# Continual Learning for Classification Problems: A Survey

Mochitha Vijayan, S. S. Sridhar

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Mochitha Vijayan, S. S. Sridhar. Continual Learning for Classification Problems: A Survey. 4th International Conference on Computational Intelligence in Data Science (ICCIDS), Mar 2021, Chennai, India. pp.156-166, 10.1007/978-3-030-92600-7_15. hal-03772949

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# Continual Learning for Classification Problems: A Survey

*Mochitha Vijayan¹, Dr. S. S. Sridhar²

¹SRM Institute of Science and Technology
¹ mv2820@srmist.edu.in

²SRM Institute of Science and Technology
²sridhars@srmist.edu.in

**Abstract.** Artificial Neural Networks performs a specific task much better than a human but fail at toddler level skills. Because this requires learning new things and transferring them to other contexts. So, the goal of general AI is to make the models continually learning as in humans. Thus, the concept of continual learning is inspired by lifelong learning in humans. However, continual learning is a challenge in the machine learning community since acquiring knowledge from data distributions that are non-stationary in general leads to catastrophic forgetting also known as catastrophic interference. For those state-of-art deep neural networks which learn from stationary data distributions, this would be a drawback. In this survey, we summarize different continual learning strategies used for classification problems which include: Regularization strategies, memory, structure, and Energy-based models.

**Keywords:** general AI, Artificial Neural Networks, Lifelong Learning, Continual Learning, Catastrophic Forgetting, classification problems.

## 1 Introduction

Deep learning holds state-of-the-performances in specific tasks in the areas of Computer vision, Natural Language Processing (NLP), Speech recognition, etc. This success is due to supervised training from huge and fixed datasets. No matter how big your training dataset is, as we grow in terms of data dimensionality and when we would like to solve more complex problems (not the toy problems), it becomes exponentially more difficult to cover the entire space of possibilities without representing the data set collected a priori. But how can we improve the scalability of models in terms of computation and memory resources and how can they adapt to new circumstances never seen before? The answer to this is to never stop learning as our brain does. So, Continual Learning [1][2] which is inspired by lifelong learning in humans is the way to deal with a higher and realistic time-scale where data (and tasks) become available only during the time.

Why continual Learning is a challenging problem?
Many connectionist models that are gradient-based such as Artificial Neural Net-
work's (ANN) suffer from Catastrophic forgetting [3][4]. This means that once
you train a network on a piece of data and when we expose it to a little new data
distribution, it tends to forget the older ones. Since every parameter of the net-
work is rewritten to suit the new data distribution. ANNs are unable to learn new
information or instances immediately. Deep NNs are the dominant approach to
machine perception, but: 1. They cannot learn new instances immediately, 2.
Learning requires multiples loops over a data set, 3. They are susceptible to cat-
astrophic forgetting if the data is not iid (independently and identically distrib-
uted).

To overcome catastrophic forgetting AI systems must be able to retain the previ-
ously learned task, acquire new knowledge and restrict the novel data from inter-
fering with the existing knowledge. That is, the system must be stable to retain
acquired knowledge without catastrophically forgetting them and must be plastic
enough to integrate novel information. This concept is being widely explored in
both biological and artificial models and is well-known as the stability-plasticity
dilemma [5][6]. Two reasons to solve catastrophic forgetting: 1. Making systems
learn like humans and animals, 2. Enabling new applications like immediate in-
ference from new input labels, to avoid retraining from scratch thereby optimiz-
ing memory and computational resources.

For a classification task, Task-IL is often artificial, Class-IL is crucial for a con-
tinual learning setting in classification problems. This survey focuses on different
continual learning strategies used for classification tasks. Furthermore, some
ideas to enhance continual learning efficiency is also being discussed. We survey
various strategies for continual learning in neural networks that mitigate cata-
strophic forgetting to different levels. We categorize the continual learning ap-
proaches used in the existing systems into Regularization strategies, Memory-
based strategies, Structure-based strategies, and Energy-Based Models.

## 2 Regularization strategies

In continual learning, regularization is used to ensure the stability of important
parameters for the previously learned tasks.

Li et al., 2018 present Learning without Forgetting (LwF) which is a hybrid of knowledge distillation (distillation loss to maintain consistency) and fine-tuning. This method has a relation with replay-based methods in a way that rather than storing or generating the samples to be replayed. Using the model learned on the previous tasks this approach labels the current task and replays them. Trying to transfer the information from an extremely regularized massive model to a smaller model. For a parameter set $\theta_s$ (shared) of all the tasks it tries to optimize the parameter $\theta_n$ of the novel task along with $\theta_s$. An extra restraint is imposed such that
for a new task the parameters $\theta_s$ and the parameters of old tasks $\theta_o$ will not deviate much to remember $\theta_o$. If for a new task, $(X_n, Y_n)$ is the training data, the old tasks output $Y_o$, and new parameters $\theta_n$(randomly choosed), then the updated parameters $\theta_s^*$, $\theta_o^*$, $\theta_n^*$ are:

$$ \theta_s^*, \theta_o^*, \theta_n^* \leftarrow \operatorname{argmin}_{\hat{\theta}_s, \hat{\theta}_o, \hat{\theta}_n} \lambda_o \mathcal{L}_{old}(Y_o, \hat{Y}_o) + \mathcal{L}_{new}(Y_n, \hat{Y}_n) + R(\hat{\theta}_s, \hat{\theta}_o, \hat{\theta}_n) $$

Here a loss is added to discourage the old task output to change for new tasks. Optimization is done both for the final layers and shared representation. They show that LwF performs better than LFL(Jung et al, 2018) which is a similar approach. The drawback of this approach is that it extremely depends on the task's relevance and the training time for one task will have a linear hike with the number of tasks learned. In multi-task learning distillation used here is a potential solution but it demands a repository of persistent data for every task learned. This method is not immediately applicable in Reinforcement Learning scenarios.

In Less-forgetting learning (LFL), Jung et al., 2018 the old task performance is preserved by protecting the shared representations. This learning model satisfies two properties, there should be clear-cut boundaries for each task and the shared parameters should be kept unchanged. For the final most hidden activations the L2 distance between them is regularized, thereby protecting the previous input to output association being learned from the old tasks. This is done by the computation of additional activations using the parameters of old tasks. This L2 loss discourages the output after $\theta_s$ (shared parameter set) from changing for new tasks, while $\theta_o$ (task-specific parameters for past tasks) remains as it is. However, it requires the computation of the old task parameters for each new data point making it computationally expensive.

Kirkpatrick et al., 2017 developed an algorithm akin to synaptic consolidation for Artificial Neural Nets known as EWC (Elastic Weight Consolidation) which focuses on task-specific synaptic consolidation. EWC allows the knowledge acquired in the previous task to be protected during a new task learning as shown in fig 1.
<figure><img src="image_3.png" /><figcaption>Fig 1. EWC assures task A is retained while training on task B.</figcaption></figure>

The importance of the parameter $\theta$ concerning a task's training data $D$ is represented as $p(\theta | D)$, the posterior distribution. While considering a scenario with tasks A (with $D_A$) and B (with $D_B$) which are independent, applying Baye's theorem to the posterior probability and then taking the log gives us,

$$ \log p(\theta | D) = \log p(D_B | \theta) + \log p(\theta | D_A) - \log p(D_B) $$

The knowledge of earlier task is held by $\log p(\theta | D_A)$, the posterior probability. EWC uses a Gaussian distribution and adds a cost term to prioritize the important weights of past tasks by using a fisher information matrix $F$ and is evaluated by its diagonal. Gaussian distribution is used since $\log p(\theta | D_A)$ is intractable.

$$ \mathcal{L}(\theta) = \mathcal{L}_B(\theta) + \sum_i \frac{\lambda}{2} F_i (\theta_i - \theta_{A,i}^*)^2 $$

EWC performed well in both supervised (permuted MNIST task framed by Goodfellow et al., 2013) and reinforcement (Atari 2600) learning scenarios. EWC's characteristic of making weights less plastic with time promotes memory retention rather than forgetting. As the number of random patterns exceeds the capacity of the network EWC degrades than the plain gradient descent. Moreover, Hopfield networks which is an EWC model suffer from the phenomenon of blackout catastrophe when the network capacity is saturated which results in the hindrance of retrieval of old knowledge and addition of new ones. The available output labels have to be summed up to calculate the diagonal of the Fisher matrix which makes its complexity linear to the number of outputs, which limits the application of this algorithm to low-dimensional output spaces. [34] show that EWC works poorly at incremental class learning.
Zenke et al., 2017 introduced intelligent synapses by maintaining an online measure of synapses (parameters like weights and bias) “importance” in solving the past tasks. These important synapses are protected from changing when the task changes. That is, the future learning is assisted by the synapses which are of less significance to the previous tasks, thereby alleviating catastrophic forgetting. A surrogate loss term is added to hinder significant variations in important parameters $\theta_k$ while learning a novel task.

Loss function:

$$ \mathcal{L}'_{\mu} = \mathcal{L}_{\mu} + c \sum_{k} \Omega_{k}^{\mu} (\theta'_{k} - \theta_{k})^{2} $$

This measure tracks parameters (past and present) and evaluates their importance online. Parameters contributing more to the loss function are more relevant. In [11], SI is shown to perform well on a multi-headed Split MNIST of their design and had shown similar performance as EWC on the permuted MNIST dataset. By using a multi-headed split CIFAR task of their design some transfer learning is also done.

In Lee et al., 2017, A L2 penalty is applied to the shared parameter changes and for learning a novel task. Models formed are merged using first or second-moment matching. IMM is a progression of EWC which performs a model-fusion separately upon learning a novel task.

Aljundi et al., 2018 proposed Memory-aware Synapses (MAS) which is a model-based method inspired by neuroplasticity and Hebbian learning in biological systems. MAS determines the significance of the parameters that adapt to the test data set using the variation in the model output function concerning the inputs, rather than the loss function. Thus, avoiding the problem of falling in local minima. Important parts of the model can be learned using unlabeled data. This computation is done online and in an unsupervised manner. MAS could achieve in terms of constant memory w.r.t the task count, ability to build on the top of a pre-trained model and to add new tasks, ability to learn from unlabelled data.

Uncertainty-guided Continual learning approach with Bayesian neural networks (UCB), Ebrahimi et al., 2020 used an uncertainty prediction strategy for continual learning. Parameters of importance are either fully safeguarded using a binary mask (UCB-P) or can be changed conditionally based on their uncertainty learning novel tasks (UCB). UCB-P avert forgetting after the initial phase of pruning by retaining a binary mask for each task. UCB doesn't take additional memory and let on a more flexible learning mechanism in the network by limiting the forgetting.
Although these regularization-based approaches can be computationally efficient in alleviating catastrophic forgetting under certain conditions, a disadvantage is that they gradually reduce the model's capacity for learning new tasks. In class-incremental learning, regularization-based methods are shown to consistently fail [30][31].

## 3 Memory-based strategies

A set of experiences, exemplars, or vectors which represent the tasks can be stored rather than storing all the observations. This provides a more efficient and scalable memory strategy. This also enables compression and high-level transfer across multiple tasks. The focus of many works is dealing with the challenge to determine which samples to store.

Robins, A., 1995 in his work interleaved new experiences with the generated patterns of previous experiences intending to make neural networks able to encode information, store, and recall them on the need for better generalization across tasks. This method performed well in alleviating catastrophic forgetting. i.e., a continual rehearsal of previous tasks is done. This continual learning strategy based on the memory is called replay or otherwise rehearsal.

Rebuffi et al., 2017 proposed iCaRL (Incremental Class and Representation Learning) which combines regularization and memory strategies. iCaRL simultaneously learns the classifier and feature extractor. It consists of three components: classification done by a nearest-mean exemplars rule, herding based exemplar selection, learning of representation that uses exemplars along with distillation intending to avoid catastrophic forgetting. One exemplar image each for all classes seen so far is stored. Then computes a model for each of the classes which is the average of each exemplar stored. The input image is classified as the class of the prototype that is close to the current feature representation. As the feature representation changes recompute the mean of exemplars.

The training set consists of samples of new data as well as the exemplars of old classes (to remind what the old classes were).

$$D \leftarrow \bigcup_{y=s,...,t} \{(x, y): x \in X^y\} \cup \bigcup_{y=1,...,s-1} \{(x, y): x \in P^y\}$$

Loss function:

$$\mathcal{L}(\theta) = - \sum_{(x_i, y_i) \in D} \left[ \sum_{y=s}^{t} \delta_{y=y_i} \log(g_y(x_i)) + \sum_{y=1}^{s-1} q_i^y \log(g_y(x_i)) \right]$$
The classification loss term will help to learn new classes and the distillation loss term will help not to forget previous outputs.

iCaRL can learn in an incremental fashion over a long period in experiments conducted on CIFAR-100 and ImageNet ILSVRC 2012 data wherein other methods fail quickly. Whereas, iCarL's performance is not appreciable when the training samples of classes are available in batch settings. iCarl's performance is heavily influenced by the number of examples it stores.

Variational Continual Learning (VCL) by Nguyen et al., 2018 uses Variational Interference (VI) which is also a replay-based method. The previous posteriori is multiplied by the likelihood of the new task data set to obtain the new posterior distribution. This is a Bayesian inference to carry out continual learning. They calculate the Kullback-Leibler (KL) (approximately a quadratic regularization with rotation) divergence between the current distribution and the previous posterior. In addition to the VCL regularization term they showed that by using a core-set, which samples examples from old tasks, VCL is experiencing less forgetting. VCL with or without core-set outperforms EWC and SI on the permuted MNIST and multi-headed split MNIST dataset. Using permuted MNIST shows to yield misleading results in the context of continual learning as shown in [29].

A replay is a phenomenon seen in rodents and humans [24]. But it is unrealistic to maintain an unlimited number of observations or exemplars. In generative models as in Shin et al., 2017, samples are not stored. Instead, generative models are trained and then used to produce data needed for rehearsal. Trying to mimic the generative nature of the hippocampus for the rehearsal of past experiences, Shin et al., 2017 proposed Deep Generative Replay (DGR) consisting of two components: a generative model and a solver. A pseudo-data that represents the previous tasks are generated and are interleaved along with new tasks. This avoids the need for explicitly revising past training data for rehearsal, thus downsizing memory requirements. The catastrophic interference problem now shifts to the training process of the generative model.

Kember et al., 2018 proposed a model for Class-IL inspired by the dual memory model [3] of a mammalian brain and the studies of recall and consolidation that happens in a mammalian brain while fear conditioning [36]. FearNet uses a hippocampal net that is responsible for recalling immediate memories, long-term (mature) memories are handled by a PFC network and a neural net that took inspiration from the basolateral amygdala for deciding whether the model should make use of the hippocampal or PFC network for that specific sample or not. Memory consolidation happens during the sleeping phase that the FearNet consolidates hippocampal network to the PFC network, hippocampal network and PFC operates as complementary memory systems. PFC is a generative neural net that generates pseudo examples that are interleaved with the new samples in the hippocampal network.
One way to enforce the gradient to stay close to the gradients from previously
learned tasks is to eliminate its interference as in Lopez-paz et al., 2017 Chaudhry,
A. et al., 2018. These methods are beneficial in multi-task learning as they can make
learning more efficient in case of opposing objectives. Lopez-Paz et al., 2017
introduced the Gradient Episodic Memory (GEM) model that brings in the positive
backward transfer to previously learned tasks. It is the first approach to accomplish
learning in one pass. GEM is characterized by an episodic memory that stores a
subset of the observed examples for a given task and alleviates catastrophic
forgetting (negative backward transfer). This model enables to learn the subset of
correlativity of a set of tasks, capable to predict desired values associated with past
or novel tasks without enforcing task descriptors. GEM's memory requirement is
high than other regularization strategies such as EWC (Kirkpatrick et al. 2017) at
the training time. As GEM is being evaluated on MNIST and CIFAR datasets it is
doubtful if it scales to more realistic problems. An inherent problem here is the
constraint on the amount of experience that can be stored in memory, which could
quickly become a limiting factor in large scale problems. Even when this method
works well in a single pass context it demands much more computation.

Chaudhry, A. et al., 2018 proposed Averaged GEM (A-GEM) which is an advanced version of GEM which alleviates the computational burden of GEM. GEM ensures that the loss of each specific previous tasks (sampled from episodic memory) at every training step does not increase. Whereas, A-GEM ensures that the average of the episodic memory loss over the past tasks at every training step does not increase. A-GEM shows the same or even better performance as GEM. A-GEM is shown to be computationally and memory-efficient as EWC and other regularization-based methods.

Scalability of the approaches that use memory for replay or rehearsals when the
number of task increases is arguable. And the rehearsal-based approaches have to
deal with the quality of samples generated which would again be a drawback.

4 Structure-based strategies

These strategies determine if the network has to be expanded to represent the new
tasks or not. Progressive networks (Rusu et al., 2016; Schwarz et al., 2018) are
dynamic architecture-based approaches where the base architecture was replicated
and some connections were included in response to new tasks. These approaches
were successful in reinforcement learning scenarios.

Mallya et al., 2018 proposed PackNet. Forgetting is alleviated by iterative pruning to completely freeze the updates on the most important parameters. A binary mask (task-specific) that indicates the importance and unimportance of parameters is saved. More specifically, a single network's capacity is used to learn multiple tasks
and is done by freeing the parameters irrelevant to the present task depending on their magnitude. This approach requires knowing the task prior to the use of a suitable mask. Ranking the importance of weight by their magnitude will not be a guaranteed "importance" indicator. Parameter importance is ranked by its magnitude in PackNet which cannot give any guarantee to be an "importance" indicator. This model relies on the explicit parametrization of importance.

Hard attention to the tasks (HAT) introduced by Serra et al., 2018 learns an attention vector to determine the important neurons (using mini-batch stochastic gradient descent and backpropagation) to the task controlling the gradient shifts. An almost-binary mask per previous tasks is used to maintain the information learned on previous tasks. HAT employs an attention-weighted L1 regularization on the attention mask. Instead of simple L1 regularization, these attention masks are lightweight structures included without changing much in the existing network. When EWC and SI adds a soft architectural regularization to the loss function, HAT adds a hard structural regularization to both the loss function and gradient magnitudes.

Rusu et al., 2016 in their work hindered any adjustments to the previous network. Instead expanded the network with a new subnetwork to be trained with new data. This progressive network retains a repository of pre-trained architectures for each learned task. If the features being learned cannot correctly represent the novel task, more neurons are added to the network to account for the features of the new task. This approach has shown favorable results for a wide variety of reinforcement learning problems when compared to other strategies that either priorly train or tweak the model incrementally with the prior knowledge only at the initialization phase. This strategy prevents catastrophic forgetting, however, without considering the difficulty of the task they add in a constant count of units for each learned task leading the complexity of the network architecture to grow and thus is suboptimal in terms of network capacity utility and performance.

Yoon et al., 2018 proposed Dynamically Expandable Networks (DEN) in which, the network expands according to the task at hand by dividing/replicating the most important neurons retraining them on new tasks. This separate stage is known as selective retraining. The important drifting units (neurons) are identified using a complex mixture of hyperparameters and heuristics. They employ L1 regularization as well as L2-transfer to condition learning, regularization constants, and a set of extra thresholds. Even though they bring in high computation this is unavoidable in a continual learning environment where several tasks have to be learned and when network capacity cannot be fixed.

When new tasks are encountered modular-based models go for explicit ways to increase architectural capacity. In recent times, several adaptive network models have emerged that expand and at the same time protects and reuse the existing representations [22]. But this leads to demanding high computational requirements
in the learning process. Schwarz et al., 2018 increase networks capacity more aggressively if needed and then prune or sometimes compress the parts of the network.

Structure-based approaches are limited to task-incremental learning settings.

# 5 Energy-based models for Continual Learning

Li et al., 2020 proposed an Energy-based model for continual learning which does not use an extra loss, memory, or model and is still performing well in class incremental learning scenarios and boundary agnostic settings which are the challenges of Continual Learning. EBMs naturally deals with the challenging problems in Continual Learning without replay. A contrastive divergence training procedure is used and it provides a natural way to deal with dynamically growing. They propose to learn new conditional gains during the training process, which makes EBMs parameter update cause less interference with old data. But EBM's takes more time than softmax-based classifier model in terms of convergence and evaluation.

# 6 Research insights

* The model (agent) should be capable of learning from both stationary and non-stationary data streams. In real-world data comes from a dynamic data distribution that keeps on changing with time. The state-of-art neural networks are provided with iid data and are allowed to loop over it again and again.

* Data streams like MNIST and permuted MNIST are highly unrealistic, most of the conventional neural nets use them. Evaluation of the existing continual learning is mostly done on toy data streams. The applicability of these approaches in a real-world setting is questionable.

* Models that work well in MNIST, CIFAR, etc tend to fail in other important paradigms as shown [34]. MNIST and CIFAR are small datasets.

* Memory and computations must be kept fixed across the models to enable a fair comparison which is not done in most of the cases.

* Evaluation of a model in terms of Task-IL, Domain-IL, and Class-IL can be done only on continual learning problems with a series of tasks with clear cut boundaries [31].

# 7 Concluding remarks and future direction
We can make artificial agents perform a particular task surprisingly much better than a human. But current artificial agents are still in their infancy due to a serious problem known as catastrophic forgetting. Continual learning as in humans is inevitable. A continual learning agent must not suffer from the phenomena of catastrophic forgetting. It means that the agent must retain its ability to perform fairly well on previously learned tasks and should be able to learn new tasks by extracting knowledge from the previous ones exhibiting positive forward transfer thereby achieving better performance and fast learning. It should be scalable by dynamically adapting to the real-time environment with varieties of tasks. It should enable positive backward transfer by gaining better performance on previous tasks after learning a new similar task. The data collected from the real-world may not be always explicitly labeled. The agent should learn from unlabeled data and even should be the recipient of tasks without clear task boundaries. Catastrophic forgetting isn't the only barrier of general AI. Not every task has a huge dataset and the challenge is to make the models learn from more than just from the samples. This survey tries not only to highlight the inevitability of continual learning but also to report the limitations of existing state-of-art neural networks in this regard.

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