M AHI N ET : A N EURAL N ETWORK FOR M ANY -C LASS F EW -S HOT L EARNING WITH C LASS H IERARCHY
Anonymous
authors
Paper under double-blind review
A BSTRACT
We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning scenarios.
Compared to the well-studied many-class many-shot and few-class few-shot problems, MCFS problem commonly occurs in practical applications but is rarely studied.
MCFS brings new challenges because it needs to distinguish between many classes, but only a few samples per class are available for training.
In this paper, we propose “memory-augmented hierarchical-classiﬁcation network (MahiNet) for MCFS learning
It addresses the “many-class” problem by exploring the class hierarchy, e g., the coarse-class label that covers a subset of ﬁne classes, which helps to narrow down the candidates for the ﬁne class and is cheaper to obtain.
MahiNet uses a convolutional neural network (CNN) to extract features, and integrates a memory-augmented attention module with a multi-layer perceptron (MLP) to produce the probabilities over coarse and ﬁne classes.
While the MLP extends the linear classiﬁer, the attention module extends a KNN classiﬁer, both together targeting the “few-shot” problem.
We design different training strategies of MahiNet for supervised learning and meta-learning.
Moreover, we propose two novel benchmark datasets mcfs ImageNet” as a subset of ImageNet) and mcfs Omniglot” (re-splitted Omniglot) speciﬁcally for MCFS problem
In experiments, we show that MahiNet outperforms several state-of-the-art models on MCFS classiﬁcation tasks in both supervised learning and meta-learning scenarios
INTRODUCTION
The representation power of deep neural networks (DNN) has dramatically improved in recent years, as deeper, wider and more complicated DNN architectures (He et al., 2016; Huang et al., 2017) have emerged to match the increasing computation power of new hardwares.
Although this brings hope for complex tasks that could be hardly solved by previous shallow models, more training data is usually required.
Hence, the scarcity of annotated data has become a new bottleneck for training more powerful DNNs.
For example, in image classiﬁcation, the number of candidate classes can easily range from hundreds to tens of thousands (i.e., many-class), but the training samples available for each class can be less than 100 (i.e., few-shot).
Additionally, in life-long learning, models are always updated once new training data becomes available, and those models are expected to quickly adapt to new classes with a few training samples.
This “many-class few-shot” problem is very common in various applications, such as image search, robot navigation and video surveillance.
Although enormous previous works have shown the remarkable power of DNN when “many-class many-shot” training data is available, their performance degrades dramatically when each class only has a few samples available for training.
In practical applications, acquiring samples of rare species is usually difﬁcult and often expensive.
In these few-shot scenarios, the model’s capacity cannot be fully utilized, and it becomes much harder to generalize the model to unseen data.
Recently, several approaches have been proposed to address the few-shot learning problem.
Most of them are based on the idea of “meta-learning”, which trains a meta-learner that can generalize to different tasks.
For classiﬁcation, each task targets a different set of classes.
Meta-learning can be categorized into two types: methods based on “learning to optimize”, and methods based on metric learning.
The former type adaptively modiﬁes the optimizer (or some parts of it) applied to the training process.
It includes methods that incorporate an RNN meta-learner (Andrychowicz et al., 2016; Li & Malik, 2017;
Ravi & Larochelle, 2017), and model-agnostic meta-learning (MAML) methods aiming to learn a
[Figure]
generally compelling initialization (Finn et al., 2017).
The latter type learns a similarity/distance metric (Vinyals et al., 2016) or a support set of samples (Snell et al., 2017) that can be generally used to build KNN classiﬁers for different tasks.
[Table]
Instead of using meta-learning, some other approaches, such as
Douze et al.
(2018), address the few-shot learning problem through data augmentation by generating artiﬁcial samples for each class.
However, most existing few-shot learning approaches only focus on “few-class” case (e.g., 5 or 10 ) per task, and performance usually collapses when the number of classes grows to hundreds or thousands.
This is because the samples per class no longer provide enough information to distinguish them from other possible samples within a large number of other classes.
And, in real-world problems, tasks are usually complicated involving many classes.
Fortunately, in practice, class hierarchy is usually available or cheaper to obtain.
As shown in Figure 1, coarse class labels might reveal the relationships among the targeted ﬁne classes.
Moreover, the samples per coarse class are sufﬁcient to train a reliable coarse classiﬁer, whose predictions are able to narrow down the candidates for ﬁne classes.
For example, a sheepdog with long hair could be easily mis-classiﬁed as mop when training samples of sheepdog are insufﬁcient.
However, if we could train a reliable dog classiﬁer, it would be much simpler to predict an image as a sheepdog than a mop given a correct prediction of the coarse class as “dog”.
Hence, class hierarchy might provide weakly supervised information to help solve the “many-class few-shot (MCFS)” problem.
1. O UR A PPROACH
In this paper, we study how to explore the class hierarchy to solve MCFS problem in both traditional supervised learning and in meta-learning.
We develop a DNN architecture “memory-augmented hierarchical-classiﬁcation networks (MahiNet)” that can be applied to both learning scenarios.
MahiNet uses a CNN, i.e., ResNet by He et al.
(2016), as a backbone network to extract features from raw images.
The CNN feeds features into coarse-class and ﬁne-class classiﬁers, and the results are combined to produce the ﬁnal prediction according to ﬁne classes as probabilities.
In this way, both the coarse-class and the ﬁne-class classiﬁers mutually help each other within MahiNet: the former helps to narrow down the candidates for the latter, while the latter provides multiple attributes per coarse class that can regularize the former.
This design leverages the relationship between ﬁne classes, and mitigates the difﬁculty caused by “many class” problem.
To the best of our knowledge, we are the ﬁrst to successfully employ the class hierarchy information to improve few-shot learning.
Previous works (Ren et al., 2018) did not achieve improvement by using the same information.
To address the “few-shot” problem, we apply two types of classiﬁers in MahiNet, i.e., MLP and Knearest neighbor (KNN), which have advantages in many-shot and few-shot situations, respectively.
We always use MLP for coarse classiﬁcation, and KNN for ﬁne classiﬁcation.
With a sufﬁcient amount of data in supervised learning, MLP is combined with KNN for ﬁne classiﬁcation; and in meta-learning when less data is available, we also use KNN for coarse classiﬁcation to assist MLP.
In Table 1, we provide a brief comparison of MahiNet with other popular models on the learning scenarios they excel.
To make the KNN learnable and more adaptive to classes with few-shot data, we use an attention module to learn the similarity/distance metric used in KNN, and a re-writable memory of limited size to store and update KNN support set during training.
In supervised learning, it is necessary to maintain and update a relatively small memory (7.2% of the dataset) by selecting a few samples, because conducting a KNN search over all available training samples is too computationally expensive in computation.
In meta-learning, the attention module can be treated as a meta-learner that learns a universal similarity metric for different tasks.
We extract a large subset of ImageNet (Deng et al., 2009) “ mcfs ImageNet” as a benchmark dataset speciﬁcally designed for MCFS problem. It contains 139,346 images from 77 non-overlapping coarse classes composed of 754 randomly sampled ﬁne classes, each has only ∼ 180 images.
Imbalance between the different classes are preserved to reﬂect the imbalance in practical problems.
We further extract “ mcfs Omniglot” from Omniglot (Lake et al., 2011) for the same purpose. We will make them publicly available later.
In experiments on these two datasets, MahiNet outperforms the widely used ResNet (He et al., 2016) in supervised learning.
In meta-learning scenario where each task convers many classes, it shows more promising performance than popular few-shot methods including prototypical networks (Snell et al., 2017) and relation networks (Yang et al., 2018).
M EMORY -A UGMENTED H IERARCHICAL -C LASSIFICATION N ETWORK 2. P ROBLEM F ORMULATION
We study supervised learning and meta-learning given a training set of n samples D
= { ( x i , y i , z i ) } ni =1 , where each sample x i ∈ X is associated with a ﬁne-class label y i ∈ Y and a coarse-class label z i ∈ Z , and is sampled from a data distribution D , i.e., ( x i , y i , z i ) ∼ D .
Here,
Y denotes the set of all the ﬁne classes, and Z denotes the set of all the coarse classes.
To deﬁne a class hierarchy for Y and Z , we further assume that each coarse class z ∈ Z covers a subset of ﬁne classes Y z , and that distinct coarse classes are associated with disjoint subsets of ﬁne classes, i.e., for any z 1 , z 2 ∈ Z , we have Y z 1 ∩ Y z 2 = ∅ .
Our goal is ﬁne-class classiﬁcation by using the class hierarchy information.
In particular, the supervised learning in this case can be formulated as:
[Equation]
where Θ is the model parameters.
In practice, we solve the corresponding empirical risk minimization (ERM) during training, i.e.,
[Equation]
In contrast, meta-learning aims to maximize the expectation of the prediction likelihood of a task drawn from a distribution of tasks.
Speciﬁcally, we assume that the subset of ﬁne classes T for each task is sampled from a distribution T , and the problem is formulated as
[Equation]
where D T refers to the distribution of samples with label y i ∈ T .
The corresponding ERM is
[Equation]
where T is a task (deﬁned by a subset of ﬁne classes) sampled from distribution T , and D T is a training set sampled from D T .
To leverage the coarse class information of z , we write Pr( y | x ; Θ) in Eq.
(1) and Eq.
[Equation]
3) as
[Equation]
where Θ f and Θ c are the model parameters for ﬁne classiﬁer and coarse classiﬁer, respectively 1 .
Accordingly, given a speciﬁc sample ( x i , y i , z i ) with its ground truth labels for coarse and ﬁne
[Figure] x
[Figure]
prediction
[Figure]
N
N
[Figure]
f i f i f i softmax
KNN prediction
M 11 M 21 M 12 M M n 1 M n M 1 m M 2 m M nm a 11 a 21 a 12 aa n 1 a na 1 m a 2 m a nm
S 1 S
S n upd a t e
E q
[Figure]
KNN Classiﬁer
Overview
[Figure]
Memory
Update (
[Figure]
classes, we can write Pr( y i | x i ; Θ) in Eq.
(2) and Eq
(4) as follows.
[Equation]
Suppose that a DNN model already produces a logit a y for each ﬁne class y , and a logit b z for each coarse class z , the two probabilities in the right hand side of Eq.
(6) are computed by applying softmax function to the logit values in the following way.
[Equation]
Therefore, we integrate both the ﬁne-class label and coarse-class label in an ERM, whose goal is to maximize the likelihood of the ground truth ﬁne-class label.
Given a DNN that can produce two logit vectors a and b for ﬁne class and coarse class, we can train it for supervised learning or meta-learning by solving the ERM problems in Eq.
(2) or Eq.
(4) (with Eq.
(6) and Eq.
(7) plugged in).
2. N ETWORK A RCHITECTURE
To address MCFS problem in both supervised learning and meta-learning scenarios, we developed a universal model, MahiNet, as in Figure 2.
MahiNet uses a CNN to extract features from raw inputs, and then applies two modules to produce coarse-class prediction and ﬁne-class prediction, respectively.
Each module includes one or two classiﬁers: either an MLP or an attention-based KNN classiﬁer or both.
Intuitively, MLP performs better when data is sufﬁcient, while the KNN classiﬁer is more stable in few-shot scenario.
Hence, we always apply MLP to coarse prediction and apply KNN to ﬁne prediction.
In addition, we use KNN to assist MLP for coarse module in metalearning, and use MLP to assist KNN for ﬁne module in supervised learning.
In the attention-based KNN classiﬁer, an attention module is trained to compute the similarity between two samples, and a re-writable memory is maintained with a highly representative support set for KNN prediction.
Our method for learning a KNN classiﬁer combines the ideas from two popular meta-learning methods, i.e., matching networks (Vinyals et al., 2016) that aims to learn a similarity metric, and prototypical networks (Snell et al., 2017) that aims to ﬁnd a representative center per class for NN search.
However, our method relies on an augmented memory rather than a bidirectional RNN for retrieving of NN in matching networks.
In contrast to prototypical networks, that only have one prototype per class, we allow multiple prototypes as long as they can ﬁt in the memory budget.
Together these two mechanisms prevent the confusion caused by subtle differences between classes in many-class scenario.
Notably, MahiNet can also be extended to “life-long learning” given this memory updat- ing mechanism.
We do not adopt the architecture used in Mishra et al.
(2018) since it requires the representations of all historical data to be stored.
2. L EARNING A KNN S IMILARITY M ETRIC WITH AN A TTENTION M ODULE
In MahiNet, we train an attention module to compute the similarity used in the KNN classiﬁer.
The attention module learns a distance metric between the feature vector f i of a given sample x i and any feature vector from the support set stored in the memory.
Speciﬁcally, we use the dot product attention similar to the one adopted in Vaswani et al.
(2017) for supervised learning, and use an Euclidean distance based attention for meta-learning, following the instruction from Snell et al.
Given a sample x i , we compute a feature vector f i ∈ R
d
by applying a backbone CNN to x i .
In the memory, we maintain a support set of m feature vectors for each class, i.e., M ∈ R C × m × d , where C is the number of classes.
The KNN classiﬁer produces the class probabilities of x i by ﬁrst calculating the attention scores between f i and each feature vector in the memory, as follows.
[Equation]
where g and h are learnable transformations for f i and the feature vectors in the memory.
We select the K nearest neighbors of f i among the m feature vectors for each class j , and compute the sum of their similarity scores as the attention score of f i to class j , i.e.,
[Equation]
We usually ﬁnd K = 1 is sufﬁcient in practice.
The predicted class probability is derived by applying a softmax function to the attention scores of f i over all C classes, i.e.,
[Equation]
[Equation] UPDATING S UPPORT S ET OF KNN
Ideally, the memory M ∈ R C × m × d can store all available training samples as the support set of the KNN classiﬁer.
In meta learning, in each episode, we sample a task with C classes and m training samples per class, and store them in the memory.
Due to the small amount of training data for each task, we can store all data in the memory.
In supervised learning, we only focus on one task, which is possible to have a large training set that cannot be entirely stored in the memory.
Hence, we set up a budget hyper-parameter m for each class.
m is the maximal number of feature vectors to be stored for one class.
Moreover, we develop a memory update mechanism to maintain a small memory with diverse and representative feature vectors (t-SNE visualization can be found in Figure 4 in Appendix E).
Intuitively, it can choose to forget or merge feature vectors that are no longer representative, and select new important feature vectors into memory.
We will show later in experiments that a small memory can result in sufﬁcient improvement, while the time cost of memory updating is negligible.
During training, for the data that can be correctly predicted by the KNN classiﬁer, we merge its feature with corresponding slots in the memory by computing their convex combination, i.e., [Equation]
[Equation]
where y i is the ground truth label, and γ = 0 .
95 is a combination weight that works well in most of our empirical studies; for input feature vector that cannot be correctly predicted, we write it to a cache C
= { C 1 , ..., C C } that stores the candidates written into the memory for the next epoch, i.e.,
[Equation]
Concurrently, we record the utility rate of the feature vectors in the memory, i.e., how many times each feature vector being selected into the K nearest neighbor during the epoch.
The rates are stored in a matrix U ∈ R C × m , and we update it as follows.
[Equation]
where µ ∈ (1 , 2) and η ∈ (0 , 1) are hyper-parameters.
At the end of each epoch, we cluster the feature vectors per class in the cache, and obtain r cluster centroids as the candidates for the memory update in the next epoch.
Then, for each class, we replace r feature vectors in the memory that have the smallest utility rate with the r cluster centroids.
T RAINING S TRATEGIES
As shown in the network structure in Figure 2, in supervised learning and meta learning, we use different combinations of MLP and KNN to produce ﬁne-class and coarse-class predictions.
The classiﬁers are combined by summing up their logits for each class, and a softmax function is used to generate the class probabilities.
Assume the MLP classiﬁers for the coarse classes and the ﬁne classes are φ ( · ; θ MLPc ) and φ ( · ; θ MLPf ) , the KNN classiﬁers for the coarse classes and the ﬁne classes are φ ( · ; θ KNNc ) and φ ( · ; θ KNNf ) .
In supervised learning, the model parameters are θ CNN , Θ c = θ MLPc and Θ f = { θ MLPf , θ KNNf } ; in meta-learning setting, the model parameters are θ CNN , Θ c
= { θ MLPc , θ KNNc } and Θ f = θ KNNf .
According to Sec. 2.1, we train MahiNet for supervised learning by solving the ERM problems in
Eq.
(2) and by solving Eq.
(4) for meta-learning.
As previously mentioned, the logits (for either ﬁne classes or coarse classes) used in those ERM problems are obtained by summing up the logits produced by the corresponding combination of classiﬁers.
Training MahiNet for Supervised learning.
In supervised learning, the memory update relies heavily on the clustering of the merged feature vectors in the cache.
To achieve relatively highquality feature vectors, We ﬁrst pretrain the CNN+MLP model by using the standard backpropagation to minimize the sum of cross entropy loss on both coarse-classes and ﬁne-classes and then ﬁne-tune the whole model (including the ﬁne-class KNN classiﬁer) with memory updates.
The training procedure of the ﬁne-tune stage is explained in Alg. 1.
[Table]
Training MahiNet for Meta-learning.
In meta learning, the memory is constant and stores features extracted from the support set for KNN classiﬁer.
The detailed training procedure can be found in
Alg. 2.
In summary, we sample each training task by randomly sampling a subset of ﬁne classes, and then randomly sample a support set S and a query set Q .
We store the CNN feature vectors of S in the memory, and train MahiNet to produce correct predictions for the samples in Q .
When sampling the training/test tasks, we allow new ﬁne classes that were not covered in any training task to appear as test tasks, but the ground set of the coarse classes is ﬁxed for both training and test.
Hence, every coarse class appearing in any test task has been seen in previous training, but the corresponding ﬁne classes belonging to this coarse class in training and test tasks can vary.
E XPERIMENTS
We propose two benchmark datasets speciﬁcally for MCFS Problem: [Equation]
, and compare them with several existing datasets in Table 2.
Please see more details in Appendix A.
Our following experimental study focuses on these two datasets.
4. S UPERVISED L EARNING E XPERIMENTS
Experiments on mcfs ImageNet.
We use ResNet18 for the backbone CNN.
The transformations g and h in the attention module are two fully connected layers followed by group normalization (Wu & He, 2018) with a residual connection.
See more detailed parameter choices in Appendix B.
[Table]
Table 3 compares MahiNet with the supervised learning model (i.e., ResNet18) and meta learning model (i.e., prototypical networks).
The results show that MahiNet outperforms the specialized models, such as ResNet18 in MCFS scenario.
Prototypical Net is a meta-learning model designed to solve few-shot classiﬁcation problems.
We train it in a supervised learning manner (i.e., on a single task with many classes and relatively much more samples per class), and include it in the comparison to test its performance on MCFS problem.
Prototypical network fails to solve MCFS problem in the supervised learning scenario.
To separately measure the contribution of the class hierarchy and the attention-based KNN classiﬁer, we conduct an ablation study that removes the KNN classiﬁer from MahiNet.
The results show that MahiNet outperforms ResNet18 even when only using the extra coarse-label information during training, and that using a KNN classiﬁer further improves the performance.
For each epoch, the average clustering time is 30s and is only 7 . 6% of the total epoch time (393s).
Within an epoch, the memory update time (0.02s) is only 9% of the total iteration time (0.22s).
4. M ETA -L EARNING E XPERIMENTS
Experiments on mcfs ImageNet.
We use the same backbone CNN, g , and h as in supervised learning.
In each task, we sample the same number of classes for training and test, and follow the training procedure in Snell et al.
More detailed parameters can be found in Appendix B.
[Table]
[Table]
Table 4 shows that MahiNet outperforms the supervised learning baseline (ResNet18) and the metalearning baseline (Prototypical Net).
For ResNet18, we follow the ﬁne-tune baseline in Finn et al.
To evaluate the contributions of each component in MahiNet, we show results of several variants in Table 4.
“Attention” indicates parametric functions for g and h , otherwise using identity mapping.
“Hierarchy” indicates the assist of class hierarchy.
For a speciﬁc task, “Mem-1” stores the average feature of all training samples for each class; “Mem-2” stores all features of the training samples; “Mem-3” is the union of “Mem-1” and “Mem-2”.
Table 4 implies: (1) Class hierarchy information can incur steady performance across all tasks; (2) Combining “Mem-1” and “Mem-2” outperforms using either of them independently; (3) Attention should be learned with class hierarchy in MCFS problem.
Because the data is usually insufﬁcient to train a reliable similarity metric to distinguish all ﬁne classes, but distinguishing the ﬁne classes in each coarse class is much easier.
Experiments on mcfs Omniglot .
We conduct experiments on the secondary benchmark mcfs ImageNet.
We use the same training setting as for mcfs ImageNet.
Following Santoro et al.
(2016), mcfs Omniglot is augmented with rotations by multiples of 90 degrees.
We do not use
ResNet18 on mcfs Omniglot, since mcfs Omniglot is a 28 × 28 small dataset, which would be easy for
ResNet18 to overﬁt.
Therefore, we use four consecutive convolutional layers as the backbone CNN and compare MahiNet with prototypical networks as in Table 5.
We do ablation study on MahiNet with/without hierarchy and MahiNet with different kinds of memory.
“Mem-3”, i.e., the union of “Mem-1” and “Mem-2”, outperforms “Mem-1”, and “Attention” mechanism can improve the performance.
Additionally, MahiNet outperforms other compared methods, which indicates the class hierarchy assists to make more accurate predictions.
In summary, experiments on the small-scale and large-scale datasets show that class hierarchy brings a stable improvement.
A T WO N EW B ENCHMARKS FOR MCFS P ROBLEM : mcfs I MAGE N ET & mcfs O MNIGLOT
ImageNet (Deng et al., 2009) may be the most widely used large-scale benchmark dataset for image classiﬁcation.
However, although it provides hierarchical information about class labels, it cannot be directly used to test the performance of MCFS learning methods.
Because a ﬁne class may belong to multiple coarse classes, and in MCFS problem, each sample has only one unique coarse-class label.
In addition, ImageNet does not satisfy the criteria of “few-shot” per class.
mini ImageNet (Vinyals et al., 2016) has been widely used as a benchmark dataset in meta-learning community to test the performance on few-shot learning task.
mini ImageNet is a subset of data extracted from ImageNet; however, its data are sourced from only 80 ﬁne classes, which is not “many-class” nor does this carry a class hierarchy.
Hence, to develop a benchmark dataset speciﬁcally for the purpose of testing the performance of
MCFS learning methods
, we extracted a subset of images from ImageNet and created a dataset called “ mcfs ImageNet”.
Table 2 compares the statistics of mcfs ImageNet with several benchmark datasets, and more details of the class hierarchies in mcfsImageNet are given in the Appendix F.
Comparing to the original ImageNet, we avoided selecting the samples that belong to more than one coarse classes into mcfs ImageNet to meet the class hierarchy requirements of MCFS problem, i.e., each ﬁne class only belongs to one coarse class.
Compared to mini ImageNet, mcfs ImageNet is about 5 × larger, and covers 754 ﬁne classes - many more than the 80 ﬁne classes in mini ImageNet.
Moreover, on average, each ﬁne class only has ∼ 185 images for training and test, which is typical
MCFS scenarios.
Additionally, the number of coarse classes in mcfs ImageNet is 77 , which is many less than 754 of the ﬁne classes.
This is consistent with the data properties found in many practical applications, where the coarse-class labels can only provide weak supervision, but each coarse class has sufﬁcient training samples.
Further, we avoided selecting coarse classes which were too broad or contained too many very different ﬁne classes.
For example, the “Misc” class in ImageNet has 20400 sub-classes, and includes both animal ( 3998 sub-classes) and plant ( 4486 sub-classes).
Omniglot (Lake et al., 2011) is a small hand-written character dataset with two levels.
However, new coarse classes appear in the test set, which is inconsistent with our MCFS settings (all the coarse classes are exposed in training, but new ﬁne classes can appear during test).
As a result, we re-split
Omniglot to fulﬁll the MCFS problem requirement and the class hierarchy information are listed in
Appendix G.
B E XPERIMENTAL S ETUP
Setup for the supervised learning.
We use ResNet18 (He et al., 2016) for the backbone CNN.
The transformation functions g and h in the attention module are two fully connected layers followed by group normalization (Wu & He, 2018) with a residual connection.
We set the memory size to m = 12 and the number of clusters to r = 3 , which can achieve a better trade-off between memory cost and performance.
Batch normalization (Ioffe & Szegedy, 2015) is applied after each convolution and before activation.
During pre-training, we apply the cross entropy loss on the probability predictions in Eq.
During ﬁne-tuning, we ﬁx the θ CNN , θ MLPc , and θ MLPf to ensure the ﬁne-tuning process is stable.
We use SGD with a mini-batch size of 128 and a cosine learning rate scheduler with an initial learning rate 0 . 1 .
µ = 1 . 05 , η = 0 .
95 , a weight decay of 0 . 0001 , and a momentum of 0 .
9 are used.
We train the model for 100 epochs during pre-training and 90 epochs for the ﬁne-tuning.
Setup for the meta learning.
We use the same backbone CNN, g , and h as in supervised learning.
In each task, we sample the same number of classes for training and test, and follow the training procedure in Snell et al.
We set an initial learning rate to 10 − 3 and reduce it by a factor 2 × every 10k iterations.
Our model is trained by Adam (Kingma & Ba, 2015) with a mini-batch size of 128 , a weight decay of 0 . 0001 , and a momentum of 0 .
We train the model for 25k iterations in total.
For class hierarchy, the objective function is the sum of the softmax with cross entropy losses on the coarse class and on the ﬁne class, respectively. [Table]
C R ELATED W ORKS
Few-shot learning has a long history.
Before deep learning, generative models (Fei-Fei et al., 2006) are trained to provide a global prior knowledge for solving the one-shot learning problem.
However, with the advent of deep learning techniques, some recent approaches (Wong & Yuille, 2015; Lake et al., 2013) use generative models to encode speciﬁc prior knowledge, such as strokes and patches.
More recently, Douze et al.
(2018) and Wang et al.
(2018) have applied hallucinations to training images and to generate more training samples, which converts a few-shot problem to a many-shot problem.
Meta-learning has been used in attempts to solve the few-shot learning problems.
Meta learning was ﬁrst proposed in the last century (Naik & Mammone, 1992; Schmidhuber, 1987), and ) but has recently seen some signiﬁcant improvements.
For example, Lake et al.
(2015) proposed a dataset of characters for meta-learningn while Koch et al.
(2015) extended this idea into a Siamese network.
A more challenging dataset (Ravi & Larochelle, 2017; Vinyals et al., 2016) was introduced later.
Researchers have also studied RNN and attention based method to overcome the few-shot problem.
More recently, Snell et al.
(2017) is proposed based on a metric learning equipped KNN.
In contrast,
Finn et al.
based their approach on the second order optimization.
Mishra et al.
(2018) uses temporal convolution to address the few-shot image recognition.
However, unlike above methods, our model leverages the class hierarchy information, and can be easily applied to both the supervised learning and meta-learning scenarios.
D C OMPARISON TO V ARIANTS OF R ELATION N ET Relation network with class
hierarchy.
We train relation network with class hierarchy in the similar manner as in MahiNet. The results are shown in table 6. It demonstrates that the class hierarchy also improves the accuracy of relation network by more than 1% , which veriﬁes the advantage of using class hierarchy in other models besides MahiNet. Relation network in high way setting.
For relation network in high way settings, we found that the network is easy to be stuck into a suboptimal solution.
After ﬁrst few iterations, the training loss stays in a high level and the training accuracy stays in a low level.
We demonstrate the training loss and training accuracy for the ﬁrst 100 iterations under different learning rate as Figure 3.
The training loss and accuracy keep the same value after 100 iterations.
E A NALYSIS OF A UGMENTED M EMORY
Visualization.
In order to show how representative and diverse the feature vectors selected into memory slots are, we visualize feature vectors in the memory and the rest image feature vectors in t-SNE in Figure 4.
In particular, we randomly sample 50 ﬁne classes marked by different colors.
Within every class, we show both the selected feature vectors in memory and feature vectors of other images from the same class.
It shows that the small number of highly selected feature vectors in memory are diverse and sufﬁciently representative of the whole class.
Memory Cost.
In experiments of supervised learning, the memory size required by MahiNet is only 754 × 12 / 125321 = 7 .
2% ( 12 samples per class for all the 754 ﬁne classes, while the training set includes 125 , 321 images in total) of the memory needed to store the whole training set.
We also tried to increase the memory size to about 10% , but the resultant improvement on performance is negligible.
In each task of meta learning, since every class only has few-shot samples, the memory
[Figure]
required to store all the data is very small.
For example, in the 20-way 1-shot setting, the memory only needs to store 20 feature vectors
[Figure]
F mcfs I MAGE N ET C LASS S PLITS
The hierarchy of coarse and ﬁne classes is shown below.
Every key (marked in bold ) in the dictionary is a coarse class, the value is a list of the ﬁne classes of this coarse classes.
n02470325 : [n02482650, n02481500, n02483362, n02481103, n02482060, n02481235, n02482474, n02481366, n02482286, n02483708] n01769347 : [n01782516, n01775370, n01772664, n01773797, n01773549, n01774384, n01777304, n01773157, n01778217, n01770081] n12855042 : [n12856479, n12855710, n12855886, n12855494, n12855365, n12856287, n12856680, n12856091] n13109733 : [n11705171, n12717224, n12734215, n12491017, n11710136, n11707827, n12634734, n12711984, n12709103, n12753245] n07806221 : [n07807834, n07808904, n07806774, n07808268, n07808587, n07806879, n07807472, n07808022, n07807594, n07808479] n01428580 : [n02583890, n01447331, n01449374, n02520147, n01439808, n02538562, n01442972, n02543565, n02527057, n01447658] n01789386 : [n01793249, n01790812, n01790304, n01795735, n01815036, n01806297, n01793085, n01796729, n01794344, n01797020] n12582231 : [n12590499, n12597466, n12587487, n12598027, n12595699, n12596148, n12583855, n12587803, n12597134, n12596345] n01816887 : [n01819734, n01819313, n01818299, n01817263, n01819465, n01817346, n01822300, n01821869, n01818832, n01818515] n12724942 : [n12728322, n12731029, n12727518, n12729521, n12726159, n12729729, n12728864, n12730544, n12725940, n12728508] n07802417 : [n07804543, n07802863, n07889193, n07804900, n07804771, n07804657, n07802963, n07803310]
n07882497 : [n07628181, n07861247, n07861158, n07594066, n07628068, n07678586, n07594155, n07679034, n07839478, n07678953] n01940736 : [n01945143, n01953594, n01944118, n01955084, n01947396, n01959029, n01965529, n01960177, n01963317, n01958346] n07911677 : [n07914586, n07915800, n07916437, n07931452, n07918309, n07914995, n07917392, n07918193, n07917133, n07916183] n12864545 : [n12865037, n12866002, n12866162, n12866459, n12865824, n12865708, n12865562, n12866635] n07886572 : [n07887192, n07890226, n07889990, n07887304, n07887967, n07888816, n07890540, n07890068, n07887461, n07888229] n01524359 : [n01561732, n01556182, n01537895, n01561452, n01593553, n01583828, n01539925, n01543632, n01535690, n01538630] n12268246 : [n12278865, n12271933, n12278650, n12277150, n12276872, n12270278, n12276477, n12273344, n12271187, n12270741] n01674216 : [n01682435, n01682714, n01680983, n01689811, n01687978, n01690466, n01678043, n01680655, n01693175, n01689081] n02084071 : [n02088466, n02101006, n02113624, n02091467, n02111277, n02087394, n02102177, n02105412, n02094258, n02106662] n02274024 : [n02305085, n02297819, n02304432, n02277742, n02302244, n02303284, n02281015, n02279972, n02276078, n02282257] n02441326 : [n02443484, n02445171, n02442572, n02446206, n02445004, n02443346, n02450295, n02448060, n02447762, n02449183] n02484322 : [n02488415, n02493793, n02494079, n02493509, n02492660, n02492948, n02487547, n02485536, n02485688, n02490811] n07901587 : [n07906111, n07902799, n07905296, n07904865, n07907037, n07904293, n07905386, n07902443, n07903101, n07902336]
n02801938 : [n02925009, n04024862, n03050864, n03390673, n03883385, n03129848, n02893608, n04204238, n03378342] n12387633 : [n12389501, n12388858, n12390099, n12389727, n12390314, n12388989, n12389130, n12388143] n04576211 : [n04474035, n03235979, n03435991, n02871314, n03193260, n02740300, n03256166, n03173929, n04026813, n04285965] n01661592 : [n01666585, n01664990, n01668665, n01671125, n01669372, n01670802, n01666228, n01669654, n01668892, n01665541] n01627424 : [n01636352, n01646555, n01633406, n01632458, n01654637, n01646802, n01641739, n01641930, n01629819, n01631354] n02131653 : [n02133704, n02133400, n02132788, n02132466, n02134084, n01322983, n02132580, n02134418]
n06271778 : [n06272612, n06276501, n06278475, n06273555, n06274760, n06273294, n06273986, n06273414, n06275471, n06277135] n13100677 : [n12162425, n12828220, n11731659, n11788727, n12513172, n12828379, n11789589, n12383737, n11769803, n12485981] n01726692 : [n01744401, n01738065, n01749939, n01732614, n01737728, n01753180, n01743936, n01733466, n01750167, n01757343] n02394477 : [n02419634, n02414290, n02396014, n02412080, n02405440, n02396427, n02415829, n02395931, n02418465, n02427470] n01604330 : [n01608814, n01611800, n01624115, n01606809, n01623615, n01606177, n01610100, n01609391, n01609956, n01604968] n02373336 : [n02377291, n02391373, n02389026, n02379329, n02378969, n02379081, n02386853, n02379908, n02382204, n02389943] n02898711 : [n04311004, n02775897, n03865557, n04479939, n03415486, n03981760, n04108822, n03233744, n03122073, n02986160] n01976146 : [n01986214, n01983674, n01988203, n01981276, n01984695, n01980166, n01978455, n01978287, n01982068, n01979874] n02062430 : [n02065726, n02071028, n02072798, n02070624, n02065263, n02069412, n02068541, n02071636, n02063662, n02069974] n02075927 : [n02080713, n02081798, n02078738, n02077384, n02077787, n02080146, n02080415, n02079851, n02076402, n02078574] n13112664 : [n12632335, n11948864, n12249542, n12861541, n12905135, n12675876, n12921868, n11865874, n12806015, n12482668] n07829412 : [n07837002, n07837755, n07837545, n07840520, n07838073, n07831267, n07832416, n07840219, n07835921, n07826091] n07892813 : [n07897438, n07898247, n07897975, n07897600, n07899533, n07899769, n07894799, n07894703, n07894451, n07896765] n09366017 : [n09398076, n09454744, n09233446, n09435739, n09452291, n09410224, n09245515, n09415671, n09295946, n09344324] n01480516 : [n01495493, n01484562, n01492569, n01484285, n01500476, n01485479, n01481498, n01489709, n01496331, n01491006] n02974697 : [n02962843, n03031012, n03498441, n03468821, n04570815, n03210372, n04035836, n03986949, n03438863, n04064747] n07927197 : [n07928696, n07928998, n07929172, n07927836, n07928163, n07928578, n07928488, n07927716, n07928790, n07928887] n11545524 : [n13230843, n13181244, n13193143, n13214485, n13231078, n13229543, n12961879, n13190747, n13183056, n12953712] n03206908 : [n03062336, n04130257, n04050933, n04242704, n04263257, n03775546, n02927764, n04499062, n03920288, n02997910] n07596684 : [n07609632, n07601686, n07600177, n07643891, n07604956, n07643200, n07608098, n07609215, n07597263, n07608533]
n07560652 : [n07561590, n07565083, n07562017, n07938007, n07562379, n07565161, n07560903, n07563366, n07564796, n07563207] n07583197 : [n07588817, n07588574, n07584423, n07585557, n07588193, n07588111, n07585107, n07586894, n07586318, n07587618] n13108841 : [n11646344, n11626585, n11656123, n11626826, n11615607, n11644462, n11615387, n11655974, n11622368, n11662371] n02164464 : [n02177196, n02174001, n02173373, n02178411, n02167944, n02175916, n02183096, n02169974, n02180875, n02181724] n13085113 : [n11874081, n11898775, n12003167, n12394118, n11949015, n11965218, n11954161, n11920133, n11919761, n12033139] n02139199 : [n02146879, n02146371, n02146700, n02140049, n02147173, n02147947, n02147328, n02147591] n07907943 : [n07910048, n07910152, n07908812, n07908411, n07910379, n07910970, n07911249, n07908567, n07908647, n07910538] n02188699 : [n02197185, n02195526, n02203152, n02201626, n02198859, n02191979, n02196119, n02202124, n02204907, n02192513] n07843775 : [n07848936, n07847917, n07848093, n07847827, n07848196, n07849733, n07616046, n07847453, n07849912, n07847585] n02121808 : [n02122430, n02123478, n02123045, n02122510, n02123159, n02122298, n02123242, n02122878, n02123394, n02123917] n11868814 : [n11876803, n11876204, n11870747, n11875523, n11879722, n11882074, n11882426, n11877646, n11877193, n11876432] n02552171 : [n02656301, n02580679, n02555863, n02565324, n01451426, n02663211, n02578928, n02654112, n02572484, n02607470] n12997654 : [n13013965, n13075684, n13053608, n13014265, n13013764, n13018088, n13020964, n13011595, n13032618, n13003522] n03764276 : [n04006067, n04308273, n03466600, n04457474, n04308397, n03549199, n03811295, n04487894, n04363082, n03466493]
n09366317 : [n09362945, n09214916, n09230202, n09472597, n09411295, n09421951, n09193705, n09396465, n09269341, n09218641]
n07679356 : [n07682808, n07685218, n07685399, n07682477, n07683039, n07680761, n07690431, n07684938, n07681691, n07681450] n07929519 : [n07919572, n07920872, n07920349, n07919441, n07920222, n07731284, n07919894, n07920663, n07920540, n07921239] n02323449 : [n02324514, n02324431, n02327842, n02324587, n02324850, n02327656, n02328150, n02325722, n02326862] n13100156 : [n12766869, n11724109, n11734698, n12455950, n11723227, n11773987, n11767877, n12935609, n12767648, n12941220] n12334293 : [n12336727, n12338454, n12336224, n12337617, n12316572, n12340581, n12338655, n12340755, n12338146, n12336973] n01909422 : [n01914830, n01917882, n01917611, n01917289, n01915700, n01913166, n01916388, n01909906, n01916481] n01838038 : [n01839949, n01842235, n01841679, n01840775, n01841441, n01839086, n01840412, n01843065, n01839330, n01840120] n02206270 : [n02213663, n02209111, n02213788, n02211627, n02218371, n02221715, n02210427, n02216211, n02221414, n02214499] n07712382 : [n07696625, n07696728, n07696839, n07697313, n07698672, n07865105, n07696977, n07697699, n07698401, n07697408]
n07811416 : [n07935043, n07820960, n07933154, n07816398, n07821758, n07812046, n07818825, n07826340, n07816164, n07820297] n12685431 : [n12686077, n12686274, n12686496, n12686676, n12687957, n12686877, n12687044, n12687462, n12687698] n12101870 : [n12139921, n12140903, n12140511, n12134486, n12123741, n12126084, n12121610, n12117326, n12130549, n12133462]
G mcfs O MNIGLOT C LASS S PLITS
The hierarchy of coarse and ﬁne classes is shown below.
Every key (marked in bold ) in the dictionary is a coarse class, the value is a list of the ﬁne classes of this coarse classes.
Training Hierarchy Classes:
Mkhedruli (Georgian) : [character10, character38, character25, character29, character21, character04, character13, character37, character34, character31, character17, character16, character03, character30, character02, character06, character24, character11, character39, character19, character07, character14, character32, character36]
Alphabet of the Magi : [character18, character05, character17, character03, character08, character01, character15, character07, character09, character10, character19, character11, character20]
Angelic : [character12, character16, character20, character06, character13, character19, character04, character03, character07, character09, character05]
Early Aramaic : [character09, character02, character07, character11, character04, character19, character16, character05, character21, character18, character06, character12, character03, character13, character10]
Old Church Slavonic (Cyrillic) :
[character21, character36, character38, character07, character15, character11, character29, character14, character43, character17, character34, character25, character41, character35, character23, character22, character20, character44, character19, character09, character10, character33, character45, character26, character32] Gujarati : [character05, character44, character06, character35, character40, character45, character07, character29, character12, character09, character24, character38, character46, character15, character32, character21, character18, character25, character04, character02, character23, character03, character31, character14, character34, character20, character37, character43, character30, character36, character26, character08, character28] Japanese (katakana) : [character31, character44, character10, character21, character33, character14, character36, character06, character11, character28, character27, character04, character26, character43, character03, character08, character12, character24, character16, character15, character35, character05, character01, character41, character25, character29, character38, character39, character22, character02]
Syriac (Serto) : [character14, character23, character03, character04, character18, character06, character02, character22, character15, character09] Tengwar : [character21, character19, character15, character13, character03, character11, character16, character10, character18, character05, character14]
Korean : [character03, character14, character35, character32, character04, character19, character15, character33, character01, character28, character09, character40, character16, character07, character39, character34, character37, character11, character36, character24, character10, character05]
Malayalam : [character37, character34, character42, character01, character10, character40, character28, character06, character17, character35, character14, character19, character38, character13, character08, character46, character47, character21, character23, character18, character36, character24, character43, character33, character03]
Japanese (hiragana) : [character44, character05, character13, character19, character31, character40, character24, character50, character07, character11, character06, character01, character32, character10, character46, character04, character47, character45, character27, character42, character36, character09, character34, character49, character12, character28, character37, character26, character23, character52, character38, character17, character25, character30] Atemayar Qelisayer : [character06, character08, character09, character16, character05, character14, character11, [Table] [Table] [Table]
[Table] [Table]
[Table]
Tibetan : [character31, [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table]
[Table]
[Table]
[Table] [Table] [Table] [Table]
: [character03, [Table] [Table] [Table]
[Table]
[Table]
[Table]
[Table]
[Table]
, character14,
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
Jawi - [Table] [Table] [Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
[Table]
] ULOG : [
[Table]
[Table]
[Table]
[Table]
[Table]
, character12,
[Table]
[Table]
[Table]
[Table]
[Table] [Table] [Table] [Table]
- acter19] Blackfoot (Canadian Aboriginal Syllabics) : [character13, character03, character12, character11, character05, character07, character01, character10] Futurama : [character22, character20, character08, character11, character05, character06, character16, character02, character13, character03, character14, character15, character17, character12]
Gurmukhi : [character34, character21, character08, character38, character04, character37, character09, character03, character26, character35, character20, character19, character41, character13, character16, character28, character10, character39, character32, character29, character33, character24, character12, character45, character22, character05] Ojibwe (Canadian Aboriginal Syllabics) : [character08, character04, character01, character12, character13, character11, character03, character10, character05, character02] Greek : [character13, character14, character06, character22, character01, character19, character08, character02, character09, character07, character04, character18, character12, character03] Armenian : [character11, character13, character35, character36, character21, character26, character01, character30, character27, character32, character40, character05, character25, character16, character22, character19, character39, character15, character14, character33, character09] Kannada : [character01, character32, character20, character28, character40, character11, character10, character17, character25, character33, character02, character19, character27, character39, character37, character38, character36, character41, character29, character23, character16, character14, character04, character18, character21, character12, character24, character09] Manipuri : [character04, character20, character24, character32, character02, character09, character33, character30, character14, character29, character16, character05, character34, character03, character13, character12,
[Table]
character10, character18, character15, character22, [Table] Oriya : [character09, character31,
[Table]
- ter45, character27, character05, character07, character11, character23, character15, [Table] [Table] , character44, character32,
[Table]
, character19, character46, character36, [Table] [Table] [Table]
- ter01, character26, character04, [Table] [Table] [Table]
Asomtavruli (Georgian) : [character10, character12, character17, character11, character03, character24, [Table] [Table] [Table]
, character22, character21, character29, character14, character23, character34, character20,
[Table] , character26, character16, character28, character04, character05, character08, [Table] Keble : [character17, character03, character15, character18, character13, character19, character10, character07,
[Table] , character26, character08, character12, character09, character11, character14, character16, character05, [Table] Arcadian : [character09, character10, character03, character16, character26, character04, character08, character18, character23, character02, character14, character22, character05, character01]
Cyrillic : [character33, character26, character01, character11, character08, character24, character22, character10, character04, character27, character07, character09, character06, character18, character20, character19, character21, character12, character25, character29, character32]
Hebrew : [character16, character02, character10, character19, character13, character01, character11, character14, character22, character12, character07, character15, character21, character05] Avesta : [character23, character21, character17, character18, character03, character25, character19, character24, character22, character06, character09, character16, character05, character26, character15]
Glagolitic : [character14, character01, character23, character42, character39, character06, character33, character03, character19, character10, character11, character37, character21, character04, character31, character41, character30, character07, character17, character35, character26, character28, character25, character29]
Ge ez : [character18, character11, character07, character22, character21, character04, character06, character13, character15, character25, character20, character12, character08, character05] Bengali : [character44, character06, character17, character45, character12, character09, character04, character32, character22, character46, character37, character14, character07, character26, character20, character41, character11, character33, character02, character40, character39, character10, character35, character28, character01, character19, character05, character27, character13] Atlantean : [character17, character26, character11, character15, character08, character19, character09, character12, character04, character18, character21, character03, character02, character06, character23] Sanskrit : [character20, character40, character24, character01, character37, character39, character28, character42, character13, character09, character02, character25, character23, character33, character19, character07, character35, character36, character17, character11, character38, character15, character16, character31, character03, character10, character26, character21, character29]
Braille : [character12, character14, character18, character15, character23, character05, character01, character10, character24, character02, character22, character11, character20, character21] Burmese (Myanmar) : [character15, character23, character33, character26, character10, character08, character30, character25, character21, character07, character31, character19, character34, character05, character29, character27, character06, character20, character03, character09, character18, character24, character22, character12] Tagalog : [character05, character14, character04, character03, character12, character15, character10, character09, character01, character17, character11]
Mongolian : [character25, character16, character11, character30, character14, character20, character18, character07, character17, character13, character19, character12, character29, character27, character08, character01, character28, character22, character26]
Inuktitut (Canadian Aboriginal Syllabics) : [character13, character05, character06, character15, character11, character16, character10, character14]
N Ko : [character23, character12, character16, character11, character32, character20, character19, character02, character10, character31, character13, character28, character18, character14, character24, character26, character21, character
[Table]
character19, character34, character05, character21, character16, character23, character37, character04, character28, character03, character32, character10, character43, character40, character48, character17, character44, character49, character06, character20] Grantha : [character39, character13, character12, character33, character35, character15, character16, character27, character20, character19, character30, character26, character42, character22, character23, character03, character02, character07, character38, character40, character25, character18, character08, character37, character32, character24]
Validation Hierarchy Classes:
Alphabet of the Magi : [character16]
Angelic : [character01, character10, character11]
Early Aramaic : [character17, character14]
Oriya : [character14, character40, character10, character21, character33, character39, character12, character41, character16]
Gujarati : [character13, character47, character33, character10, character22] Japanese (katakana) : [character17, character46, character45, character30, character40, character07, character18]
Syriac (Serto) : [character13, character12, character17, character21, character08, character20, character19]
Tengwar : [character09, character06, character22]
Korean : [character25, character29, character26, character38, character06]
Malayalam : [character12, character09, character30, character11, character31, character44, character39, character32, character04]
Arcadian : [character13, character19, character07, character06]
Atemayar Qelisayer : [character18, character24, character25, character22]
Tibetan : [character32, character11, character12, character41, character35]
Sylheti : [character25, character01, character26, character06]
Old Church Slavonic (Cyrillic) : [character16, character28, character01, character12, character40, character42, character39]
ULOG : [character07, character22, character06, character17, character14, character20, character18, character10]
Syriac (Estrangelo) : [character12, character06]
Tagalog : [character08]
Blackfoot (Canadian Aboriginal Syllabics) : [character09, character08]
Futurama : [character25, character10, character04, character26, character24, character19, character01]
Gurmukhi : [character18, character17, character43, character25, character07, character42, character06, character02]
Ojibwe (Canadian Aboriginal Syllabics) : [character06, character09]
Mkhedruli (Georgian) : [character40, character33, character22, character26, character05, character27, character15, character12, character28] Armenian : [character37, character18, character08, character17]
Kannada : [character15, character13, character08, character26, character05, character35, character07, character34, character30] Manipuri : [character06, character36, character11, character27, character38, character26] Anglo-Saxon Futhorc : [character25, character24, character06]
Asomtavruli (Georgian) : [character02, character09, character15, character07, character39, character18, character30]
Keble : [character24, character20, character04, character23, character01]
Japanese (hiragana) : [character22, character02, character33, character41, character14, character16, character51] Braille : [character13, character26, character04, character25, character17]
Hebrew : [character20, character03, character18, character06, character09] Avesta : [character10, character01, character08, character11, character13, character [Table] [Table]
[Table] [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table] [Table] [Table] [Table]
[Table]
[Table] [Table] [Table] Inuktitut (
[Table]
Syllabics) : [character [Table] ter
[Table]
[Table]
[Table]
[Table]
[Table] [Table] [Table] [char
[Table] [Table] [Table] Mkhedruli (Georgian) : [character01, character18, character20, character41, character08, character09, character
[Table]
Alphabet of the Magi : [character14, character04, character13, character06, character02, character12]
Angelic : [character02, character [Table] character
[Table]
character [Table] character15, character18]
Early
[Table]
: [character01, character08, character [Table]
character
[Table]
Oriya : [character30, character
[Table]
character [Table] character17,
[Table] [Table]
, character08, character20, character24, character23, character04, character17, character02, character07, character12]
Greek : [character20, character15, character17, character16, character23, character11]
Sylheti : [character02, character10, character07, character19, character15, character21, character11, character09]
Braille : [character09, character16, character07, character08, character19, character06, character03]
Burmese (Myanmar) : [character01, character16, character11, character28, character17, character04, character02]
Futurama : [character21, character23, character09, character18, character07]
Mongolian : [character02, character09, character06, character05, character21, character04, character10] Inuktitut (Canadian Aboriginal Syllabics) : [character01, character03, character04, character07] N Ko : [character27, character07, character04, character22, character17, character08, character05, character29] Blackfoot (Canadian Aboriginal Syllabics) :
[character06, character02, character04, character14] Balinese : [character08, character10, character22, character16, character21] Aurek-Besh : [character04, character01] Tiﬁnagh : [character12, character53, character51, character46, character55, character25, character22, character14, character47, character01, character27, character29] Grantha : [character10, character34, character29, character04, character05, character06, character43, character36, character28, character09, character41]