Generative vs. Discriminative: Rethinking The Meta-Continual Learning
Authors: Mohammad Amin Banayeean Zade
Rasoul Mirzaiezadeh
Hosein Hasani
Mahdieh Soleymani Baghshah
Venue: NeurIPS 2021 Poster (2021)
Keywords: Continual Learning
Meta-Learning
Meta-Continual Learning
Generative Classifier
Bayesian Classifier
Neuro-Inspired Artificial Intelligence

Abstract: Deep neural networks have achieved human-level capabilities in various learning tasks. However, they generally lose performance in more realistic scenarios like learning in a continual manner. In contrast, humans can incorporate their prior knowledge to learn new concepts efficiently without forgetting older ones. In this work, we leverage meta-learning to encourage the model to learn how to learn continually. Inspired by human concept learning, we develop a generative classifier that efficiently uses data-driven experience to learn new concepts even from few samples while being immune to forgetting. Along with cognitive and theoretical insights, extensive experiments on standard benchmarks demonstrate the effectiveness of the proposed method. The ability to remember all previous concepts, with negligible computational and structural overheads, suggests that generative models provide a natural way for alleviating catastrophic forgetting, which is a major drawback of discriminative models.

Generative vs Discriminative: Rethinking The Meta-Continual Learning
Mohammadamin Banayeeanzade, Rasoul Mirzaiezadeh', Hosein Hasani", Mahdieh Soleymani Baghshah
Department of Computer Engineering Sharif University of Technology
m. banayeean@gmail. com, hasanih@ce. sharif edu, sollymani@sharif..om
mizzaierasoul7@gmai.. com
Abstract
Deep neural networks have achieved human-level capabilities in various learning tasks. However, they generally lose performance in more realistic scenarios like learning in a continual manner. In contrast, humans can incorporate their prior knowledge to learn new concepts efficiently without forgetting older ones. In this work, we leverage meta-learning encourage the model learn how learn continually. Inspired by human concept learning, we develop generative classifier that efficiently uses data-driven experience learn new concepts even from few samples while being immune to forgetting. Along with cognitive and theoretical insights, extensive experiments on standard benchmarks demonstrate the effectiveness of the proposed method. The ability to remember all previous concepts, with negligible computational and structural overheads, suggests that generative models provide a natural way for alleviating catastrophic forgetting, which a major drawback of discriminative models. The code publicly available at htttt::///// //tt:::///ttttt giihh........ com/ wwwaammaaaGeeCCCC.
Introduction
Deep learning methods have gained great success in wide variety of tasks in various fields [26 28 However, in many real-world scenarios, where the data samples are neither i.i.d. nor available all at once, most of them lose performance the older data points; phenomenon known catastrophic forgetting [3 Continual learning, also called lifelong learning, aims to tackle this problem (48).
Animals intelligent learning agents easily learn sequence of different tasks with minimum interference and forgetting [55] When facing new problems, the brain does not rewire of the wirings 37 5] but utilizes lifelong accumulated inductive biases to efficiently learn new concepts 4. In the field of cognitive and neuroscience, there exist two special cases concept learning named prototypical and exemplar-based learning 44 59 77. Bayesian inference is another aspect of learning in the brain which aims to consider uncertainty [24 16 23 this paper, we integrate the hypothesis of generative concept learning and the Bayesian approach by considering a distribution over each concept. Figure[]compn compares different characteristics and expressive power of the mentioned concept learning approaches. Inspired by the biological mechanism of learning, we suggest that the generative approach in category learning is an important principle for continual learning problems. Although the Bayesian approach requires proper priors about each concept,
Equul contribution
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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Exemplar
Prototypical
Bayesian
Figure 1: A simple schematic of exemplar-base based learning (left), prototypical- based learning (center), and the proposed Bayesian approach (right). Exemplar- baasld learning suffers from high memory consumption and also the risk of overfitting, like I-NN classifiers. Prototypical-basee learning is memory efficient but also prone to underfitting- Our probabilistic approach enables using complex enough distributions over each category to capture class variations.
meta-learning can be used to provide data-driven prior knowledge or statistics from the previously encountered concepts similar to the biological intelligent systems [4).
Meta-learning is an endeavor gather experience from solving related problems in order solve new unseen ones more efficiently; which have been used to improve the learning process in different areas [9]. In this work, we employ meta-learning to derive proper inductive biases as well a powerful feature extractor for a continual learning problem from a collection of similar continual learning problems. By taking advantage of these inductive biases, we formulate the category learning problem from probabilistic generative approach. Our main contributions are as follows:
We take motivation from cognitive and neuroscience about meta-continual learning in intelligent animals and especially make use of bio-inspired concept learning to eradicate catastrophic forgetting.
We investigate the problem of discriminative approaches in continual learning and propose generative classifiers as a general way of mitigating catastrophic forgetting.
Encouraged by generative classifiers, we propose a new discriminative classifier called PGLR, to reduce the inherent catastrophic forgetting problem of discriminative approaches.
Existing prototypical learning is improved by adding extra statistics through the Bayesian approach.
Different components of the proposed method can be implemented in fully incremental setting which is useful in the shortage of data or computational resources.
We achieve state-of-the-art accuracy with notable gap compared to the existing methods.
2 Related Works
Continual Learning: Three main approaches have been proposed to address the forgetting issue
333 (i) Replay-baan based methods rely on reusing samples from previous training tasks either by keeping
them in an explicit episodic memory [30] 36 6 [ or generating pseudo-samples via deep generative
model 4 53 50
(ii) Methods based on parameter isolation dynamically expand the model as
the data for new tasks arrive by introducing task-specific weights 40. 57 42 masks (22 58) (iii)
Regularization-bast based methods consider probability distribution, typically the Gaussian family, over parameters and penalize the substantial deviations from the prior distribution learned through the earlier tasks. Taking a Bayesian approach will Iead to an incremental posterior update which is naturally consistent with continual learning (32), while considering point estimation for the
parameters will result in a regularization term in the objective function 45
60) 22]. Besides
theoretical foundations, simplifying assumptions and approximations often make the regularization-
based methods fail when the number of tasks is large and they are more prone to catastrophic forgetting compared to the first two approaches [49].
Compared to the first approach, merely storing low dimensional sufficient statistics of categories, makes our model extremely memory efficient and applicable even when there are thousands of tasks or categories. However, our method more related to the second approach in the sense that we isolate class-specific parameters. Like the Bayesian methods (32), we also consider distribution over

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parameters. Nevertheless in our method, using generative classifiers and restricting the distribution to the class-specific parameters enables exact closed-fome solutions with zero forgetting.
Most of the existing continual learning methods use a discriminative approach but there exist some prototypical or exemplar-based models which are related our method in the sense that they utilize a generative approach for final classification [36]. However, they are not completely immune forgetting and also less memory efficient since they store a considerable number of high-dimensional input examples.
Meta-Learning: Existing methods in the literature of meta-learning can be categorized into optimization-based [T0] 351, black-box 4Т [4], and metric-based [46, 47 [6]] approaches. In this paper we use metric-based methods that meta-learn an embedding space in which metric-based classifier performs well. Some methods called Bayesian meta-learning approach the problem from probabilistic point of view, obtaining a distribution over the problem-specific parameters, therefore capable of providing information about the uncertainty of learned model [15] [I [54]. We also
provide a probabilistic framework capable of using various statistics of data and learnable prior distributions.
Meta-Continual Learning: Both continual and meta-learning have mutual impacts on each other, introducing two new research branches [8]: Continual meta-learning (18 21 and meta-Continual learning 17 38 20 3J. In the second branch, various techniques from meta-learning are used to tackle catastrophic forgetting. Here, especially focus the settings in which explicit episodic meta- meta-training on continual problems is used [20] 31. OML [20) meta-learns a representation network to avoid interference between the continual tasks and reduce the catastrophic forgetting. ANML B also takes the same approach but instead of merely having a representation network, it generates a data-dependent mask that modulates the activity of neurons in the prediction network.
Motivated by them, we utilize episodic meta-learning to tackle the continual learning problem, but instead of having discriminative approach, propose probabilistic generative method that is completely immune to forgetting. Our approach falls into metric-based meta-learning, as opposed to the prior methods that are optimization-based 20
3 Preliminaries
Meta-Learning: In the meta-learning setting, we have access to a set of meta-training problems D Pmeta-train which help learn a prior knowledge and thus generalize unseen problems with data from D mestatess Each problem is pair of support and query sets, i.e. (S, Q), and labels from mmetta-tain do not intersect with the labels D metts-css. The mentioned prior knowledge can be encoded in the meta-pant mota-parameters which is utilized by a problem-specific model parameterized by á to solve new problem instance, The overall learning procedure of the meta- meta-parameters can be formulated as [1]
0 argmax log P(0 D meta-tminn
And the distribution of the mrblem-speccffe parameters, given support set S, can be formulated -oo P( S,0) (0 D Dreet-train d0
P (6) S, Deeet-trann
2 P 0) (0*) 'D Dmettatmii P ( S,0*).
While some works model this distribution, others use point estimate as:
argmax log P (g) 8,
Meta-Continual Learning: meta- meta-learning scenario where each individual problem (S, Q) is continual, i.e. the support-se" set observed continually, is called meta-continual learning. We consider support stream as = (S,, ..., S.,..., ...), in which S, {(*), yf) | data point and the corresponding label in S, respectively. Each S, is accessible only at time-step t due to continual learning restriction. The query-set labels as those in S. The objective here is to perform well Q after sequentially observing all of
[S.] and the of and yf are the ith
set of samples sharing the same set of
3

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0
0
No
Ko
Φ
te)
2
Ba
X
Z
Figure 2: Graphical models for the discriminative (left), generative (center), and our (right) approach.
the samples available in S. We use the notation Sx and Sy for the data points and their labels in S respectively, and the same holds for Qx and Qy Furthermore Sx shows the data points with the label y = e available in S, i.e. S (x](xx, e) E S).
In this paper, we consider a model immune to catastrophic forgetting if the accuracy and decision boundaries of the model in continual learning and i.i.d. scenarios remain identical.
In the lifelong-learning literature, each S; is called a learning task which may contain the data points and corresponding labels for multiple classes. With this in mind, three standard benchmarks are introduced for evaluation: taak-nncremettl, benchmark is known as the most difficult in which each class is only observed in a single task while at the test-time the model is expected to classify across all observed classes from all tasks [49]. However, proposed method is completely agnostic to the order in which data samples arrive and produces the same model, even in an extreme setting that we refer to as fully incremental. In this setting, only one sample is available at each time step and each data point is visited exactly once. In fact, the only assumption in this work is that the samples with the same label in S are i.i.d., namely P(S*) Heess-((r))
inmmainincremmentl, and class inseemmacceet...... The latest
4 Method
Although recently meta-learning representations for continual learning have been introduced to alleviate the catastrophic forgetting [20] 3], these methods still greatly suffer from catastrophic
forgetting. One probable reason is that they have constructed their methods based on discriminative approaches. Meanwhile, it is reported that the human brain benefits from generative approach
in category learning [4 2 59 7 and this raises the question of whether humans capabilities in continual learning stems from their generative approach the problem. While further studies by the neuroscience community are needed to investigate the exact relationship between biological category learning and the forgetting concept, here we provide some theoretical insights which shed light on the topic. In the following subsections, we elaborate on this by first discussing the drawbacks of the existing meta-continual learning methods which originates from their discriminative nature. Then, we show how the generative approach can resolve the catastrophic forgetting problem of meta-continual learning and finally, the proposed generative model for continual learning is presented.
4.1 Generative vs. Discriminative Approach
Probabilistic classifiers generally can be categorized into (1) Discriminative and (2) Generative models where they respectively model P(Y X), and P(X Y), demonstrated by Figure
Given classification problem S (SSx, Sy), the discriminative form of Equation 2 is:
p( Sx. Sy. 8*) x P(Sy SP()) 0*).
(4)
In continual-learming settings, there is partial access to S each time step, therefore the learning agent is prone to catastrophic forgetting. To clarify this, assume a class-incrent incremnarem setting, where at each time step, the data only one class accessible trivial solution for each time step / (assuming uninformative prior P( (0') is model that assigns high probability the currently available label even for samples from other categories. Therefore, the solution for each time step works poorly other time steps.
all the parameters are updated. Here,

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100.0%
50.3%
90.9%
97.7%
97.4%
57.2%
97.2%
POUR
100.0%
90.9% 94.7% 95-4% 93.5% 83.0%
82 90
Figure 3: Comparison of discriminative and generative approaches on toy dataset in continual and i.idd scenarios. The first and second rows show the results of a Gaussian naive Bayes classifier and logistic regression as generative and discriminative classifiers respectively. The last row shows the performance of the described PGLR model. The average accuracy on all observed classes, current class samples, and the decision boundaries of each model are shown from the first to the sixth column. The last column shows the performance of each model in the i.i.d. batch learning setting.
The other choice for classifier formulation is the generative model which can be formulated as follows:
P(ś
0*) x P(Sx o, Sy 0*).
In this approach, there is interference between learning of different classes and hence it does suffer from forgetting. In fact, at each time step. only the parameters of those classes visited at that time step are changed and parameters other classes are neither utilized nor updated. With this in mind, the following theoretical statements are presented:
Statement 1. In the iaasseincrementll scenarios, the generative classifiers immune forgetting. given any class conditional parametric distributions.
In the fully incremental scenarios, the generative classifiers immune forgetting, the class conditional distributions have eeeementally-updataae sufficient statistics. the case of Bayesian inference, this condition is satisfied if class conditional distributions have conjugate priors.
Statement 2.
To provide more insights, here we compare Gaussian naive Bayes classifier (NB) and logistic regression (LR) common generative and discriminative classifiers on continual learning problem. We also implement pseudo-generative version the LR classifier (PGLR) to reduce the forgetting problem which is an inherent characteristic of the LR classifier. In the PGLR model, only the class- specific parameters are updated during optimization and the others remain frozen (see supplementary materials). Class-specific updates make the PGLR classifier prevent interference of tasks during learning. As shown in Figure 3 unlike the discriminative model, the generative models are immune forgetting and there is no difference between the accuracy and decision boundaries of the continual (sixth column) and i.i.d. (seventh column) scenarios.
step closer to generative models and
4.2 Proposed Model
As mentioned, generative classifiers are suitable for continual learning problems. However, the main challenge here is that training a reasonably expressive feature extractor is not straightforward in fully generative manner. Hence, we employ meta-learning to tackle this challenge and propose generative meta-continual learning (GeMCL) method. Like OML 20, we use feature extractor network (X): X > "d parametrized by v. that embeds the input into proper d-dimensional representation space. However, inspired by the biological mechanism of concept learning, we incorporate generative Bayesian classifier instead of using a discriminative one. Indeed, to have tractable generative model, proper representation space is first prepared by the embedding function and the optimal weights for this function are obtained via meta-training procedure. Then, the hypee-parameters of the generative model in this space computed based on D Dmcta-trann
5

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M
12
Sc+1
St
fup
72
2 88
71
23
11
2n
#
x
fup
Q
Z1
Figure 4: The overall procedure of a continual episode GeMCL, demonstrating learning of the classifier parameters as the support data arrives (top), and classification of query samples given the learned class distributions (bottom).
In the meta-test phase, the generative model on the test classes is formed using incrementally arriving samples in the embedding space and the meta-learned hyper-parameters. In this phase, same as the previous works (20 3], the embedding parameters vú are fixed. Moreover, in the prior continual learning works, it was investigated that the early representation layers less responsible for forgetting, and remain nearly unchanged even after training for new tasks (34). In fact, even pretrained feature extractor along with a generative classifier outperforms the previous meta-continual models that are discriminative. We will investigate this more in Section 5
4.2.1 Bayesian Generative Model
To derive a generative model, we need to choose a parametric family of distributions in the d- dimensional embedding space. We choose a Gaussian distribution to model each P(z Y = c) where = fo (X) e Rd. In this generative model, we introduce μº Rd A Rd as the mean and precision of the class conditional Gaussian distributions respectively:
VIsesoP Y=ly=c,phie (1:0) =N ps, d
(6)
where C' denotes the number of observed classes, 4 2. = {ur ... S and X = (X),
are the set parameters for Gaussian distributions. To obtain a Bayesian perspective, we consider Normal-Gamm prior for the mean and variance of each class:
P (nf X2 co, Bo, No. mo) x I N (og no, (NO Ga (A9 ao. 80)

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where ag. Su Ko, ff are the sapam--arameters of the generative model. Now, given the support set of each class in the embedding space, i.c. (5x if (z) Vr E Sx). the posterior and the predictive distributions are in the form of
and student's t-distribution respectively:
P P( X fx((x)) coo Sn Ko. Ma) II N (ng ph.g (KEA))))) Ga (Ag o Bn.))
(8)
(ny + +1] o
II 120 (2) (2)1
( fx(()) or, 9o. Ko. po)
=
where of, S..j K Png are the posterior parameters after observing n samples of the class More specifically, by considering the first two moments of the Gaussian distribution as the incremental sufficient statistics, we can formulate the mentioned parameters as:
n = 15%, En. no (EE
E
-- +
n
(n 11)-))--111 + Tn.j 1 [
(10)
Kyn = Ko + n phi +n Frid
NT.
a = 0g 2: n.j = 8o (7n.. (2%,,) ) +
Kon ( (HO)
2(xo+n²)
Therefore, at the test time, suffices to merely store the first and the second-order moments and compute the above posterior parameters for each class separately (refer to Figure 4). These moments can be updated incrementally as each sample arrives, and consequently, this model has zero forgetting based on SStatemen 2
is noteworthy that all continual learning algorithms have to somehow support the new incoming classes, hence they have the obligation to expand the classifier parameters. While some of them mention this issue directly [36], others may consider an upper bound on the number of classes [20]. Compared to their methods, approach has assumption on the maximum number of incoming classes, making it flexible for unknown length sequence of classes.
Using Equation 3 we also propose a method called GeMCL-MAP, which uses MAP estimation for the mean and precision of the Gaussian distributions instead of the predictive distribution:
PMAP, AAAP argmnaxP (p5,X X (S ao, So, Ko. No) = ph A
0
BE
(11)
( fo( ap, 3o, Nig Mo) Rz N PMAP. (AMAA))
In order adjust the hyperparameters for the prior distribution, chose f4n 0 and Ain 0 to provide a flat prior distribution for (s. or 3n are meta-learned as described in the next section.
4.2.2 Meta-Training And Meta-Testing
Following the previous meta-learning works, we first use episodic meta- meta-learning to train the parame- ters of the embedding network. Although we consider generative model in the embedding space, in the meta-training phase the embedding function itself is trained using discriminative objective to avoid trivial solutions like fxf c. So using the generative forms presented in the previous section, we write the cross-entropy loss for single episode as:
((bb) = E( log P (y fe(z), Sy, 00, 36)
PIe. = Ei log P(fo(=)) ).0.
=- log ΣS=
De_ (x) (S (SQ) ).00%))
(12)

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Here, dg and Po are two hyperparameters that define the shape of prior Gamma distribution for the precision parameter. During the meta-training, we set them to large values to better regularize the contractile behavior of embedding samples by imposing high variance on the embedding space of each category. Before the meta-testing phase, we calculate within-category variances of meta-train data embeddings and then use the obtained distribution to infer the amount of og and Po by maximum likelihood estimation (see supplementary materials for more details).
Finally, in the meta-lesting phase, we use estimated &g and 30 for the prior distributions and update the class-specific posterior parameters as the support stream arrives. Then, classify a query data point, we use i = argmaxP (f a PM P% (%)) as the predicted label.
5 Experiments
We have performed our experiments on Omniglot [27], Mini-ImageNet [51], and CIFAR- 100 [25] datasets. For all these datasets, we used the backbone proposed in [46] with an input size of 84 x 84, which uses less than 115K parameters compared to more than 2.9M ones in the prior works 20) This backbone is meta-trained to maximum of 20K for Omniglot and 30K for Mini-ImageNet, and CIFAR- 100 datasets and the best performing model is selected using carly stopping. The training is done with learning rate of 0.001, decaying to half every 0.1 of the training length.
The Ominglot dataset commonly used in the meta-learning literature, containing 1623 classes of handwritten characters each with 20 samples. We use 763 and 200 classes for meta-train and meta-validation respectively, and others for meta-test. The reported experiments are done using 20-way 5-ohot train episodes and 200-way 15-shot validation episodes with 15 and 5 query samples respectively.
The Mini-ImageNet dataset is a subset of the ImageNet [39]. originally proposed for evaluating few-shot learning algorithms [5]]. The dataset consists of 100 classes with 600 samples for each class and is divided into 64, 16, 20 classes for train, validation, and test meta-phases respectively, For this dataset, used 20-way 10-shot and 20-way 30-shot train and validation episodes respectively with 30 query samples for both. We apply horizontal flip and random crop augmentations during meta-training.
The CIFAR-100 dataset, contains 100 classes with 500 train and 100 test samples for each class. Following recent work [29 we use 70 and 30 classes for meta-train and meta-test phases respectively. We use 10-way 10-shot episodes with 30 query samples for meta-training on this dataset.
For further insights, we introduce the following baselines in addition to the mentioned prior meta- continual learning methods (OML and ANML).
We implement fully discriminative baseline similar OML methodology but incorporating the simple backbone used in the other baselines. Moreover, some implementation details of OML are omitted in this baseline, to purely compare different aspects of our proposed methods (refer the supplementary materials for details).
Meta-Tres Trained Logistic Regression (MTLR):
Pseudo-Generativ Logistic Regression (PGLR): This method was introduced in Section 4.1 to limit the amount of forgetting in the discriminative settings. This baseline can be obtained by applying two modifications to MTT.R: (i) To compute the logits, the class-specific weights are normalized before dot- pro-production. (ii) During the optimization, instead of updating all weights of the classifier head, only the weights corresponding to the available sample are updated (see supplementary materials).
This method was originally introduced for few-shot classification 446]. Here, we employ this approach for the meta-continual learning scenarios. Indeed, this model is special case of our proposed method by choosing a unit-variance Gaussian model, and completely omitting the prior distributions in Section 4.2.1 and merely using the maximum likelihood estimation instead.
Prototypical:
Pretrained: To clarify the impact of meta-training on different models, we pretrain the same backbone and replace it with the meta-trained feature extractors in some experiments.
8

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Orsreggut (First Cins Accuracy!
Oreiigitt (Average Acceracy)
CHAR1109 (Average Accuracyl
GoNCCL
MUL
AMPS
OME
35
OLMC
FSL1
NGL
ANML
ICC
200
300
400
300
300
350
530
Figure 5: Effect of increasing the number of classes in Omniglot dataset measured based the first seen class accuracy (left) and the overall accuracy (middle). Similar behavior for the average accuracy can be observed in CIFAR-100 dataset when the number of classes increases (right).
Mine- imagenet (Averape Acceracyl
Mini Iww.annttttttttommcooooooo.ee..e Accuracy)
imagenet (Averrage Accuracyl
C2
pTTAA
CenOo.
PV--A.
HTU)
Num. Classec
Num Shate
350
Num. Shoft
Figure 6: Effect of increasing the number of classes (left) and the number of samples per class (middle and right) in Mini-Imagenet dataset. The latter effect is measured on both the overall performance (right) and the performance on the first seen class (middle).
5.1 Results
In Figure 5 and we evaluate our baselines, proposed methods, and two previous meta-continual methods from different perspectives. As shown, GeMCL outperforms OML and ANML by large margin on both datasets. This margin grows as the length of continual problems increases. In fact, when observing more classes, the catastrophic forgetting causes more notable performance drop in the discriminative models. Comparing the first class accuracy during test episodes, gives even better insights on the forgetting issue, as the earlier seen samples are more likely to be forgotten. Specifically. the comparably small performance loss of the generative models (GeMCL and Prototypical) due to generalization issues rather than forgetting. Another way of enlarging the problem size is by observing more samples for each class. While more support data is expected to enhance the performance, forgetting issue causes lower accuracy in OMI. However, as the generative models do not suffer from forgetting, they perform even better in higher shots. Note that ANML and OML are very sensitive to the value of the inner-lcarning rate and tune it for each different episode setup (see supplementary materials). This results selecting significantly small learning rates for longer episodes which trades better learning of each individual class for lower forgetting.
The prototypical baseline performs pretty well compared to the discriminative models, but its lower performance compared to GeMCL shows the effect of using additional statistics and trainable prior distributions, especially with more shots or classes the performance gap increases. mentioning that the PGLR model also considerably resists forgetting while being less sensitive to learning rate value. This reflects the potential benefits of the proposed pseudo- -ennr-iveeeraivee approach compared to discriminative ones.
worth

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Table 1: The performance of the MTLR (diseriminative), PGLR sereuudo-geerative). and GeMCL
(generative) methods in their original meta-learning approach compared with their performance when using pretrained feature extractor. All of the models are evaluated on Mini-Imagenet with 20-way 100-shot settings and Omniglot dataset with 600-way 15-shot settings.
Head for Pretrained Backbone
Meta-train
Dataset
Mode
MTLR
PGLR
GeMCL
MTLR
PGLR
GeMCI.
Continual
32.8+a.1
54.241.
55.9
31.1
53.2
59.220.0
Mini-Imagenet
IID
60.9
55.8
55.9
48.9a
57.0
59.2
Continual
23.61o.7
61.0
75.9
61.9
72.8
86.910.
Omniglot
IID
77.8
74.2+0.a
75.9
82.9
86.8
86.9
The i.i.d. and continual settings are compared in Table showing that generative approaches are more robust to accuracy fall in continual learning. The performance of GeMCL is also superior to most of the baselines even in the i.i.d. settings. Furthermore, The results of using a pretrained feature extractor compared to meta-training show that GeMCL properly utilizes meta-learning to achieve better performance, which is not the case for MTLR and PGLR in some settings.
Discussion
In the present study, inspired by neuroscience, we propose probabilistic generative classifier that is completely immune to catastrophic forgetting. Meta-learning makes training a deep generative classi- fier feasible and provides rich feature extractor as well as prior knowledge about hyperparameters. Using this feature extractor, the proposed lightweight generative classifier achieves high accuracy for new unseen continual learning problems. It noteworthy that our proposed method meta-learns hyperparameters on the meta-train dataset, and uses the same values for all meta-test episodes, while the optimization-basee methods require inner learning rate tuning for various settings at test time. Moreover, we extend our approach to discriminative classifiers by introducing a pseudo- generative model which not only less sensitive to inner-learning rate but also notably more robust to forgetting.
Our proposed method is efficient in different aspects: First, the employed backbone is light and overall computations negligible compared the current deep learning methods other meta-continual learning approaches. Opposed to the previous meta-continual methods our proposed method does not second-order optimization and is more computationally efficient by design. Second, our method is scalable and memory-efficient in the sense that it does not store data samples, in contrast to the memory-based continual learning methods [30] 36).
The proposed method has three main components which are basically inspired by neuroscience. First, the generative approach makes method immune forgetting. Second, meta-learning facilitates generative continual learning by providing a two-stage learning framework: slow learning in which backbone parameters and prior distributions meta-trained, and fast learning in which class-related parameters are learned. Third, the Bayesian approach improves the performance and interpretability of the model by considering uncertainty.
In this paper, we have focused on solving some principal problems with existing meta-continual methods. However, there still exists some shortcomings which need to be addressed. These methods require a meta-train dataset to train a good embedding network which is not always available in some applications. Additionally, during the meta-testing, the embedding function does not adapt to new samples. This property offers protection from catastrophic forgetting, but it reduces the forward and backward transfer capabilities which are additional desired properties for continual learning methods. Furthermore, freezing the backbone may reduce the generalization capability that affects the overall performance, especially in scenarios that the number of continual tasks is limited and forgetting not a major issue. Enabling further training of backbone during the meta-test phase could be a valuable direction for future studies. Especially, combining the other continual learning methods with the proposed method can offer forward and backward transfer in the meta-test phase and provide a desired trade-off between catastrophic forgetting, memory usage, and knowledge transfer.
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13


Reviews:
[{"review_id": "xU1pucWDV5", "reviewer": "Reviewer_vJhk", "summary": "This paper proposes a probabilistic generative classifier that is immune to catastrophic forgetting. The proposed lightweight generative classifier achieves high accuracy for new unseen continual learning problems.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "[Strengths] \n\nThe writing of the article is very good.\nThe method have achieved relatively high classification accuracy. The method of experimental comparison is comprehensive.\n\n[Weaknesses]\n\nIn line 140-141, why the generative model is completely immune to catastrophic forgetting, needs a deeper explanation.] ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors adequately addressed the limitations and potential negative societal impact of their work.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}, {"review_id": "gMlkWESd1uK", "reviewer": "Reviewer_TJWB", "summary": "The authors propose the generative classifier for meta continual learning. This approach is an extension of a well-known method for few-shot learning called prototypical networks. The proposed method is evaluated on two challenging continual learning datasets (Omniglot and MiniImagenet) and compared to other methodsin this field as well as adequate baselines. \nThe main contributions of the paper can be summarized as:\n- The introduction of the new method for continual learning using the generative classifier. \n- Clearly explained and visualized with toy example the difference between catastrophic forgetting in case of generative and discriminative classifiers.\n- Precisely formulated and justified statements about immunity to catastrophic forgetting.\n- Insightful empirical analysis of the proposed method (mostly covered in the appendix). \n", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Originality: The paper presents an approach to meta continual learning using a generative classifier. The proposed method is closely related to the method introduced for few-shot learning called Prototypical Networks. Authors points out that Prototypical Networks is a special case of their method. This suggests that the proposed method should be traeted as a valuable extension of the existing algorithm rather than a novel approach. \nThe proposed method is immune to catastrophic forgetting i.e., at the end of continual training, its performance is equal to the performance of the same model in standard i.i.d setting, which is remarkable. However, this is achieved explicitly by two design choices: static embedding network, which is frozen after the meta training phase, and parameter isolation enforced by the generative classifier. While this approach offers immunity to catastrophic forgetting, it simultaneously forbids the network to continuously adapt to upcoming data and reuse previously learned knowledge with transfer learning. This raises the question of whether the approach is a continual learning method. \n\nQuality: The paper is a complete piece of work that starts with introducing the general idea backed up by the toy example demonstrating the advantage of the proposed solution. Next section presents the mathematical details to conclude the paper with the section of empirical results validating the proposed method. The experimental section is thorough and well written and the proposed baselines are sensible. However, I have a few questions which were not answered in this section. I will be more than happy to discuss them with the authors. The statements presented in the paper are precise, and the argumentation in favor of these statements is convincing. The only exception is the claim that the authors make in the introduction section: “Encouraged by generative classifiers, we propose a new update scheme for discriminative classifiers to reduce the catastrophic forgetting problem.” If I understand correctly, the authors refer here to the PGLR baseline in which only the part of the classifying layer is updated according to the present task. I find it challenging to understand the novelty of this method since all the classifiers working in the regime of Task Incremental scenario works the same way. I would appreciate it if the authors elaborate on this topic.\n\nAdditional questions to the authors:\nThe model’s effectiveness is linked to the quality of the pretrained embedding network, and the paper lacks the thorough discussion of this part. I enlist the following questions, which may help to clarify this part.\nIn all experiments the meta train split forms a larger part of the whole dataset. How the size of the meta-train dataset impacts the overall performance of the method? Does the perforamcen plateaus at some point or does it constantly improve with the bigger meta train dataset?\nRegarding results in Table 2 (appnedix). Why the use of OML backbone results in worse results? This backbone is almost 40 x bigger than the backbone used in the main experiments, yet it achieves significantly worse results. Is it a general tendency that the bigger the backbone the worse the results? \nI miss the details about learning procedure of the pretrained backbone. In Table 1 (main paper) the difference between pretrained backbone and meta learning on ImageNet is relatively small while in case of Omniglot is substantially bigger. What might be the reason for this?\n \nThe last question is rather technical. In Fig.4 (main paper) X axis ends on 600th class while the test set should be composed of 723 classes because the meta train and meta validation split has 900 classes and the whole dataset is composed of 1623. What is the reason for this?\n\n\nClarity: This paper is well written and has a correct structure. The code enclosed in supplementary files is well-structured and easy to follow. Additionally, the details for experimental results are clearly presented. \n\nSignificance: Authors presents the method clearly and evaluates is effectiveness on challenging benchmarks on which it achieves state-of-the-art results compared to other methods in this field. However, as mentioned earlier, I find it inappropriate to classify this method as a continual learning method due to its abovementioned limitations. Nevertheless, the proposed solution to use the generative approach for classification in continual learning is a valuable insight. It could serve as a building block for other methods in this field. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors correctly identified the main limitations of this method, however, did not provide any discussion on how these limitations can be circumvented. Additionally, the authors did not provide any discussion about how this method can be further developed and what are the possible future research paths. The other issue is the evaluation procedure for the method. To assign class for any datasample during the test the method finds maximum probability over all already known class distributions. This leads to the linear growth of the method runtime and memory requirements  with respect to the classes. I would be interested to see if the authors has any potential ideas how to reduce this requirements?", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "6"}, "extra_text": {}}, {"review_id": "eaw9K9x_uE", "reviewer": "Reviewer_UVEJ", "summary": "Motivated by biological principles, the authors propose to combine a generative classifier and a meta-learned discriminative embedding network to address meta-continual learning. The results show that the method is more robust against forgetting.", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Originality: \nThe idea is moderately novel, since essentialy replaces the prototype classifier used in some methods (eg. iCArL) by a Bayesian version, i.e. a generative classifier. The method is evaluated in the standard benchmarks. \n\nQuality:\nThe submission seems sound.The claims are supported by several experiments. \n\nClarity:\nThe paper is generally well written and clear. The figures as well. However, the authors overemphasize the connections with human learning.\n\nSignificance:\nThe results are positive and state-of-the-art, and the discriminative-generative framework is useful. Another advantage is its computational efficiency and scalability.\n\nComments:\n- Results from other families of meta-learning should be included.\n- It is not bd clear the actual connection to biological the authors mention in the motivation, and the mechanism of concept learning.\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors mention on passing positive impact, but not limitations nor potential negative impact.\nNote that the claim that lower energy consumption makes the model more \"planet-friendly\" is usually not true. Actually, it is often the opposite (e.g. rebound effect).", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "5"}, "extra_text": {}}, {"review_id": "KcuJdM8MMF", "reviewer": "Reviewer_DcGp", "summary": "This paper proposes a probabilistic generative approach using meta-learning for continual learning. It is inspired by cognitive and neuroscience about meta-continual learning to address catastrophic forgetting. It presents the problems occurring in the discriminative approaches and suggests how to handle them by using generative classifiers. Using new update scheme for discriminative\nclassifiers, it shows that the catastrophic forgetting problem is reduced.\nIt also improves the existing prototypical learning by Bayesian approach.\n\n\n\n", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Strong Points:\n1- The paper is well organized and easy to follow. It provides sufficient information for each component used in the model and sare code for cross-checking the results.\n\n2-  It shows the use of meta-learning in continual learning and presents the advantage of the generative model over the discriminative model. It proposes a way to improve the performance of the discriminative model by a new updated scheme that reduces the catastrophic forgetting problem.\n\n3-  The proposed model is implemented in the fully incremental\nsetting. It includes a solid ablation analysis for each component.\n\nWeaknesses:\n1-  There are several existing approaches for Meta-Continual Learning [a,b].  It is unclear to me the exact differences between the existing and the proposed method except for the generative approach.  Would you please provide a precise difference and justify how it handles the shortcoming compared to previous approaches.\n\n2- Experimental results are missing for the CIFR-100 dataset.\n\n3- Can you apply the same meta-learning trick with discriminative approaches? Then it will be helpful to see the contribution to the generative approach.\n\n4- It should include some non-meta learning approaches for comparison like [c].\n\n5-  This approach can be implemented for online continual learning? If yes, then how?\n\n[a]- Meta-Learning Representations for Continual Learning, NeurIPS 2019.\n\n[b]- La-MAML: Look-ahead Meta-Learning for Continual Learning, NeurIPS 2020.\n\n[c]- Online Class-Incremental Continual Learning with Adversarial Shapley Value, AAAI 2021.\n\n\n\n\n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Please see the weaknesses in the main review section.  Include the block diagram for the proposed approach in the main paper.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "6"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper addresses catastrophic forgetting in continual learning using inspirations from cognitive and neuroscience. The drawbacks of discriminative models are first demonstrated, and then a probabilistic generative method is presented, leveraging prototypical learning by Bayesian approach.  Experimental results confirm the effectiveness of the new method.

All reviewers and I find the paper interesting and well written.  The new method is efficient and effective in practice, and the intuition is well illustrated.  The rebuttal well addressed some concerns, and the authors are encouraged to incorporate them into the final version.
Decision: Accept (Poster)