Relational Embedding for Few-Shot Classification

by   Dahyun Kang, et al.

We propose to address the problem of few-shot classification by meta-learning "what to observe" and "where to attend" in a relational perspective. Our method leverages relational patterns within and between images via self-correlational representation (SCR) and cross-correlational attention (CCA). Within each image, the SCR module transforms a base feature map into a self-correlation tensor and learns to extract structural patterns from the tensor. Between the images, the CCA module computes cross-correlation between two image representations and learns to produce co-attention between them. Our Relational Embedding Network (RENet) combines the two relational modules to learn relational embedding in an end-to-end manner. In experimental evaluation, it achieves consistent improvements over state-of-the-art methods on four widely used few-shot classification benchmarks of miniImageNet, tieredImageNet, CUB-200-2011, and CIFAR-FS.



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1 Introduction

Few-shot image classification [11, 75, 55, 28]

aims to learn new visual concepts from a small number of examples. The task is defined to classify a given query image into target classes, each of which is unseen during training and represented by only a few support images. Recent methods 

[75, 66, 49, 1, 35, 52, 20, 83, 87, 5] tackle the problem by meta-learning a deep embedding function such that the distance between images on the embedding space conforms to their semantic distance. The learned embedding function, however, often overfits to irrelevant features [14, 4, 9] and thus fails to transfer to new classes not yet observed in training. While deep neural features provide rich semantic information, it remains challenging to learn a generalizable embedding without being distracted by spurious features.

Figure 1: Relational embedding process and its attentional effects. The base image features are transformed via self-correlation to capture structural patterns within each image and then co-attended via cross-correlation to focus on semantically relevant contents between the images. (a), (b), and (c) visualize the activation maps of base features, self-correlational representation, and cross-correlational attention, respectively. See Sec. 5.6 for details.

The central tenet of our approach is that relational patterns, , meta-patterns, may generalize better than individual patterns; an item obtains a meaning in comparison with other items in a system, and thus relevant information can be extracted from the relational structure of items. On this basis, we propose to learn “what to observe” and “where to attend” in a relational perspective and combine them to produce relational embeddings for few-shot learning.

We achieve this goal by leveraging relational patterns within and between images via (1) self-correlational representation (SCR) and (2) cross-correlational attention

(CCA). The SCR module transforms a base representation into its self-correlation tensor and learns to extract structural patterns from it. Self-correlation of a deep feature map encodes rich semantic structures by correlating each activation of the feature map to its neighborhood. We perform representation learning on top of it to make relevant structural patterns of the image stand out (Fig. 

1 (a)(b)). On the other hand, the CCA module computes cross-correlation between two image representations and learns to produce co-attention from it. Cross-correlation encodes semantic correspondence relations between the two images. We learn high-dimensional convolutions on the cross-correlation tensor to refine it via convolutional matching and produce adaptive co-attention based on semantic relations between the query and the support (Fig. 1 (b)(c)).

The proposed method combines the two modules to learn relational embeddings in an end-to-end manner; it extracts relational patterns within each image (via SCR), generates relational attention between the images (via CCA), and aggregates the cross-attended self-correlation representations to produce the embeddings for few-shot classification. Experiments on four standard benchmark datasets demonstrate that the proposed SCR and CCA modules are effective at highlighting the target object regions and significantly improve few-shot image classification accuracy.

Figure 2: Overall architecture of RENet. The base representations, and , are transformed to self-correlation tensors, and , which are then updated by the convolutional block to self-correlational representations, and , respectively. The cross-correlation is computed between the pair of image representations and then refined by the convolutional block to , which is bidirectionally aggregated to generate co-attention maps, and . These co-attention maps are applied to corresponding image representations, and , and their attended features are aggregated to produce the final relational embeddings, and , respectively.

2 Related work

Few-shot classification. Recent few-shot classification methods are roughly categorized into three approaches. The metric-based approach aims to learn an embedding function that maps images to a metric space such that the relevance between a pair of images is distinguished based on their distance [28, 75, 66, 49, 1, 35, 33, 52, 20, 83, 87, 36, 9]. The optimization-based approach meta-learns how to rapidly update models online given a small number of support samples [12, 84, 61, 55, 69]. The two aforementioned lines of work formulate few-shot classification as a meta-learning problem [63, 2, 19]

. The transfer-learning approach 

[6, 73, 8, 79, 38, 16, 51, 59, 90] has recently shown that the standard transfer learning procedure [85, 48]

of early pre-training and subsequent fine-tuning is a strong baseline for few-shot learning with deep backbone networks. Among these, our work belongs to the metric-based approach. The main idea behind a metric-based few-shot classifier is that real images are distributed on some manifolds of interest, thus the embedding function adequately trained on the training classes can be transferred to embed images of unseen target classes by interpolating or extrapolating the features 

[72, 64]. Our work improves the transferability of embedding by learning self- and cross-relational patterns that can better generalize to unseen classes.

Self-correlation. Self-correlation or self-similarity reveals a structural layout of an image by measuring similarities of a local patch within its neighborhood [65]. Early work uses the self-correlation itself as a robust descriptor for visual correspondence [74], object detection [7], and action recognition [26, 25]. Recent work of [27, 89, 31]

adopts self-correlation as an intermediate feature transform for a deep neural network and shows that it helps the network learn an effective representation for semantic correspondence 

[27], image translation [89], and video understanding [31]. Inspired by the work, we introduce the SCR module for few-shot classification. Unlike self-correlation used in the previous work, however, our SCR module uses channel-wise self-correlation to preserve rich semantic information for image recognition. Note that while self-attention [78, 54] also computes self-correlation values as attention weights for aggregation, it does not use the self-correlation tensor directly for representation learning and thus is distinct from this line of research.


Cross-correlation has long been used as a core component for a wide range of correspondence-related problems in computer vision. It is commonly implemented as a cost-volume or correlation layer in a neural network, which computes matching costs or similarities between two feature maps, and is used for stereo-matching 

[86, 40], optical flow [10, 67, 82], visual correspondence [44, 45, 58, 34, 42], semantic segmentation [68, 43], video action recognition [77, 30], video object segmentation [47, 22], among others. Some recent few-shot classification methods [87, 35, 20, 9] adopt cross-correlation between a query and each support to identify relevant regions for classification. However, none of them [87, 35, 9, 20] leverage geometric relations of features in cross-correlation and they often suffer from unreliable correlation due to the large variation of appearance. Unlike these previous methods, our CCA module learns to refine the cross-correlation tensor with 4D convolution, filtering out geometrically inconsistent correlations [58, 42], to obtain reliable co-attention. In our experiment, we provide an in-depth comparison with the most related work of [20].

Our contribution can be summarized as follows:

  • We propose to learn the self-correlational representation for few-shot classification, which extracts transferable structural patterns within an image.

  • We present the cross-correlational attention module for few-shot classification, which learns reliable co-attention between images via convolutional filtering.

  • Experiments on four standard benchmarks show our method achieves the state of the art, and ablation studies validate the effectiveness of the components.

3 Preliminary on few-shot classification

Few-shot classification aims to classify images into target classes given only a few images for each class. Deep neural networks are vulnerable to overfitting with such a small amount of annotated samples, and most few-shot classification methods [75, 55, 66] thus adopt a meta-learning framework with episodic training for few-shot adaptation. In few-shot classification, a model is optimized using training data from classes and then evaluated on test data from unseen classes where . Both and consist of multiple episodes, each of which contains a query set and a support set of image-label pairs for each classes, , -way -shot episode [11, 75]. During training, we iteratively sample an episode from and train the model to learn a mapping from to . During testing, the model uses the learned mapping to classify as one of classes in the support set sampled from .

4 Our approach

In this section, we introduce the Relational Embedding Network (RENet) that addresses the challenge of generalization to unseen target classes in a relational perspective. Figure 2 illustrates the overall architecture, consisting of two main learnable modules: self-correlational representation (SCR) module and cross-correlational attention (CCA) module. We first present a brief overview of the proposed architecture in Sec. 4.1. We then present technical details of SCR and CCA in Sec. 4.2 and Sec. 4.3 respectively, and describe our training objective in Sec. 4.4.

4.1 Architecture overview

Given a pair of a query and one of support images, and , a backbone feature extractor provides base representations, and . The SCR module transforms the base representations to self-correlational representations, and , by analyzing feature correlations within an image representation in a convolutional manner. The CCA module then takes the self-correlational representations to generate co-attention maps, and , which give spatial attention weights on aggregating and to image embeddings, and . This process illustrated in Fig. 2 is applied to all support images in parallel, and then the query is classified as the class of its nearest support embedding.

4.2 Self-Correlational Representation (SCR)

The SCR module takes the base representation 111For notational simplicity, we omit subscripts q and s in this subsection. and transforms it to focus more on relevant regions in an image, preparing a reliable input to the CCA module that analyzes feature correlations between a pair of different images. Figure 3 illustrates the architecture of the SCR module.

Self-correlation computation.

Given a base representation , we compute the Hadamard product of a

-dimensional vector at each position

and those at its neighborhood and collect them into a self-correlation tensor . With an abuse of notation, the tensor can be represented as a function with a -dimensional vector output:


where corresponds to a relative position in the neighborhood window such that and

, including the center position. Note that the edges of the feature map are zero-padded for sampling off the edges. The similar type of self-correlation, , self-similarity, has been used as a relational descriptor for images and videos that suppresses variations in appearance and reveals structural patterns 

[65]. Unlike the previous methods [65, 7, 25], which reduce a pair of feature vectors into a scalar correlation value, we use the channel-wise correlation, preserving rich semantics of the feature vectors for classification.

Self-correlational representation learning.

To analyze the self-correlation patterns in , we apply a series of 2D convolutions along dimensions. As shown in Fig. 3, the convolutional block follows a bottleneck structure [71] for computational efficiency, which is comprised of a point-wise convolution layer for channel size reduction, two

convolution layers for transformation, and another point-wise convolution for channel size recovery. Between the convolutions, batch normalization


and ReLU 

[46] are inserted. This convolutional block gradually aggregates local correlation patterns without padding, thus reducing their spatial dimensions from to such that the output has the same size with , , . This process of analyzing structural patterns may be complementary to appearance patterns in the base representation . We thus combine the two representations to produce the self-correlational representation :


which reinforces the base features with relational features and helps the few-shot learner better understand “what to observe” within an image. Our experiments show that SCR is robust to intra-class variations and helps generalization to unseen target classes.

Figure 3: Architecture of SCR and CCA modules. (a): The SCR module captures relational patterns in the input self-correlation by convolving it over dimensions. The result is added to the base representation to form the self-correlational representation (Eq. 2). (b): The CCA module refines the cross-correlation which will be summarized into co-attention maps, and (Eq. 4).

4.3 Cross-Correlational Attention (CCA)

The CCA module takes an input pair of query and support SCRs, and , and produces corresponding attention maps, and . These spatial attention maps are used to aggregate each representation to an embedding vector. Figure 3 visualizes the pipeline of the CCA module.

Cross-correlation computation. We first transform both query and support representations, and , into more compact representations using a point-wise convolutional layer, reducing its channel dimension to . From the outputs, and , we construct a 4-dimensional correlation tensor :


where denotes a spatial position on the feature map and

means the cosine similarity between two features.

Convolutional matching. The cross-correlation tensor may contain unreliable correlations, , matching scores, due to the large appearance variations in the few-shot learning setup. To disambiguate those unreliable matches, we employ the convolutional matching process [58, 42] that refines the tensor by 4D convolutions with matching kernels; 4D convolution on the tensor plays the role of geometric matching by analyzing the consensus of neighboring matches in the 4D space. As shown in Fig. 3, the convolutional matching block consists of two 4D convolutional layers; the first convolution produces multiple correlation tensors with multiple matching kernels, increases channel size to , and the second convolution aggregates them to a single 4D correlation tensor, , . Batch normalization and ReLU are inserted between the convolutions. We empirically found that two 4D convolutional layers are sufficient for our CCA module.

Co-attention computation.

From the refined tensor , we produce co-attention maps, and , which reveal relevant contents between the query and the support. The attention map for the query is computed by


where is a position at the feature map and is a temperature factor. Since is a matching score between the positions and , the attention value of Eq. (4) can be interpreted as converting the matching score of

, , a position at the query image, to the average probability of

being matched to a position at the support image. The attention map for the support is similarly computed by switching the query and the support in Eq. (4).

These co-attention maps improve few-shot classification accuracy by meta-learning cross-correlational patterns and adapting “where to attend” with respect to the images given at test time.

4.4 Learning relational embedding

In this subsection, we derive relational embeddings and from and . We then conclude our method by describing the learning objective.

Attentive pooling.

To obtain the final embedding of the query, , each position of is multiplied by the spatial attention map followed by pooling:


Note that the elements of sum up to 1, and thus the attentive embedding is a convex combination of attended in the context of the support. The final embedding of the support is computed similarly by attending the support feature map by followed by pooling:


On an -way -shot classification setting, this co-attentive pooling generates a set of different views of a query, , and a set of support embeddings attended in the context of the query, .

Learning objective.

The proposed RENet is end-to-end trainable from scratch. While most of the recent few-shot classification methods adopt the two-stage training scheme [61, 81, 83, 87] of initial pre-training and subsequent episodic training, we adopt the single-stage training scheme [20, 49] that jointly trains the proposed modules as well as the backbone network by combining two losses: the anchor-based classification loss and the metric-based classification loss . First, is computed with an additional fully-connected classification layer on top of average-pooled base representation . This loss guides the model to correctly classify a query of class :


where and are weights and biases in the fully-connected layer, respectively. Next, the metric-based loss  [75, 66] is computed by cosine similarity between a query and support prototype embeddings. Before computing the loss, we average the query embedding vectors each of which is attended in the context of support from class to compute . Similarly, we average the support embeddings for each class to obtain a set of prototype embeddings: . The metric-based loss guides the model to map a query embedding close to the prototype embedding of the same class:


where is cosine similarity and is a scalar temperature factor. At inference, the class of the query is predicted as that of the nearest prototype.

The objective combines the two losses:


where is a hyper-parameter that balances the loss terms. Note that the fully-connected layer involved in computing is discarded during inference.

5 Experimental results

In this section, we evaluate RENet on standard benchmarks and compare the results with the recent state of the arts. We also conduct ablation studies to validate the effect of the major components. For additional results and analyses, we refer the readers to our appendix.

5.1 Datasets

For evaluation, we use four standard benchmarks for few-shot classification: miniImageNet, tieredImageNet, CUB-200-2011, and CIFAR-FS. miniImageNet [75] is a subset of ImageNet [60]

consisting of 60,000 images uniformly distributed over 100 object classes. The train/validation/test splits consist of 64/16/20 object classes, respectively.

tieredImageNet [57] is a challenging dataset in which train/validation/test splits are disjoint in terms of super-classes from the ImageNet hierarchy, which typically demands better generalization than other datasets. The respective train/validation/test splits consist of 20/6/8 super-classes, which are super-sets of 351/97/160 sub-classes. CUB-200-2011 (CUB) [76] is a dataset for fine-grained classification of bird species, consisting of 100/50/50 object classes for train/validation/test splits, respectively. Following the recent work of [87, 83], we use pre-cropped images to human-annotated bounding boxes. CIFAR-FS [3] is built upon CIFAR-100 [29] dataset. Following the recent work of [3], we use the same train/validation/test splits consisting of 64/16/20 object classes, respectively. For all the datasets, , , and are disjoint in terms of object classes such that .

5.2 Implementation details

We adopt ResNet12 [18] following the recent few-shot classification work [56, 49, 83, 87]. The backbone network takes an image with spatial size of as an input and provides a base representation followed by shifting its channel activations by the channel mean of an episode [87]. For our CCA module, we adopt separable 4D convolutions [82] with kernel size of for its effectiveness in approximating the original 4D convolutions [58] as well as efficiency in terms of both memory and time. The output of the 4D convolution

is normalized such that the entities in the pair of spatial map to be zero-mean and unit-variance to stabilize training. We set

in SCR and in CCA module. For the -way

-shot evaluation, we test 15 query samples for each class in an episode and report average classification accuracy with 95% confidence intervals of randomly sampled 2,000 test episodes. The hyperparameter

is set to 0.25, 0.5, 1.5 for ImageNet derivatives, CIFAR-FS, CUB, respectively. is set to 2 for CUB and 5 otherwise. We set in our experiments.

method backbone 5-way 1-shot 5-way 5-shot
cosine classifier [6] ResNet12 55.43 0.81 77.18 0.61
TADAM [49] ResNet12 58.50 0.30 76.70 0.30
Shot-Free [56] ResNet12 59.04 77.64
TPN [39] ResNet12 59.46 75.65
PPA [53] WRN-28-10 59.60 0.41 73.74 0.19
wDAE-GNN [17] WRN-28-10 61.07 0.15 76.75 0.11
MTL [69] ResNet12 61.20 1.80 75.50 0.80
LEO [61] WRN-28-10 61.76 0.08 77.59 0.12
RFS-simple [73] ResNet12 62.02 0.63 79.64 0.44
DC [37] ResNet18 62.53 0.19 79.77 0.19
ProtoNet [66] ResNet12 62.39 0.21 80.53 0.14
MetaOptNet [32] ResNet12 62.64 0.82 78.63 0.46
SimpleShot [80] ResNet18 62.85 0.20 80.02 0.14
MatchNet [75] ResNet12 63.08 0.80 75.99 0.60
S2M2 [41] ResNet34 63.74 0.18 79.45 0.12
CAN [20] ResNet12 63.85 0.48 79.44 0.34
NegMargin [38] ResNet12 63.85 0.81 81.57 0.56
CTM [33] ResNet18 64.12 0.82 80.51 0.13
DeepEMD [87] ResNet12 65.91 0.82 82.41 0.56
FEAT [83] ResNet12 66.78 0.20 82.05 0.14
RENet (ours) ResNet12 67.60 0.44 82.58 0.30
(a) Results on miniImageNet dataset.
method backbone 5-way 1-shot 5-way 5-shot
cosine classifier [6] ResNet12 61.49 0.91 82.37 0.67
Shot-Free [56] ResNet12 63.52 82.59
TPN [39] ResNet12 59.91 0.94 73.30 0.75
PPA [53] WRN-28-10 65.65 0.92 83.40 0.65
wDAE-GNN [17] WRN-28-10 68.18 0.16 83.09 0.12
LEO [61] WRN-28-10 66.33 0.05 81.44 0.09
MetaOptNet [32] ResNet12 65.99 0.72 81.56 0.53
ProtoNet [66] ResNet12 68.23 0.23 84.03 0.16
MatchNet [75] ResNet12 68.50 0.92 80.60 0.71
CTM [33] ResNet18 68.41 0.39 84.28 1.73
RFS-simple [73] ResNet12 69.74 0.72 84.41 0.55
CAN [20] ResNet12 69.89 0.51 84.23 0.37
FEAT [83] ResNet12 70.80 0.23 84.79 0.16
DeepEMD [87] ResNet12 71.16 0.87 86.03 0.58
RENet (ours) ResNet12 71.61 0.51 85.28 0.35
(b) Results on tieredImageNet dataset.
Table 1: Comparison with the state-of-the-art 5-way 1-shot and 5-way 5-shot accuracy (%) with 95% confidence intervals on (a) miniImageNet and (b) tieredImageNet. “” denotes larger backbones than ResNet12.
method backbone 5-way 1-shot 5-way 5-shot
ProtoNet [66] ResNet12 66.09 0.92 82.50 0.58
RelationNet [70] ResNet34 66.20 0.99 82.30 0.58
MAML [70] ResNet34 67.28 1.08 83.47 0.59
cosine classifier [6] ResNet12 67.30 0.86 84.75 0.60
MatchNet [75] ResNet12 71.87 0.85 85.08 0.57
NegMargin [38] ResNet18 72.66 0.85 89.40 0.43
S2M2 [41] ResNet34 72.92 0.83 86.55 0.51
FEAT* [83] ResNet12 73.27 0.22 85.77 0.14
DeepEMD [87] ResNet12 75.65 0.83 88.69 0.50
RENet (ours) ResNet12 79.49 0.44 91.11 0.24
(a) Results on CUB-200-2011 dataset.
method backbone 5-way 1-shot 5-way 5-shot
cosine classifier [6] ResNet34 60.39 0.28 72.85 0.65
S2M2 [41] ResNet34 62.77 0.23 75.75 0.13
Shot-Free [56] ResNet12 69.2 84.7
RFS-simple [73] ResNet12 71.5 0.8 86.0 0.5
ProtoNet [66] ResNet12 72.2 0.7 83.5 0.5
MetaOptNet [32] ResNet12 72.6 0.7 84.3 0.5
Boosting [15] WRN-28-10 73.6 0.3 86.0 0.2
RENet (ours) ResNet12 74.51 0.46 86.60 0.32
(b) Results on CIFAR-FS dataset.
Table 2: Comparison with the state-of-the-art 5-way 1-shot and 5-way 5-shot accuracy (%) with 95% confidence intervals on (a) CUB-200-2011 and (b) CIFAR-FS. “” denotes larger backbones than ResNet12, and “*” denotes reproduced one.

5.3 Comparison to the state-of-the-art methods

Tables 1 and 2 compare RENet and current few-shot classification methods on four datasets. Our model uses a smaller backbone than that of several methods [53, 17, 61, 41] yet sets a new state of the art in both 5-way 1-shot and 5-shot settings on miniImageNet, CUB-200-2011, and CIFAR-FS datasets while being comparable to DeepEMD [87] on tieredImageNet. Note that DeepEMD iteratively performs back-propagation steps at each inference, which is very slow; it takes 8 hours to evaluate 2,000 5-way 5-shot episodes while ours takes 1.5 minutes on the same machine with an Intel i7-7820X CPU and an NVIDIA TitanXp GPU. We also find RENet outperforms transfer learning methods [6, 80, 38, 73] that are not explicitly designed to learn cross-relation between a query and supports. However, RENet benefits from explicitly meta-learning cross-image relations and is able to better recognize image relevance adaptively to given few-shot examples.

Figure 4:

Learning curves of the GAP baseline and SCR in terms of accuracy (%) with 95 % confidence intervals on CUB-200-2011. The curves for the first 40 epochs are omitted.

SCR CCA mini- CUB ImageNet 65.33 77.54 66.66 (+1.33) 78.69 (+1.15) 65.90 (+0.57) 78.49 (+0.95) 67.60 (+2.27) 79.49 (+1.95) Table 3: Effects of SCR and CCA. id CCA channel sizes mini- CUB ImgNet (a) 65.33 77.54 (b) 65.73 77.75 (c) 1 1 1 65.75 78.05 (d) 64 16 1 66.18 78.10 (e) 1 16 1 65.90 78.49 Table 4: Effects of CCA variants. Figure 5: Effects of the group size in SCR on miniImageNet.

5.4 Ablation studies

To investigate the effects of core modules in RENet, we conduct extensive ablation studies either in the absence of each module or by replacing them with others and compare the results in the 5-way 1-shot setting. For ease of comparison, we use a baseline model called GAP baseline that applies global-average pooling to base representations to obtain final embeddings.

Effects of the proposed modules. Table 3 summarizes the effects of the SCR and CCA modules. Without SCR, the model skips self-correlational learning, replacing its output with the base representation . Without CCA, the model skips computing cross-correlation and obtains final image embeddings by simply averaging either or . Both modules consistently improve classification accuracies on both datasets. From the results, we observe that the effectiveness of CCA is more solid on CUB than that on miniImageNet. As the CCA module provides co-attention from the geometric consensus in cross-correlation patterns, it is particularly beneficial for a task where objects across different classes exhibit small geometric variations. We also experimentally show that the self-correlational representation generalizes well to unseen classes than the base representation does as seen in Fig. 4; the SCR achieves lower training accuracy but higher validation accuracy than the GAP baseline.

Design choices of SCR. To see the effectiveness of channel-wise correlation in SCR, we replace the Hadamard product in Eq. (1) with group-wise cosine similarity in computing a self-correlation and interpolate the group size . Namely, a group size compresses the channels of self-correlation, and becomes equivalent to the proposed method. Figure 5 shows that the self-correlation with , which represents the feature relation as a similarity scalar, is already effective, and further, the performance gradually increases as smaller group sizes are used; the model benefits from relational information, and the effect becomes greater with richer relation in the channel-wise correlation as similarly observed in [88].

Design choices of CCA. We vary the components in the CCA module and denote the variants from (b) to (d) in Table 4 to verify our design choice. In this study, we exclude SCR learning to focus on the impact of the CCA. We first examine a non-parametric baseline (b) by ablating all learnable parameters in the CCA module, , we replace in Eq. (4) with the cross-correlation between and . It shows marginal improvement from the GAP baseline (a), which implies that the naïve cross-correlation hardly gives reliable co-attention maps. Another variant (c) validates that the hidden channel dimension (Fig. 3) helps the model capture diverse cross-correlation patterns. The last variant (d) constructs cross-correlation preserving the channel dimension using Hadamard product instead of cosine similarity in Eq. (3). Although it provides much information to the module and requires more learnable parameters ((d): 797.3K vs. (e): 45.8K), it is not very effective than the proposed one (e) possibly because too abundant correlations between two independent images negatively affect model generalization.

Figure 6: Effects of RENet. (a): Channel activation of base representation. (b): Channel activation of SCR. (c): Attention map of CCA.
Figure 7: Co-attention comparison with CAN [20]. Our CCA better attends to common objects against confusing backgrounds.
method self cross mini- CUB # add.
ImgNet params.
GAP baseline 65.38 77.54 0K
SE [21] ✓(self-attn) 63.34 78.40 83.8K
non-local [78] ✓(self-attn) 65.00 77.11 822.1K
local [54] ✓(self-attn) 66.26 78.19 1644.1K
SCE [23] ✓(self-sim) 63.39 78.43 89.2K
CAN* [20] 65.66 77.77 0.3K
SCR ✓(self-corr) 66.66 78.69 157.3K
CCA 66.00 78.49 45.8K
SCR + CCA ✓(self-corr) 67.60 79.49 203.2K
Table 5: Accuracy (%) and the number of additional learnable parameters of other relation-based methods. “*” denotes reproduced one under a controlled environment for a fair comparison, and underline denotes the best performance among others.

5.5 Comparison with other attention modules

In Table 5, we compare the proposed modules with other attention modules by replacing ours with others. We first compare self-attention methods [78, 54, 21] that attend to appearance features based on feature similarity, while our SCR module extracts relational features based on local self-correlation. In the comparison, SCR outperforms self-attention methods, suggesting the effectiveness of learning self-correlation patterns for few-shot learning. We find that learning such relational patterns of “how each feature correlates with its neighbors” is transferable to unseen classes and compensates the lack of data issue of few-shot learning. While SCR outperforms most methods, it closely competes with SCE [23] on CUB. SCE computes cosine similarity between a reference position and its neighbors and concatenates their similarities at the channel dimension in a fixed order. SCE is powerful on the CUB dataset (77.54% 78.43%) that has relatively little pose variation across images, however, it is disadvantageous on the miniImageNet dataset (65.33% 63.39%). This is because SCE imprints the positional order in channel indices, which limits observing diverse neighborhood relations, whereas SCR uses multiple channels to capture various relations with neighbors.

In Table 5, we also observe that CCA performs better than CAN [20]

as well as other self-attention methods with a reasonable amount of additional parameters. CAN first averages a 4D cross-correlation to a 2D correlation tensor and feeds it to multi-layer perceptrons that produce an attention mask, which is repeated similarly by switching the query and the support to generate co-attention maps. We empirically find that the process of averaging the initial 4D correlation collapses fine and crucial match details between images. Figure 

7 shows two examples that CAN is overwhelmed by dominant backgrounds and hardly attends to small objects. Whereas, the CCA module updates cross-correlations while retaining the spatial dimensions hence successfully attends to relevant objects.

Combining the SCR and the CCA modules, our model outperforms all the other methods.

5.6 Qualitative results

The relational embedding process and its attentional effects are shown in Figs. 1 and 6. The columns (a) and (b) visualize the averaged channel activation of the base representation and the self-correlational representation , respectively. The column (c) visualizes the 2D attention map . The images are randomly sampled from the miniImageNet validation set, and activations are bi-linearly interpolated to the input image size. The results demonstrate that the SCR module can deactivate irrelevant features via learning self-correlation with neighborhood, , the activation of a building behind a truck decreases. The subsequent CCA module generates co-attention maps that focus on the common context between a query and a support, , the hands grasping the bars are co-attended.

6 Conclusion

In this work, we have proposed the relational embedding network for few-shot classification, which leverages the self-correlational representation and the cross-correlational attention. Combining the two modules, our method has achieved the state of the art on the four standard benchmarks. One of our experimental observations is that self-attention mechanism [78, 54] is prone to overfitting to the training set so that it does not generalize to unseen classes in the few-shot learning context. Our work, however, has shown that learning structural correlations between visual features better generalizes to unseen object classes and brings performance improvement to few-shot image recognition, suggesting a promising direction of relational knowledge as a transferable prior.


This work was supported by Samsung Electronics Co., Ltd. (IO201208-07822-01) and the IITP grants (No.2019-0-01906, AI Graduate School Program - POSTECH) (No.2021-0-00537, Visual common sense through self-supervised learning for restoration of invisible parts in images) funded by Ministry of Science and ICT, Korea.


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A Appendix

In this appendix, we provide additional details and results of our method.

a.1 Alternative derivation of relational embedding

Equations (4), (5), and (6) in the main paper describe the process of deriving relational embeddings, and , using pre-computed co-attention maps, and , where the attention maps themselves provide interpretable visualization, , Fig. 1(c) in the main paper. In this section, we derive and in an alternative way of not explicitly introducing the attention maps, and , but multiplying a feature map by cross-correlation, which is used in spatial attention work [68, 13, 62]. Let us denote the normalized cross-correlation tensor in Eq. (4) by


and reshape it to a 2D matrix: .

The relational embedding is equivalently derived by multiplying two matrices and followed by average pooling:


Here, is considered as softly-aligning the query feature map in the light of each position of the support using the cross-correlation .

Likewise, the relational embedding is computed as


a.2 Comprehensive details on implementation

For training, we use an SGD optimizer with a momentum of 0.9 and a learning rate of 0.1. We train 1-shot models for 80 epochs and decay the learning rate by a factor of 0.05 at each {60, 70} epoch. To train 5-shot models, we run 60 epochs and decay the learning rate at each {40, 50} epoch. We randomly construct a training batch of size 128 for the ImageNet family [75, 57] and 64 for CUB [76] & CIFAR-FS [3] to compute . This objective is jointly optimized from scratch with and as described in Sec. 4.4. For a fair comparison, we adopt the same image sizes, the backbone network, the data augmentation techniques, and the embedding normalization following the recent work of [87, 83].

a.3 Ablation studies

We provide more ablation studies on CUB [76] and miniImageNet [75] in the 5-way 1-shot setting.

self-correlation category of mini CUB
computation neighbors ImgNet
✗  (GAP baseline) 65.33 77.54
absolute 66.41 76.34
relative 66.66 78.69
Table a.6: Comparison between absolute and relative neighborhood space in computing the self-correlation tensor .

a.3.1 Self-correlation computation with relative vs. absolute neighbors

We validate the importance of relative neighborhood correlations of a self-correlation tensor in Table a.6. We set such that the two models have the same input sizes for a fair comparison. The results show the superiority of the relative neighborhood correlation. An advantage of the relative correlation over the absolute one is that relative correlations provide a translation-invariant neighborhood space. For example, let us consider a self-correlation between a reference position and its neighbors. While an absolute correlation provides a variable neighborhood space as translates by : , a relative correlation provides a consistent view of the neighborhood space no matter how moves: .

4D convolution mini CUB GPU time
kernels ImgNet (ms)
✗  (GAP baseline) 65.33 77.54 27.74
vanilla 4D [58] 65.59 78.89 60.35
separable 4D [82] 65.90 78.49 34.97
Table a.7: Comparison between 4D convolutions for .

a.3.2 Separable vs. vanilla 4D convolution on CCA

Comparison between the original vanilla 4D convolutional kernels [58] and separable 4D kernels [82] is summarized in Table a.7, where we adopt the separable one for its efficiency. Note that the separable 4D kernels approximate the vanilla kernels by two sequential and kernels followed by a point-wise convolution. The reported GPU time in Table a.7 is an average time for processing an episode and is measured using a CUDA event wrapper in PyTorch [50]. While the two kinds of kernels closely compete with each other in terms of accuracy, the separable one consumes less computational costs.

method 5-way 1-shot # add.
accuracy (%) params
CAN [20] 63.85 0.48 0.3K
RENet (ours) 67.60 0.44 203.2K
LEO [61] 61.76 0.08 248.8K
CTM [33] 64.12 0.82 305.8K
FEAT [83] 66.78 0.20 1640.3K
MTL [69] 61.20 1.80 4301.1K
wDAE [17] 61.07 0.15 11273.2K
Table a.8: Performance comparison in terms of model size and accuracy (%) on miniImageNet.

a.3.3 Number of parameters

We measure the number of additional model parameters of recent methods and compare them with RENet in Table a.8. Table a.8 studies the effect of additional parameters only so we collect publicly available codes of methods that use additional parameterized modules [20, 61, 33, 83, 69, 17], and intentionally omit [6, 32, 38, 41, 66, 73, 80, 87] as their trainable parameters are either in the backbone network or in the last fully-connected layer. Compared to the largest model [17], ours performs significantly better (67.60 vs. 61.07) while introducing 55 times less additional capacity (203.2K vs. 11.2M).

Figure a.8: Accuracy (%) of varying on miniImageNet.

a.3.4 Temperature for co-attention computation

We investigate the impact of the hyper-parameter that controls the smoothness of the output attention map (Eq. (4)). As its name “temperature” suggests, a higher temperature outputs a smoother attention map, while a lower temperature outputs a peakier one. Figure a.8 shows that the temperature has a certain point that maximizes the accuracy by appropriately balancing the smoothness factor. Interestingly, an extremely high temperature degrades accuracy by making all attention scores evenly distributed. It is noteworthy that our full model RENet with a range of outperforms all existing methods on the dataset.

Figure a.9: Accuracy (%) of varying on miniImageNet.
Figure a.10: Effects of SCR on miniImageNet. “CCA w/ SCR” captures fine details between two images while “CCA w/o SCR” often fails. The “base feature map” and “SCR” columns visualize average channel activations. The “CCA w/ SCR” and “CCA w/o SCR” columns visualize co-attention maps.

a.3.5 Local window size for SCR

To evaluate the effectiveness of learning relational features from local neighborhood correlation, we vary the local window size of a self-correlation tensor . As shown in Fig a.9, the accuracy steadily increases as more neighborhood correlations are learned, which indicates that learning relational structures is favorable for few-shot recognition. Note that SCR with already outperforms the GAP baseline, which is an effect of learning from 2-normalized features (Eq. 1). Despite the consistent accuracy gain from observing wide local window, we choose for all experiments to limit the space complexity increased by a factor of .

Figure a.11: Co-attention maps on multi-object queries on miniImageNet. The proposed CCA module can adaptively capture multiple objects in a query depending on the context of each support instance.
Figure a.12: Visualization of cross-correlation on miniImageNet. (a): Top 10 matches in (initial cross-correlation). (b): Top 10 matches in (refined cross-correlation). Unreliable matches are filtered through .

a.4 Qualitative results

To demonstrate the effects of our method, we present additional qualitative results. All images are sampled from the miniImageNet validation set in the 5-way 1-shot setting.

a.4.1 Effects of SCR

We ablate the SCR module and demonstrate the effects of SCR in Fig. a.10. The results show that “CCA w/ SCR” successfully attends to fine characteristics than “CCA w/o SCR” does, implying that the SCR module provides reliable representation for the subsequent CCA module.

a.4.2 Co-attention maps on multi-object queries

Given a multi-object image as a query, we examine if the object regions can be adaptively highlighted depending on the support semantics in Fig. a.11. The CCA module successfully captures query regions that are semantically related with each support image. This effect accords with the motivation of the CCA module, which is to adaptively provide “where to attend” between two image contexts.

a.4.3 Cross-correlation refinement via

We demonstrate the effect of 4D convolutional block that filters out unreliable matches in the initial cross-correlation by analyzing neighborhood consensus patterns. We visualize the top 10 matches among matching candidates computed by of matching scores from each side. As shown in Fig. a.12, the initial cross-correlation exhibits many spurious matches misled by indistinguishable appearance, , matching two regions of the sky, whereas the updated cross-correlation shows reliable and meaningful matches, , matching two sails.