigates the computational overhead.\n\n2) During inference, our method does not introduce additional computational overhead, resulting in efficient inference and good generalization.\n\n### Weaknesses (2)  &  Questions (5) & Questions (6)\n\n### Response 1:  Using Resnet-101 and ViT as backbones.\n\nWe validate our method with Resnet-101 and ViT as backbones, as shown in Table 6 (Please see Table 6 in the global rebuttal). It can be seen that our method effectively scales to different backbones and demonstrates certain performance advantages.\n\n### Response 2: Verifying cosine loss.\n\nWe validate cosine similarity as an alternative to MSE, as shown in Table 7 (Please see Table 7 in the global rebuttal). It can be observed that MSE and cosine similarity yield nearly equivalent performance. \n\n### Response 3: About KL divergence.\n\nIn our alignment prior, we use the predictions from the main branch as an anchor, and expect the high/low-frequency predictions to align with this anchor. To achieve this, we use KL divergence as the metric. The reasons are as follows. First, since the anchor is dynamically changing during training, meaning the entropy of the anchor is not constant, cross-entropy is not suitable. Second, our alignment loss is asymmetric, so JS divergence is also not applicable. In addition, Wasserstein-1 distance could serve as an alternative to KL divergence. However, it requires computing the optimal transport between different prediction distributions, which involves quadratic programming and results in higher computational complexity.\n\n### Weaknesses (3)\n### Response : \n\nThanks for the suggestions. In this work, we resort to the image decomposition prior which have been proved shared across different images despite their domains, i.e., each image can be decomposed into complementary low-frequency content details and high-frequency robust structural characteristics. More importantly, we specially establish a feature reconstruction prior and a prediction consistency prior to separately encourage the consistency. This allows for collectively guiding the network’s meta-learning process with the aim of learning cross-domain generalizable embeddings.  We will supplement more theoretical analysis into the manuscript.\n\n### Questions (1) \n### Response : \n\nWe validate the hyper-parameters in FFT(e.g., radius ratio), which determines the boundary between high and low frequencies. The results are shown in Table 8 (Please see Table 8 in the global rebuttal). It can be observed that this hyper-parameter does not significantly affect the overall performance. We set it to 0.5 for all cases.\n\n\n### Questions (2) \n### Response 1 :  About training epoch.\n\nWe validate the impact of training epochs on performance. The results are shown in Table 9 (Please see Table 9 in the global rebuttal). It can be observed that as the number of epochs increases, performance initially rises and then declines. However, since we cannot link to the test data during the training phase, we can only judge based on the loss curve during training (please see Fig. 2 in Response.pdf). We observed that the loss tends to converge around 50 epochs. Therefore, we set it to 50 for all cases. \n\n### Response 2 :  About loss curve and landscape.\n\nWe provide the loss optimization curve and loss landscape in Fig. 2. As can be seen, the baseline tends to over-fit at the relatively early epochs. In contrast, with the assistance of prior regularization, our method can mitigate over-fitting to some extent. For the loss landscape, we followed the implementation in [1].  Firstly, randomly perturb the model trained in the source domain in 2000 directions; Secondly, perform inference on the target domain for each perturbed model, and record the loss value; Finally, we visualize the loss landscape based on the recorded loss values and directions. It can be seen that, compared to the baseline, the trained model of the proposed method is more robust to unknown perturbations. For example, the loss values in our method converge within a certain range. In contrast, the baseline method's loss values tend to diverge. This demonstrates the good generalization ability of our method.\n\n[1] Visualizing the loss landscape of neural nets. NIPS, 2018.\n\n### Questions (3)\n### Response :  \n\nWe designed a variant experiment that utilizes the raw support set to predict high-frequency and low-frequency query. The results are shown in Table 10 (Please see Table 10 in the global rebuttal). It can be seen that this variant also achieves significant improvements over the baseline. However, the performance of this variant is slightly lower than our original approach. This may be because independently using high-frequency or low-frequency support images to predict high-frequency or low-frequency query images can more explicitly utilize the diverse frequency information.\n\n### Questions (4)\n### Response :  \n\nWe supplement some experiments to verify alternative mechanisms, and the results are shown in Table 11 (Please see the global rebuttal). We compared three update mechanisms. Case 1: we keep parameters shared among the three branches. Case 2: non-shared parameters between the three branches and joint training in an end-to-end manner. Case 3 (Ours): EMA strategy to update. As can be seen, our method achieves the best performance.\n\n### Questions  (7)\n### Response : \n\nThanks for the suggestions. We will supplement those results into the main text.", "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": "gccB7Vr1wl", "reviewer": "Reviewer_HqaU", "summary": "This paper introduces a novel framework for cross-domain few-shot learning. The input images are first decomposed into low-frequency content and high-frequency structure using FFT. Then, the PRM-Net includes three branches, low-frequency, high-frequency, and main branch. The PRM-Net includes two priors to regularize the feature embedding network. The approach shows state-of-the-art results on multiple benchmarks.", "questions": "1. How do you see the value of research in the (cross-domain) few-shot learning while the foundation models can perform well in zero-shot tasks?\n2. Is it possible to combine this approach with fine-tuning strategies to further enhance performance in certain domains?", "limitations": "n/a", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The use of frequency decomposition to address CD-FSL task is easy to understand and implement.\n2. The method is thoroughly evaluated on multiple benchmarks.\n3. The method achieves state-of-the-art results on multiple benchmarks.\n4. The paper provides a clear and detailed description of each component of the method.", "weaknesses": "1. The method avoids additional inference costs, however, the decomposition and additional branches (high-low frequency branches) could introduce significant computational overhead. Moreover, the improvement by incorporating the reconstruction prior seems marginal according to Table 3.\n2. Lack of proper citation for the datasets mentioned in section 3.1, e.g., CropDisease, CUB, ISIC.\n3. The reliance on fixed decomposition strategies like FFT might not be optimal for some scenarios, e.g., the foreground objects have similar colors to the background, or the background is complex. The whole model cannot be trained end-to-end due to FFT.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "## To Reviewer HqaU :\n\n### Weaknesses (1)\n\n### Response 1 : About computational overhead.\n\n1) Thanks for the comments. The proposed method indeed introduces additional computational cost during the training phase. We will further clarify this weakness in the manuscript.\n\n2) We present the computational costs of our method during the training and inference phases in Table 2 and  3 (Due to character limitations, please see  \"To Reviewer SF8W\".), respectively.  As shown, the backbone and the feature reconstruction network in our method are lightweight, which to some extent mitigates the computational overhead of the high and low-frequency branches. In addition, a portion of the computational overhead of our method comes from the FFT. In future work, we will explore the use of efficient, learnable image decomposition techniques, employing differentiable kernels to capture information from different frequency bands of the images.\n\n3) During the inference, the proposed method does not introduce additional computational overhead, resulting in efficient inference and good generalization.\n\n### Response 2 : About the reconstruction prior.\n\nWe have analyzed the reconstruction prior in the manuscript (please see \"Effectiveness of the proposed frequency prior\" in 4.3. Ablation study.) and performed experiments (please see Table 3 in the manuscript). We copy the results from the manuscript here, as shown in Table 12. It can be seen that compared with the baseline, the proposed reconstruction prior can achieve better performance. This demonstrates the contribution of the proposed reconstruction prior.\n\n**Table 12 : Verifying  the alignment and reconstruction prior under 5-way 1-shot (5-way 5-shot ) setting.**\n|　Method　|　CUB　|　Places　|　Plantae　|　CropDisease　|　Ave.　|\n|---|---|---|---|---|---|\n|　Baseline　|　47.05 (67.99) |　51.09 (71.74) 　|　39.26 (57.82) 　| 　 70.22 (89.54) 　|　 51.90 (71.77) 　|\n|　Ours just alignment 　|　50.79 (72.65) |　51.42 (73.22) 　|　41.05 (60.93) 　| 　70.80 (90.11) 　|　53.51 ( 74.22) 　|\n|　Ours just reconstruction　|　50.55 (71.39)　| 　51.96 (72.60)　| 　41.11 (60.22)　| 　70.04 (89.44)　| 　53.41 (73.41)　| \n|　Ours (alignment + reconstruction) |　51.55 (73.61 ) 　|　52.06 (73.78)|　41.55 (61.39)　| 　71.47 (90.68)|　54.16 (74.87)　|\n\n### Weaknesses (2)\n\n### Response : \n\nThanks for the suggestion. We will supplement the references for CropDisease, CUB, and ISIC in the manuscript. \n### Weaknesses (3)\n\n### Response : \n\nThanks for the comments. We will further clarify this weakness in the manuscript. To alleviate this problem, we will explore the use of learnable image decomposition methods as an alternative to FFT. Essentially, FFT uses fixed kernels for signal decomposition, making it difficult to achieve data-adaptive decomposition. We are considering designing differentiable kernels to separately extract high-frequency and low-frequency information from images. Additionally, we consider constructing a model that generates kernel parameters conditioned on the original image for data-adaptive image decomposition. We will validate it in future work.\n\n### Questions (1) \n\n### Response : \n\nWe think that it is valuable to study cross-domain few-shot learning (CD-FSL) in the era of foundation models. The reasons are as follows.\n\n1) Adapting foundation models to CD-FSL has practical value. The core elements of CD-FSL are feature initialization and rapid adaptation. Early research has concentrated on using meta-learning methods to learn a good feature initialization model in the source domain, and then quickly adapting the model to the target task with a small number of labeled samples.The foundation models essentially accomplished the first step of FSL. In future research, effectively adapting large models to cross-domain few-shot tasks is valuable.\n\n2) Exploring the adaptation of foundation models to extreme CD-FSL holds significant research value. \nPrevious work [1] explored applying pre-trained foundation models to extreme cross-domain few-shot tasks. For comparison, we implemented our method under the same settings, and the results are shown in Table 13. As can be seen, even with the assistance of pre-trained foundation models, these methods still perform poorly in extreme cross-domain scenarios (e.g., Chest, ISIC, etc.).\nTherefore, exploring the adaptability of foundational models to extreme CD-FSL tasks is valuable.\n\n**Table 13 : Performance using the foundation model as feature initialization.**\n|Method|Backbone|Setting|CUB|Cars|Places|Plantae|Chest|ISIC|EuroSAT|CropDisease|Ave.|\n|---|---|---|---|---|---|---|---|---|---|---|---|\n|　P>M>F[2]　|　ViT-S (DINO pretrain)　|　1-shot　|　78.13　|　37.24　|　71.11　|　53.60　|　21.73　|　30.36　|　70.74　|　80.79　|　55.46　|\n|　**Ours**　|　ViT-S (DINO pretrain)　|　1-shot　|　85.07　|　42.82　|　73.71　|　56.6　|　23.32　|　35.13　|　72.03　|　81.82　|　58.81　|\n|　P>M>F[2]　|　ViT-S (DINO pretrain)　|　5-shot　|　-　|　-　|　-　|　-　|　27.27　|　50.12　|　85.98　|　92.96　|　-　|\n|　**Ours**　|　ViT-S (DINO pretrain)　|　5-shot　|　97.5　|　74.6　|　89.24　|　81.63　|　26.31　|　51.72　|　89.95　|　95.93　|　75.86　|\n\n[1] Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference, CVPR 2022.\n\n### Questions (2) \n### Response : \n\nFollowing the suggestion, we have fine-tuned our method on target domain. Following the common fine-tuning strategies, for each few-shot task in the target domain, we fine-tune the model using the support set, and then test it on the query set. Due to time constraints, we have conducted experiments on the EuroSAT and ISIC target datasets as examples, as shown in Table 14. It can be seen that, through fine-tuning, the performance of the proposed method can be further improved. For example, on the EuroSAT dataset, fine-tuning the proposed method improved performance by 1.55%.\n\n**Table 14 : Performance when fine-tuning our method under 5-way 5-shot setting.**\n|　Method　|　EuroSAT　|　ISIC 　|\n|---|---|---|\n|　Ours 　|　81.24　|　48.70　|　\n|　Ours+fine-tuning　|　 82.79 |　49.50　|", "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:
Author Response for ``Meta-Exploiting Frequency Prior for Cross-Domain Few-Shot Learning''

We would like to express our gratitude to the AC and the reviewers for their valuable comments and suggestions. Over the past week, we have responded to all comments mentioned by the reviewers. The response includes:
1) evaluating the computational overhead during the training phase.
2) clarifying the prior assumptions and theoretical advantages of the proposed method.
3) supplementing the experiments in the in-domain setting.
4) validating different image decomposition methods, hyper-parameters in FFT, training epochs, the loss optimization curve and loss landscape.
5) supplementing experiments with different backbone networks, such as Resnet-101 and ViT.
6) validating different update strategies, the choice of loss functions, and variants using the original images for prediction.
7) verifying the performance of the proposed method with further fine-tuning, etc.

For detailed responses, please refer to each reviewer's rebuttal window. Additionally, since we cannot upload figures in the reviewer's rebuttal window, we have included all figures in a separate "Response.pdf" within this global rebuttal window. Besides, due to character limitations in the reviewer's window, we have placed some experimental result tables in this global rebuttal window.


**Table 6 : Performance of the proposed method on different backbone networks under 5-way setting. The results of ProtoNet[1] are derived from our reproduction, and the results  of P>M>F[2] were copied from its paper.**
|Method|Backbone|Setting|CUB|Cars|Places|Plantae|Chest|ISIC|EuroSAT|CropDisease|Ave.|
|---|---|---|---|---|---|---|---|---|---|---|---|
|　ProtoNet[1]　|　Resnet101　|　1-shot　|　52.14　|　35.08 　|　52.40 　|　39.01　|　22.01　|　33.34　|　62.30　|　68.34　|　45.57　|
|　**Ours**　|　Resnet101　|　1-shot　|　53.98　|　37.95　|　52.06　|　42.44　|　22.32　|　36.10　|　62.54　|　71.74　|　47.39　|
|　ProtoNet[1]　|　Resnet101　|　5-shot　|　75.05　|　51.48　|　73.29　|　58.41　|　26.18　|　47.96　|　78.09　|　88.96　|　62.42　|
|　**Ours**　|　Resnet101　|　5-shot　|　76.87　|　56.80　|　74.61　|　61.64　|　26.44　|　50.20　|　80.17　|　90.57　|　64.66　|

|Method|Backbone|Setting|CUB|Cars|Places|Plantae|Chest|ISIC|EuroSAT|CropDisease|Ave.|
|---|---|---|---|---|---|---|---|---|---|---|---|
|　P>M>F[2]　|　ViT-S (DINO pretrain)　|　1-shot　|　78.13　|　37.24　|　71.11　|　53.60　|　21.73　|　30.36　|　70.74　|　80.79　|　55.46　|
|　**Ours**　|　ViT-S (DINO pretrain)　|　1-shot　|　85.07　|　42.82　|　73.71　|　56.6　|　23.32　|　35.13　|　72.03　|　81.82　|　58.81　|
|　P>M>F[2]　|　ViT-S (DINO pretrain)　|　5-shot　|　-　|　-　|　-　|　-　|　27.27　|　50.12　|　85.98　|　92.96　|　-　|
|　**Ours**　|　ViT-S (DINO pretrain)　|　5-shot　|　97.5　|　74.6　|　89.24　|　81.63　|　26.31　|　51.72　|　89.95　|　95.93　|　75.86　|

[1] Prototypical networks for few-shot learning，NIPS 2017.

[2] Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference, CVPR 2022.



**Table 7 : Verifying cosine loss under 5-way 1-shot (5-shot) setting.**
|　Method　|　CUB　|　Places　|　Plantae　|　CropDisease　|　Ave.　|
|---|---|---|---|---|---|
|　Cosine similarity loss　|　51.50 (73.54) |　52.08 (73.78) 　|　41.54 (61.40) 　| 　 71.49 (90.66) 　|　 54.15 (74.84) 　|
|　MSE　loss　|　51.55 (73.61 ) 　|　52.06 (73.78)　|　41.55 (61.39)　| 　71.47 (90.68)|　54.16 (74.87)　|




**Table 8 : Verifying the hyper-parameters in FFT under 5-way 1-shot (5-shot ) setting.**
|　Radius_ratio　|　CUB　|　Places　|　Plantae　|　CropDisease　|
|---|---|---|---|---|
|　0.1　|　51.14 (73.25)　|　51.95 (73.76) 　|　41.40 (61.33) 　| 　 71.68 (90.89) 　|
|　0.3　|　51.27 (73.33)　|　52.18 (73.81) 　|　41.47 (61.44) 　| 　 71.67 (90.83) 　|
|　**0.5**　|　51.55 (73.61)　|　52.06 (73.78)　 |　41.55 (61.39)　 | 　 71.47 (90.68)　 |
|　0.7　|　51.30 (73.35)　|　51.89 (73.79) 　|　41.33 (61.28) 　| 　 71.37 (90.61) 　|
|　0.9　|　51.23 (73.10)　|　52.00 (73.85) 　|　41.30 (61.27) 　| 　 71.54 (90.63) 　|


**Table 9 : Verifying the training epoch under 5-way 1-shot (5-shot ) setting.**
|　Epoch　|　CUB　|　Places　|　Plantae　|　CropDisease　|
|---|---|---|---|---|
|　40　|　51.12 (72.88)　|　52.53 (74.04) 　|　41.04 (60.71) 　| 　 71.15 (90.56) 　|
|　**50**　|　51.55 (73.61)　|　52.06 (73.78)　 |　41.55 (61.39)　 | 　 71.47 (90.68)　 |
|　60　|　51.00 (73.45)　|　51.60 (73.59) 　|　41.39 (61.06) 　| 　 71.17 (90.33) 　|
|　80　|　50.69 (72.80)　|　51.87 (73.34) 　|　40.88 (60.87) 　| 　 70.75 (90.27) 　|
|　100　|　50.02 (72.12)　|　51.44 (73.15) 　|　40.91 (60.98) 　| 　 70.36 (90.19) 　|


**Table 10 : Verifying the variant that predict within the raw image support set under 5-way 1-shot (5-shot ) setting.**
|　Method　|　CUB　|　Places　|　Plantae　|　CropDisease　|　Ave.　|
|---|---|---|---|---|---|
|　Baseline　|　47.05 (67.99) |　51.09 (71.74) 　|　39.26 (57.82) 　| 　 70.22 (89.54) 　|　 51.90 (71.77) 　|
|　Variant　|　51.32 (73.18) 　|　52.12 (73.87) 　|　41.61 (61.10)　| 　70.91 (90.19) 　|　53.99 (74.58)　|
|　Ours　|　51.55 (73.61 ) 　|　52.06 (73.78) 　|　41.55 (61.39)　| 　71.47 (90.68) 　|　54.16 (74.87)　|



**Table 11 : Comparing alternative update mechanisms under 5-way 1-shot (5-shot) setting.**
|　Method　|　CUB　|　Places　|　Plantae　|　CropDisease　|　Ave.　|
|---|---|---|---|---|---|
|　Baseline　|　47.05 (67.99) |　51.09 (71.74) 　|　39.26 (57.82) 　| 　 70.22 (89.54) 　|　 51.90 (71.77) 　|
|　Case 1　|　50.76 (72.56) |　51.83 (72.76) 　|　40.73 (60.46) 　| 　69.47 (89.56) 　|　53.19 (73.83) 　|
|　Case 2　|　50.93 (72.59) | 　52.36 (73.84) | 　41.00 (60.74) |　 70.65 (90.40)　|　53.73 (74.39) |
|　Case 2 (ours)　|　51.55 (73.61 ) 　|　52.06 (73.78)|　41.55 (61.39)　| 　71.47 (90.68)　|　54.16 (74.87)　|

Meta-review: In this paper, the authors propose to improve cross-domain few-shot learning by decomposing images into high- and low-frequency components. Extensive experimental results are provided to show the effectiveness of the proposed method. After the rebuttal period, this paper receives consistent positive ratings. Therefore, it is a clear acceptance.
Decision: Accept (poster)