Uncertainty-guided Continual Learning with Bayesian Neural Networks
Authors: Sayna Ebrahimi
Mohamed Elhoseiny
Trevor Darrell
Marcus Rohrbach
Venue:  (2020)
Keywords: continual learning
catastrophic forgetting

Abstract: Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-based continual learning algorithms  need an external representation and extra computation to measure the parameters' \textit{importance}. In contrast, we propose Uncertainty-guided Continual Bayesian Neural Networks (UCB), where the learning rate adapts according to the uncertainty defined in the probability distribution of the weights in  networks. Uncertainty is a natural way to identify \textit{what to remember} and \textit{what to change} as we continually learn,  and thus mitigate catastrophic forgetting. We also show a variant of our model, which uses uncertainty for weight pruning 
and retains task performance after pruning by saving binary masks per tasks. We evaluate our UCB approach extensively on diverse object classification datasets with short and long sequences of tasks and report superior or on-par performance compared to existing approaches. Additionally, we show that our model does not necessarily need task information at test time, i.e. it does not presume knowledge of which task a sample belongs to.

Published as a conference paper at ICLR 2020
UNCERTAINTY-GUIDEL CONTINUAL LEARNING WITH BAYESIAN NEURAL NETWORKS
Sayna Ebrahimi
Mohamed Elhoseiny!
Trevor Darrell
Marcus Rohrbach Facebook Al Research
UC Berkeley
KAUST, Stanford University
UC Berkeley
ABSTRACT
Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-bn based continual learning algorithms need an external representation and extra computation to measure the parameters' importance. In contrast, we propose Uncertainty- guided Continual Bayesian Neural Networks (UCB), where the learning rate adapts according to the uncertainty defined in the probability distribution of the weights in networks. Uncertainty is a natural way to identify what to remember and what to change continually learn, and thus mitigate catastrophic forgetting. We also show a variant of our model, which uses uncertainty for weight pruning and retains task performance after pruning by saving binary masks per tasks. We evaluate our UCB approach extensively on diverse object classification datasets with short and long sequences of tasks and report superior or on-par performance compared existing approaches. Additionally, we show that our model does not necessarily need task information at test time, i.c. it does not presume knowledge of which task a sample belongs to.
INTRODUCTION
Humans can easily accumulate and maintain knowledge gained from previously observed tasks, and continuously learn to solve new problems or tasks. Artificial learning systems typically forget prior tasks when they cannot access all training data once but are presented with task data in sequence.
Overcoming these challenges is the focus of continual learning, sometimes also referred to as lifelong learning or sequential learning. Catastrophic forgetting (McCloskey Cohen 1989 McClelland et al. 1995) refers to the significant drop in the performance of a learner when switching from trained task to a new one. This phenomenon occurs because trained parameters on the initial task change in favor of learning new objectives.
Given network of limited capacity, one way to address this problem is to identify the importance of each parameter and penalize further changes to those parameters that were deemed to be important for the previous tasks (Kirkpatrick et al. 2017 Aljundi et al.) 2018 Zenke et al., 2017). An alternative is to freeze the most important parameters and allow future tasks only adapt the remaining parameters to new tasks (Mallya & Lazebnik] 2018). Such models rely on the explicit parametrization of importance. We propose here implicit uncertainty-guided importance representation.
Bayesian approaches to neural networks (MacKay 1992b) can potentially avoid some of the pitfalls of explicit parameterization of importance in regular neural networks. Bayesian techniques, naturally account for uncertainty in parameters estimates. These networks represent each parameter with distribution defined by mean and variance over possible values drawn from shared latent probability distribution (Blundell et al. 2015). Variational inference can approximate posterior distributions using Monte Carlo sampling for gradient estimation. These networks act like ensemble methods in that they reduce the prediction variance but only use twice the number of parameters present in regular neural network. We propose to use the predicted mean and variance of the latent distributions to characterize the importance of each parameter. We perform continual learning with
Conresponding author: sayna boyra@berkeeey.ee Work done while Facehook Al Research

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Published as a conference paper at ICLR 2020
pbyl 2,
plal K.t (2 ply)
p(o)
p(o)
p(a
(8)
(b)
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Training Task
Training Task 2
Figure I: Illustration of the evolution of weight distributions uncertain weights adapt more quickly- when learning two tasks using UCB. (a) weight parameter initialized by distributions initialized with mean and variance values randomly sampled from (0, 0.1). ) (b) posterior distribution after learning task one; while 01 and 0g exhibit lower uncertainties after learning the first task, 03. 0s. and 0g have larger uncertainties, making them available learn more tasks. (c) a second task is learned using higher learning rates for previously uncertain parameters (0), 82, 0g, and 64) while learning rates for 0, and O2 are reduced. Size of the arrows indicate the magnitude of the change of the distribution mean upon gradient update.
Bayesian neural networks by controlling the learning rate of each parameter as a function of its iillustaates uncertainty. Filuste]il how posterior distributions evolve for certain and uncertain weight distributions while learning two consecutive tasks. Intuitively, the more uncertain a parameter is, the more learnable it can be and therefore, larger gradient steps can be taken for it to learn the current task. As a hard version of this regularization technique, we also show that pruming, i.c., preventing the most important model parameters from any change and learning new tasks with the remaining parameters, can be also integrated into UCB. We refer to this method as UCB-P.
We propose to perform continual learning with Bayesian neural networks and develop new method which exploits the inherent measure of uncertainty therein to adapt the learning rate of individual parameters (Sec. 4.. Second, we introduce hard-threshold variant our method that decides which parameters to freeze (Sec. 4.2) Third, in Sec. 5 we extensively validate our approach experimentally, comparing to prior art both on single datasets split into different tasks, as well as for the more difficult scenario of learning a sequence of different datasets. Forth, in contrast to most prior work, our approach does not rely on knowledge about task boundaries at inference time, which humans do not need and might not be always available. We show in Sec. 6 that approach naturally supports this scenario and does not require task information at test time, sometimes also referred to as a "single head" scenario for all tasks. We refer evaluation metric of "single head" model without task information at test time as "generalized accuracy". Our code is available at https:/ githhb...uu... con/ Sa Sawnaabaaaimm////......
Contributions:
2 RELATED WORK
Conceptually, approaches to continual learning can be divided into the following categories: dynamic architectural methods, memory- based methods, and regularization methods.
Dynamic architectural methods: In this setting, the architecture grows while keeping past knowl- edge fixed and storing new knowledge in different forms such additional layers, nodes, modules. In this approach, the objective function remains fixed whereas the model capacity grows -often exponentially- with the number of tasks. Progressive networks (Rusu et al.) 2016 Schwarz al.) 2018) was one of the earliest works in this direction and was successfully applied to reinforcement learning problems; the base architecture was duplicated and lateral connections added in response to new tasks. Dynamically Expandable Network (DEN) (Yoon al.) 2018)) also expands its network by selecting drifting units and retraining them on new tasks. In contrast to our method, these approaches require the architecture grow with each new task.
Memory-based methods: In this regime, previous information is partially stored to be used later as form of rehearsal (Robins 1995). Gradient episodic memory (GEM) (Lopez-Paz et al.) (017)) uses this idea to store the data at the end each episode to be used later to prevent gradient updates from deviating from their previous values. GEM also allows for positive backward knowledge transfer, i.e,
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an improvement on previously learned tasks, and it was the first method capable of learning using a single training example. Recent approaches in this category have mitigated forgetting by using external data combined with distillation loss and/or confidence- based sampling strategies to select
the most representative samples. (Castro et al. 2018 Wu et al. 2019 Lee et al. 2019)
Regularization methods: In these approaches. significant changes to the representation learned for previous tasks are prevented. This can be performed through regularizing the objective function or directly enforced on weight parameters. Typically, this importance measure is engineered to represent the importance of each parameter. Inspired by Bayesian learning, in elastic weight consolidation (EWC) method (Kirkpatrick et al., 2017) important parameters are those to have the highest in terms of the Fisher information matrix. In Synaptic Intelligence (SI) (Zenke et al.) (017)) this parameter importance notion is engineered to correlate with the loss function: parameters that contribute more to the loss are more important. Similar to SI, Memory-aware Synapses (MAS) (Aljundi et al.) 2018) proposed an online way of computing importance adaptive to the test set using the change in the model outputs w.r.t the inputs. While all the above algorithms are task-dependent, in parallel development to this work, (Aljundi et al. 2019) has recently investigated task-free continual learning by building upon MAS and using protocol to update the weights instead of waiting until the tasks are finished. PackNet (Mallya & Lazebnik 2018) used iterative pruning to fully restrict gradient updates on important weights via binary masks. This method requires knowing which task is being tested to use the appropriate mask. PackNet also ranks the weight importance by their magnitude which is not guaranteed to be a proper importance indicative. HAT (Serra et al., (0188) identifies important neurons by learning an attention vector to the task embedding to control the gradient propagation. It maintains the information learned on previous tasks using an almost-binary mask per previous tasks.
Bayesian approaches: Using Bayesian approach in learning neural networks has been studied for few decades (MacKay| 1992bla), Several approaches have been proposed for Bayesian neural networks. based on, e.g., the Laplace approximation (MacKay, 1992a), Hamiltonian Monte Carlo (Neal 2012), variational inference (Hinton Van Camp) 1993 Graves (01T), and probabilistic backpropagation HHernández-Looaag & Adams] (015). Variational continual learning (Nguyen et al., 2018) uses Bayesian inference to perform continual learning where new posterior distribution is simply obtained by multiplying the previous posterior by the likelihood of the dataset belonging to the new task. They also showed that by using a core-set, a small representative set of data from previous tasks, VCL can experience less forgetting. In contrast, to use their predictive uncertainty to perform continual learning. Moreover, we do not use episodic memory or any other way access or store previous data in our approach.
rely Bayesian neural networks
Natural gradient descent methods: A fast natural gradient descent method for variational inference was introduced in (Khan & Nielsen 2018) in which, the Fisher Information matrix is approx using the generalized Gauss-Newton method. In contrast, in our work, we use classic gradient descent. Although second order optimization algorithms are proven to be more accurate than the first order methods, they add considerable computational cost. Tseran et al. (0018); Chen et al. (2019) both investigate the effect of natural gradient descent methods as an alternative to classic gradient descent used in VCL and EWC methods. GNG (Chen et al. 2019) uses Gaussian natural gradients in the Adam optimizer [Kingma & Bal 2014) the framework of VCL because as opposed to conventional gradient methods which perform in Fuclidian space, natural gradients cause a small difference in terms of distributions following the changes in parameters in the Riemannian space. Similar to VCL,
they obtained their best performance by adding coreset of previous examples. Tseran et al. (2018)
introduce two modifications to VCL called Natural- (N- VCL) and VCL- Vadam. N- V-LCL TTeern
et al. 2018) uses Gauss-Newtor approximation introduced by (Schraudolph) 2002 Graves 2011)
to estimate the VCL objective function and used natural gradient method proposed in (Khan et al. 2018) to exploit the Riemannian geometry of the variational posterior by scaling the gradient with an adaptive learning rate equal to o obtained by approximating the Fisher Information matrix in an online fashion. VCL-Vadam (Tseran et al.) 2018) is simpler version of N-VCL to trade-off accuracy for simplicity which uses Vadam (Khan et al. 2018) to update the gradients by perturbing the weights with a Gaussian noise using reparameterization trick and scaling by -1 instead of its squared. N-VCL/VCL- Vadam both use variational inference to adapt the learning rate within Adam optimizer at every time step, whereas in our method below, gradient decent is used with constant learning rate during each task where learning rate scales with uncertainty only after finishing task. We show extensive comparison with state-of-the-art results on short and relatively long sequence of vision datasets with Bayesian convolutional neural networks, whereas VCL- Vadam only rely on
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multi-layer perceptron networks. We also like highlight that this is the first work which evaluates and shows the working of convolutional Bayesian Neural Networks rather than only fully connected MLP models for continual learning.
BACKGROUND: VARIATIONAL MAYES-BY-BACKEN
In this section, we review the (Blundell et al. 2013); to learn a probability distribution over network parameters. (Blundell et al.) 2015) showed a comparable performance dropout on the MNIST dataset. In Bayesian models, latent variables are drawn from a prior density p( w) which are related to the observations through the likelihood p(x w). During inference, the posterior distribution pl w (x) is computed conditioned data. However, in practice, this probability distribution is intractable and is often estimated through approximate inference. Markov Chain Monte Carlo (MCMC) sampling (Hastings 1970) has been widely used and explored for this purpose, see (Robert & Casella 2013) for different methods under this category. However, MCMC algorithms, despite providing guarantees for finding asymptotically exact samples from the target distribution, are not suitable for large datasets and/or large models as they are bounded by speed and scalability issues. Alternatively, variational inference provides a faster solution to the same problem in which the posterior is approximated using optimization rather than being sampled from a chain (Hinton & Van Camp, 1993). Variational inference methods always take advantage of fast optimization techniques such stochastic methods or distributed methods, which allow them to explore data models quickly. See (Blei et al. 2017) for a complete review the theory and (Shridhar al., (2188) for more discussion on how to use Bayes by Backprop (BBB) in convolutioal neural networks.
(BBB) framework which was introduced by
propagation-compeee
algorithm which acts as a regularizer and yields
the given imput
3.1 BAYES BY BACKPROP (BBB)
Let x IR" be a set of observed variables and w be a set latent variables. A neural network, as probabilistic model P(y)x x, w), given set of training examples D = (x. can output y which belongs to a set of classes by using the set of weight parameters w. Variational inference aims to calculate this conditional probability distribution to the exact posterior by solving an optimization problem.
the latent variables by finding the closest proxy
We first assume family of probability densities over the latent variables parametrized by 9, i.e., q(w (w) We then find the closest member of this family to the true conditional probability of interest P P(w[DD by minimizing the Kullback-Leibh (KI.) divergence between and P which is equivalent to minimizing variational free energy or maximizing the expected lower bound:
0 = arg ming KL ([(((00)])P(ww))))
The objective function can be written as:
(BBB D) KL [[[([])]][P((w)
-Ey( (0) log (Pg(P))))))
(2)
Eq. can be approximated using N Monte Carlo samples w, from the variational posterior [Blnndell al. 2015):
LBBB(O,
Σ log logg(w.10) log P(w,) log(((D)ww))
We assume q(w(d) to have Gaussian pdf with diagonal covariance and parametrized by 0 (p. p). A sample weight of the variational posterior can be obtained by sampling from unit Gaussian and reparametrized by w = l + o where e is the noise drawn from unit Gaussian, and is pointwise multipliation. Standard deviation is parametrized as a log(1 + exp(p)) and thus is always positive. For the prior, as suggested by Blundell et al. (2015). a scale mixture of two Gaussian pdfs are chosen which are zero-centered while having different variances of of and o.. The uncertainty obtained for every parameter has been successfully used in model compression (Han et al. 2015) and uncertainty- based exploration in reinforcement learning (Blundell et al., 2015). In this work we propose to use this framework to learn sequential tasks without forgetting using per-weight uncertainties.
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4 UNCERTAINTY-GGIDEE CONTINUAL LEARNING IN BAYESIAN NEURAL NETWORKS
In this section, we introduce Uncertainty-guider Continual learning approach with Bayesian neural networks (UCB), which exploits the estimated uncertainty of the parameters' posterior distribution to regulate the change in "important" parameters both in soft way (Section 4.1) setting a hard threshold (Section
4.1 UCB WITH LEARNING RATE REGULARIZATION
A common strategy to perform continual learning is to reduce forgetting by regularizing further changes in the model representation based on parameters' importance. In UCB the regularization is performed with the learning rate such that the learning rate of each parameter and hence its gradient update becomes a function of its importance. As shown in the following equations, in particular, we scale the learning rate of μ and p for each parameter distribution inversely proportional to its importance Ω to reduce changes in important parameters while allowing less important parameters to alter more in favor of learning new tasks.
an an/Spp ap + ar/Rp
(4)
(5)
The core idea of this work is to base the definition of importance on the well-defined uncertainty in parameters distribution of Bayesian neural networks, i.e., setting the importance be inversely proportional to the standard deviation a which represents the parameter uncertainty in the Baysian neural network:
Ω 1/o
(6)
We explore different options to set Q in our ablation study presented in Section A.2 of the appendix, Table I We empirically found that Ω2 = 1/ a and not adapting the learning rate for (i.e. S2p = 1) yields the highest accuracy and the least forgetting.
The key benefit of UCB with learning rate as the regularizer is that it neither requires additional memory, as opposed to pruning technique nor tracking the change in parameters with respect the previously learned task, as needed in common weight regularization methods.
More importantly, this method does not need to aware of task switching as it only needs to adjust the learning rates of the means in the posterior distribution based on their current uncertainty. The complete algorithm for UCB is shown in Algorithm with parameter update function given in Algorithm
4.2
UCB USING WRIGHT PRUNING (UCB-P)
In this section, we introduce a variant of our method, UCB-P, which is related to recent efforts in weight pruning in the context reducing inference computation and network compression (Liu et Molchanoo et al. 2016). More specifically, weight pruming has been recently used in continual learning (Mallya Lazebnik 2018), where the goal is to continue learning multiple tasks using single network's capacity. (Mallya & Lazebnik 2018) accomplished this by freeing up parameters deemed to be unimportant to the current task according to their magnitude. Forgetting is prevented in pruning by saving task-specific binary mask of important vs. unimportant parameters. Here, we adapt pruning to Bayesian neural networks. Specifically, we propose a different criterion for measuring importance: the statistically groundded uncertainty defined in Bayesian neural networks.
Unlike regular deep neural networks, in a BBB model weight parameters are represented by proba- bility distributions parametrized by their mean and standard deviation. Similar to (Blundell et al.) 2015). in order to take into account both mean and standard deviation, we use the signal-to-noise ratio (SNR) for each parameter defined as
Ω SNR Iu//a
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Algorithm 1 Unncrtaiity-guuiee Continual Learning with Bayesian Neural Networks UCB
I: Require Training data for all tasks D (x, (mean of posterior), P. and (std for the scaled mixture Gaussian pdf of prior), (weighting factor for prior), N (number of samples in mini-batch), M (Number minibatches per epoch), initial learning rate (ao)
2: a₂ = ap = Okg
3: for every task do
4: repeat
5:
N'O0,)
a log(1 + exp(p))
Ensures a always positive
7:
w = + a0E
>w = [WI...., Way w posterior samples of weights
4 Σ NN log.N(ww 14,0² o²)
== Log-posteriar
1a Σ log (T. 0.
l = Log-prior
Σ log(p(D)w.)
= Log-likelihhoo of data
11:
LBBB 17 7111- (3)
12:
F 1 an BLBBB,
13:
p p- ap VLBBB,
14:
until loss plateaus
15:
Cx,. Op LeamingRaeeUppaaeeay..ouk 0pp
D See Algorithm 2 for UCB and for UCB-P
16:
end for
Algorithm 2 LearningRateUiiatee in UCB
Algorithm 3 LearninggRaeeUplatee UCB-P
I: function LeaminnRRacUUdddteecc. Opp 0)
1: function LeamingRaiclUpdateeo.... Gp:: (A)
for each parameter
for each parameter j in each layer /
3:
22, - 1/a
3:
Ω <- lo//o
D> Signal to noise ratio
4: S2p +-
4: if [2]] top 1% of Lts in then
5: de c- C2 2444
5:
(t a.
6:
Oip 1 0ppS2p
end if
7:
for
end for
8:
end function
8: end function
SNR a commonly used measure in signal processing to distinguish between "useful" information from unwanted noise contained in signal. In the context of neural models, the SNR can be thought as an indicative of parameter importance; the higher the SNR, the more effective or important the parameter is the model predictions for given task.
UCB-P, as shown in Algorithms/ T and is performed as follows: for every layer, convolutional or fully-connected, the parameters
ordered by their SNR value and those with the lowest importance are pruned (set to zero). The pruned parameters are marked using a binary mask so that they can be used later in learning new tasks whereas the important parameters remain fixed throughout training on future tasks. Once a task is learned, an associated binary mask is saved which will be used during inference recover key parameters and hence the exact performance the desired task.
The overhead memory per parameter in encoding the mask as well as saving it on the disk as follows. Assuming we have tasks learn using single network, the total number of required bits to encode an accumulated mask for parameter is at max log, n bits assuming a parameter deemed be important from task and kept being encoded in the mask.
RESULTS
5.1 EXPERIMENTAL SETUP
Datasets: We evaluate our approach in two common scenarios for continual learning: 1) class- incremental learning of single or two randomly alternating datasets, where each task covers only a subset of the classes in a dataset, and 2) continual learning multiple datasets, where each task
dataset. We use Split MNIST with 5 tasks (5-Split MNIST) similar to (Nguyen et al. 2018
Chen et al. 2019 Tseran et al. 2018) and permuted MNIST (Srivastava et al. 2013) for class incremental learning with similar experimental settings used in (Serra et al. 2018 8 seran et al. 2018). Furthermore, to have a better understanding of our method, we evaluate our approach on continually learning sequence of datasets with different distributions using the identical sequence

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as in (Serra et al. 2018), which includes FaceScrub (Ng & Winkler 2014). MNIST, CIFAR 100.
NotMNIST [Bulatov (21T)) SVHN (Netzer et al. 2011), CI TrinticSigns (Stallkamp et al.
201T, and IIS (Xiao et al. 2017). Details of each are summarized in Table in appendix.
No data augmentation of any kind has been used in our analysis.
Within the Bayesian framework, we compare to three models which do not incorporate the importance of parameters, namely fine-tuning, feature extraction, and joint training. In fine-tuning (BBB-FT), training continues upon arrival of new tasks without any forgetting avoidance strategy. Feature extraction, denoted as (BBB-FE), refers to freezing all layers in the network after training the first task and training only the last layer for the remaining tasks. In joint training (BBB-JT) we learn all the tasks jointly in multitask learning fashion which serves as the upper bound for average accuracy on all tasks, as does not adhere to the continual learning scenario. We also perform the counterparts for FT, FE, and JT using ordinary neural networks and denote them as ORD-FT, ORD- FE, and ORD-JT. From the prior work, we compare with state-of-thee-re approaches including Elastic Weight Consolidation (EWC) (Kirkpatrick et al. 2017). Incremental Moment Matching (IMM) (Lee) ct al. 2017). Learning Without Forgetting (LWF) F) (Li & Hoiem 2016). cess-oogggt Learning
Baselines:
(LFL) (Jung et al. 2016), PathNet (Fermando et al. 2017). Progressive neural networks (PNNs) (Rusu
ct al. 2016), and Hard Attention Mask (HAT) (Serra et al. 2018) using implementations provided by 2018). On Permuted MNIST results for ST (Zenke al. 2017) reported from (Serra
(Serra et al.
iet al. 2018)_ On Split and Permuted MNIST, results for VCL (Nguyen et al. 2018) are obtained using
their original provided code whereas for VCL-GNG (Chen et al. 2019) and VCL-Vadane (Tseran
it al. 2018)) results are reported from the original work without re- re-implemennattonn Because our method lies into the regularization-best based regime, we only compare against baselines which do not benefit from episodic or coreset memory.
Unlike commonly used tuning techniques which use a validation set composed of all classes in the dataset, we only rely on the first two task and their validations set, similar to the setup in (Chaudhry et al. 2019). all our experiments we consider a 0.15 split for the validation set on the first two tasks. After tuning, training starts from the beginning of the sequence. Our scheme is different from (Chaudhry et al. 2019), where the models are trained on the first (e.g. three) tasks for validation and then training restarted for the remaining ones and the reported performance is only on the remaining tasks.
Hyperparameter tuning:
Training details: It is important to note that in all experiments, no pre-trained model is used. We used stochastic gradient descent with a batch size of 64 and a learning rate of 0.01, decaying by factor of 0.3 once the loss plateaued. Dataset splits and batch shuffle are identically in all UCB experiments and all baselines.
Pruning procedure and mask size: Once task is learned, we compute the performance drop for set of arbitrary pruning percentages from the maximum training accuracy achieved when no pruning is applied. The pruning portion is then chosen using a threshold beyond which the performance drop is not accepted. Mask size is chosen without having the knowledge of how many tasks to learn in the future. Upon learning each task we used a uniform distribution of pruning ratios (50- (50-100% and picked the ratio resulted in at most 1%. 2%, and 3% forgetting for MNIST, CIFAR, and Stasks experiments, respectively. We did not tune this parameter because in our hyperparameter tuning, we only assume we have validation sets of the first two tasks.
Parameter regularization and importance measurement: Table ablates different ways to com- pute the importance Ω of an parameter in Eq. 4 and 5 As shown in Table ① the configuration that yields the highest accuracy and the least forgetting (maximum BWT) occurs when the learning rate regularization is performed only on μ of the posteriors using S2 1/ as the importance and
Op- 1.
Performance measurement: Let be the total number of tasks. Once all are learned, we evaluate our model on all n tasks. ACC is the average test classification accuracy across all tasks. To measure forgetting we report backward transfer, BWT, which indicates how much learning new tasks has influenced the performance on previous tasks. While BWT < directly reports catastrophic forgetting, BWT 0 indicates that learning new tasks has helped with the preceding tasks, Formally, BWT and ACC are as follows:
BWT
=
1
Σ Rin - R ACC =
" R
(8)
n 1=1
i=1
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Table Variants of learning rate regularization and importance measurement on 2-Split MNIST
Method
Importance f
BWT (%)
ACC (%)
UCB
1/a
0.00
99.2
UCB
1/a
-0.04
98.7
UCB
x
1/a
-0.02
98.0
UCB
|u//a
98.4
UCB
jel/a
-0.52
98.7
UCB
X
1w//
-0.32
98.8
UCB-P
X
-0.01
99.0
UCB-P
-0.01
Table 2: Continually learning on different datasets. BWT and ACC in (*) denotes that methods do not adhere to the continual learning setup: BBB-JT and ORD-JT serve as the upper bound for ACC for BBB/ORD networks, respectively. denotes results reported by (Serra et al. 2018). i denotes the result reported from original work. BWT was not reported in 3 and t. All others results are (re)produced by and are averaged over 3 runs with standard deviations given in Section A.3 of the appendix.
(a) S-Split MNITT 5 tasks.
(b) Permuted MNIST. 10 permutations.
(c) Alternating CIFARIO/100
(d) Sequence of 8 tasks
Method
BWT
ACC
Method
Params
BWT ACC
Method
BWT
ACC
Method
BWT
ACC
VCI. VCI-Vudamt
99.17
SI
O.IM
86.0
PathNet
0.00
28.94
L.F..
-10.0
8.61
VCL-GNGF
96.50
EWC
0.1M
88.2
LWF
-37.9
42.93
PathNet
0.00
20.22
VCL
-0.56
98.20
HAT
0.1M
-91.6
LFL
-24.22
47.67
LWF
-51.3
28.22
VCL-Vadamt
0.1M
86.34
IMM
-12.23
-38.5
FWC
-4.20
95.78
VCL-GNG
0.1M
90.50
PNN
0.00
70.73
FWC
-18.04 50.68
HAT
0.00
99.59
EWC
-1.53
72.46
PNN
0.00 76.78
ORD-FT
99.18
90.60
UCB (Ours)
0.1M
-0.38
91.44
HAT
-0.04
78.32
HAT
-0.14 81.59
ORD-FE
0.00
98.54
LWF
1.9M
331.17
65.65
BRB-FE
-0.04
51.04
BBR-FT
-23. 43.09
BBB-FT
-6.45 93.42
IMM
1.9M
-7.14
BBB-FT
68.89
BBB-FE
58.07
BBB-FE
0.00 98.76
HAT
1.9M
0.03 97.34
LCB-P (Ours)
-1.89
77.32
UCB-P (Ours)
-2.54
80.38
(Ouns)
.0.72 99.32
BAR_PT
1.9M
(Ours)
(Ours)
UCB (Ours)
0.00 99.63
BBB-FE
1,9M
0.02 93.54
BRR-IT
1.52
83.93
BAR-IT
-1.2
84.1
ORD-JT'
0.00 99.78
UCB-P (Our))
1.9M
-0,95 97.21
BBB-JT"
0.00 99.87
UCB (Ours)
1.9M
0.03 42
BBB-IT
1.9M
0.00 98.12
where Rs, is the test classification accuracy on task after sequentially finishing learning the n task. Note that in UCB-P, R,,; refers the test accuracy on task before pruning and Ri,, after pruning which is equivalent to the end of sequence performance. In Section 6 we show that our UCB model can be used when tasks labels are not available at inference time by training it with a "single head" architecture with sum of number of classes for all tasks. We refer to the ACC measured for this scenario as "Generalized Accuracy".
5.2 5 S-SPLIT MNIST
We first present results for class incremental learning of MNIST (5-Split MNIST) in which we learn the digits 0 9 in five tasks with 2 classes at a time in pairs of 0/1, 2/3, 4/5, 6/7, and 8/9. Table 2a shows the results for reference baselines in Bayesian and non-Bayesian neural networks including fine-tuning (BBB-FT, ORD-FT), feature extraction (BBB-FE, ORD-FE) and, joint training (BBB-JT, ORD-JT) averaged over runs and standard deviations are given in Table the appendix. Although the MNIST dataset is an "easy" dataset, we observe throughout all experiments that Bayesian fine-tuning and joint training perform significantly better than their counterparts. ORD-FT and ORD-JT. For Bayesian methods, we compare against VCL and its variations named as VCL with Variational Adam Vadam), VCL with Adam and Gaussian natural gradients (VCL-GNG). For non- non-Bayeen -a-aaessinn methods, we compare against HAT, IMM, and VCL-Vadam (ACC=99.11 in average accuracy. However,
EWC (EWC can be regarded as Bayesian-inspired outperforming VCL (ACC-98. 20%% and VCL-GNG (ACC=96.500 full comparison is not possible because forgetting was not reported for Vadam and GNG. Nevertheless, UCB (ACC=99.623 66%%) is able surpass all the baselines including TCL-Vadam in average accuracy while in zero forgetting it is on par with HAT (ACC=99.55) 59%). We also report results on incrementally learning MNIST in two tasks (2-Split MNIST) in Table 8 in the appendix, where compare
appears to be
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against PackNet, HAT, and LWF where PackNet, HAT, UCB-P, and UCB have zero forgetting while UCB has marginally higher accuracy than all others.
5.3 PERMUTED MNIST
Permuted MNIST is popular variant of the MNIST dataset evaluate continual learning approaches in which each task is considered as a random permutation of the original MNIST pixels. Following the literature, we learn a sequence of 10 random permutations and report average accuracy at the end. Table 2 shows ACC and BWT of UCB and UCB-P in comparison to sate-of-the--ee models using a small and a large network with 1M and 1.9M parameters, respectively (architecture details given in Section A..2 of the appendix). The accuracy achieved by UCB (ACC=91 .44 + 0.04%) using the small network outperforms the ACC reported by |Serra et al. (2018) for SI (ACC=86.0% EWC (ACC=88.1) 2%).. while HAT attains slightly better performance (ACC=91.6%) Comparing the average accuracy reported in VCL-Vadam (ACC=86.34))) and VCL-GNG (ACC=90.50%)) as well as obtained results for VCL. (ACC=88.80)) 80%) shows UCB with BWT=(0.03% + 0.00%) is able to outperform other Bayesian approaches in accuracy while forgetting significantly less compared to VCL with BWT=-7.3 7.9%% 7.9%. While we do not experiment with memory in this work, not surprisingly adding memory to most approaches will improve their performance significantly as it allows looking into past tasks, E.g. Chen al. 20199) report ACC-94.37% for VCL-GNC when adding a memory of size 200.
Next, we compare the results for the larger network (1.9M). While HAT and UCB have zero forgetting, UCB, reaching ACC=97.42 42 + 0.01 %, performs better than all baselines including HAT which obtains ACC=97.34 + 0.05% using 1.9M parameters. We also observe again that BBB-FT, despite being not specifically penalized to prevent forgetting, exhibits reasonable negative BWT values, performing better than IMM and LWF baselines. It is close to joint training, BBB-JT, with ACC=98.1%) which can be seen an upper bound.
5.4 ALTERNATING CIFARIO AND CIFAR100
In this experiment, we randomly alternate between class incremental learning of CIFARIO and CIFAR100. Both datasets are divided into 5 tasks each with 2 and 20 classes per task, respectively. Table 2c presents ACC and BWT obtained with UCB-P, UCB, and three BBB reference methods compared against various continual learning baselines. Among the baselines presented in Table [2c PNN and PathNet are the only pero-forgetting forgetting-uuaranted approaches. It is interesting to note that in this setup, some baselines (PathNet, LWF, and LFL.) do not perform better than the naive accuracy achieved by feature extraction. PathNet suffers from bad pre-assignment of the network's 's capacity per task which causes poor performance on the initial task from which never recovers. IMM performs almost similar to fine-tuning in ACC, yet forgets more. PNN, EWC, and HAT are the only baselines that perform better than BBB-FE and BBB-FT. EWC and HAT are both allowed to forget by construction, however. HAT shows zero forgetting behavior. While EWC is outperformed by both of our UCB variants, HAT exhibits 1 1% better ACC over UCB-P. Despite having a slightly higher forgetting, the overall accuracy of UCB is higher, reaching 79.4%. BBB-JT in this experiment achieves a positive BWT which shows that learning the entire sequence improves the performance on earlier tasks.
5.5 MULTIPLE DATASETS LEARNING
Finally, we present our results for continual learning of 8 tasks using UCB-P and UCB in Table 2d Similar to the previous experiments we look at both ACC and BWT obtained for UCB-P, UCB, BBB references (FT, FE, JT) well as various baselines. Considering the ACC achieved by BBB-FE or BBB-FT 1%) as a lower bound we observe again that some baselines are not able to do better than BBB-FT including LFL, PathNet, LWF, IMM, and EWC while PNN and HAT remain the only strong baselines for our UCB-P and UCB approaches. UCB-P again outperforms PNN by 3.6% in ACC. HAT exhibits only 00.1% BWT, but our UCB achieves 2.4% higher ACC.
6 SINGLE HEAD AND GENERALIZED ACCURACY OF UCB
UCB can be used even if the task information not given at test time. For this purpose, at training time, instead of using separate fully connected classification head for each task, we use a single

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Published as a conference paper at ICLR 2020
Table 3: Single Head vs. Multi-Head architecture and Generalized vs. Standard Accuracy. Generalized accuracy means that task information is not available test time. SM, PM, CF. and ST denote the 5-Split MNIST, Permuted MNIST, Alternating CIFARIO/100 and sequence of tasks, respectively.
Generalized ACC
ACC
Single Head
Single Head
Multi Head
Exp
UCB
BBB-FT
UCB
BBB-FT
UCB
BBB-FT
SM
98.7
98.1
98.9
98.7
99.2
98.4
PM
92.5
86.1
95.1
88.3
97.7
90.0
CF
71.2
65.2
74.3
67.8
79.4
68.9
8T
76.8
47.6
79.9
53.2
84.0
43.1
head with the total number of outputs for all tasks. For example in the 8-dataset experiment we only one head with 293 number of output classes, rather than using 8 separate heads, during training and inference time.
Table presents results for UCB and BBB-FT trained with single head against having multi-head architecture, in columns 4-7. Interestingly, we see only a small performance degrade for UCB from training with multi-head to single head. The ACC reduction is 0.3%, 2.6%, 5.1%. and 4.1% for 2-Split MNIST, Permuted MNIST, Alternating CIFAR10/100, and sequence of 8 tasks experiments, respectively.
We evaluated UCB and BBB-FT with more challenging metric where the prediction space covers the classes across all the tasks. Hence, confusion of similar class labels across tasks can be measured. Performance for this condition is reported as Generalized ACC in T columns 2-3. We observe a small performance reduction in going from ACC to Generalized ACC, suggesting non-significant confusion caused by the presence of more number of classes at test time. The performance degradation from ACC to Generalized ACC 0.2%, 2.6%, 3. 3.1,, and 3.1% for 2-Split MNIST, Permuted MNIST, Altemating CIFAR 10/100, and sequence of 8 tasks, respectively. This shows that UCB can perform competitively in more realistic conditions such as unavailability of task information at test time. We believe the main insight of our approach is that instead of computing additional measurements of importance, which are often task, input or output dependent, we directly use predicted weight uncertainty to find important parameters. We can freeze them using binary mask, as in UCB-P, or regularize changes conditioned on current uncertainty, as in UCB.
7 CONCLUSION
In this work, we propose a continual learning formulation with Bayesian neural networks, called UCB, that uses uncertainty predictions to perform continual learning: important parameters can be either fully preserved through a saved binary mask (UCB-P) or allowed change conditioned on their uncertainty for learning new tasks (UCB). We demonstrated how the probabilistic uncertainty distributions per weight are helpful to continually learning short and long sequences of benchmark datasets compared against baselines and prior work. We show that UCB performs superior on par with state-of- oottt--f-the-aat art models such as HAT (Serra et al., 2018) across all the experiments. Choosing between the two UCB variants depends on the application scenario: While UCB-P enforces no forgetting after the initial pruning stage by saving a small binary mask per task, UCB does not require additional memory and allows for more learning flexibility the network by allowing small forgetting to occur. UCB can also be used in a single head setting where the right subset of classes belonging to the task is not known during inference leading to competitive model that can be deployed where it is not possible to distinguish tasks in continuous stream of the data at test time. UCB can also be deployed in a single head scenario and where tasks information is not available at test time.
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A
APPENDIX
A.1 DATASETS
Table 4 shows summary of the datasets utilized in our work along with their size and number of classes. In all the experiments resized images to 32 x 32 3 if necessary. For datasets with monochromatic images, we replicate the image across all RGB channels.
Table 4: Utilized datasets summary
Names
# #Classes
Train
Test
FaceScrub Ng & Winkler 2014)
100
20,600
2,289
MNIST LeCun al. 1998)
10
60,000
10,000
CIFARIOU Knzhevsky Hinton 2009
100
50,000
10,000
NotMNIST Bulatov 2011)
10
16,853
1,873
SVHN (Ntzerr et al 2011)
10
73,257
26,032
CIFAR to (Knzhevsky & Hinton 2009)
10
39,209
12,630
TrinficSigns (Stallkamp
201
43
39,209
12,630
FashionMNIST (Xiao al.
2017)
60,000
10,000
A.2 IMPLEMENTATION DETAILS
In this section we take closer look at elements of our UCB model on MNIST and evaluate variants of parameter regularization, importance measurement, as well as the effect of the number of samples drawn from the posited posterior.
Bayes-by-backen backprop (BBB) Hyperparamters: SableBsshows the search space for hyperparamters in the BBB algorithm Blundell et al. (2015) which we used for tuning on the validation set of the first two tasks.
Table Search space for hyperparamters in BBB given by Blundell et 20155
BBB hyperparamters
-log 01 1,,
logg 02 7,8] (0.25,0.5.0.75)
π
Search space
Network architecture: For Split MNIST and Permuted MNIST experiments, we have used two- layer perceptron which has 1200 units. Because there more number of parameters our Bayesian neural network compared to its equivalent regular neural net, we ensured fair comparison by matching the total number of parameters between the two be 1.9M unless otherwise is stated. For the multiple datasets learning scenario, as well as alternating incremental CIFAR 10/100 datasets, we have used a ResNet18 Bayesian neural network with 7.1111.3M parameters depending on the experiment. However, the majority of the baselines provided in this work are originally developed using some variants of AlexNet structure and altering that, e.g. to ResNet18, resulted in degrading in their reported and experimented performance shown in Table Therefore, kept the architecture for baselines as AlexNet and ours as ResNet18 and only matched their number of parameters to ensure having equal capacity across different approaches.
Table 6: Continually learning CIFAR10/100 using AlexNet and ResNet18 for UCB (our method) and HAT (Serra et al. 2018). BWT and ACC in %. All results are (re)produced by us.
Method
BWT
ACC
HAT (AlexNet)
0.0
78.3
HAT (ResNet18)
9.0
56.8
UCB (AlexNet)
0.7
79.44
UCB (ResNet18)
0.7
79.70
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Number of Monte Carlo samples: UCB is ensured to be robust random noise using multiple samples drawn from posteriors. Here we explore different number of samples and the effect on final performance for ACC and BWT. We have used 22 1/a importance and regularization has been performed on mean values only. Following the result Table we chose the number of samples to be 10 for all experiments.
Table 7: Number of Monte Carlo samples (N) in 2-Split MNIST
Method
N
BWT (%)
ACC (%)
UCB
0.00
98.0
UCB
0.00
98.3
UCB
-0.15
99.0
UCB
10
0.00
99.2
UCB
15
-0.01
98.3
A.3 ADDITIONAL RESULTS
Here we include some additional results such as Table 8 for 2-split MNIST and some complementary results for tables the main text as follows:
10 and include standard deviation for results
shown in Table 2a
2b 2c
respectively.
Table Continually learning on 2-Split MNIST. BWT and ACC in %. (*) denotes that methods do not adhere to the continual learning setup: BBB-JT and ORD-JT serve the upper bound for ACC for BBB/ORD networks, respectively, All results are (re)produced by us.
Method
BWT
ACC
PackNet [Mallya & Lazebnik 2018)
0.04 0.01
98.91 = 0.03
LWF Li & Horem 2016)
0.22
99.12 = 0.03
HAT Serra et al. 2018
99.02 0.00
ORD-FT
6.81
92.42 0.02
ORD-FE
0.04+0.04
97.90 0.04
BBB-FT
0.61 0.61 0.03
98.44 = 0.03
BBB-FE
0.02
98.03 0.05
UCB-P (Ours)
0.03
99.02 0.01
UCB (Ours)
0.01 0.00
99.18 0.01
ORD-JT"
0.02 1 0.03
99.13 0.03
BBB-JT"
0.03 1 0.02
99.51 0.02
Table 9: Continually learning on 5 5-Split MNIST. BWT and ACC in %. (*) denotes that methods do not adhere the continual leamning setup: BBB-JT JT and ORD-JT serve the upper bound for ACC for BBB/ORD networks, respectively. All results (re)produced by
Method
BWT
ACC
VCL-Vadam Tseran et al.
2018
99.17 1 0.05
VCL-GNG (Chen
96.50 0.07
VCL (Nguynn ct 2018
-0.56 1.56+0.09
98.20
IMM
LLe ct al 2017
-1..20 +.20
88.54 + 1.56
1.56
EWC
Kirkpatrick al.
2017
1.20
95.78 1.08
HAT (Sera
2018
0.00
99.59 0.02
ORD-FT"
9.18+1.12
90.60 1.12
ORD-FE"
0.00 + 1.56
98.54 + 1.57
BBB-FT*
-6.45 + 1.99
93.42 + 1.98
BBB-FE*
0.00 2.23
98.76 2.23
UCB-P (Ours)
-0.72
99.32 1 0.04
UCB (Ours)
0.00 - 0.04
99.63 + 0.03
ORD-JT"
0.00 = 0.02
#.002
BBB-JT*
0.00 0.01
99.87 + 0.01
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Table 10: Continually learning on Permuted MNIST. BWT and ACC in %. (*) denotes that method does not adhere to the continual learning setup: BBB-JT serves the upper bound for ACC for BBB network. $ denotes results reported by (Serra al. 2018). denotes the result reported from original work. BWT was not reported in & and j. All others results are (re)produced by us.
Method
#Params
BWT
ACC
(Zenke 2
0.1M
86.0
EWC (Kirkpatrick ct al. 2017
0.1M
88.2
HAT (Serra
2018
0.1M
91.6
VCL- Vadam
0.1M
93.34
VCL-GNGf
0.1M
94.62
VCL
0.IM
-7.90 = 0.23
88,80 0.23
UCB
(Ous)
0.1M
0.02 -038
91.44 0.04
LWF Li & Hoiem 2016
1.9M
-1.177
65.65 0.05
IMM
[Lcc ct al. 2017)
1.9M
-7.14 0.07
90.51 + 0.08
HAT (Srra
2018
1.9M
0.03
97.34 + 0.05
BBB-FT
1.9M
-0.58 = 0.05
90.01 0.05
BBB-FE
1.9M
0.02
93.54 0.04
UCB-P (Ours)
1,M
0.95 - 0.06
97.24 0.06
UCB (Ours)
1.9M
0.03 = 0.00
97.42 + 0.01
BBB-JT'
1.9M
0.00 0.00
98.12 0.01
Table 11: Continually learning CIFAR10/100. BWT and ACC in %. (*) denotes that method does not adhere to the continual learning setup: BBB-JT serves as the upper bound for ACC for BBB network. All results are (re)produced us.
Method
BWT
ACC
PathNet (Fernando
2017
0.00 0.00
28.94 0.03
LWF
Li Horem
2016
-37.9 0.32
42.93 = 0.30
LFI.
Jung ct al.
2016
-24.22 0.21
47.67 + 0.22
IMM
LTe al.
2017
-12.23 + 0.06
69.37 = 0.06
PNN
Rusu al.
2016
0.00 0.00
70.73 0.08
EWC
Kirkpatrick et al.
2017
-1.53 0.07
72.46 0.06
HAT
Serra et al.
2018
0.04 0.06
78.32 1 0.06
BBB-FT
FE
0.04
51.04 1 0.03
BBB-FT
-7.43
68.89 0.07
UCB-P (Ours)
-1.89 0.03
77.32 0.03
UCB (Ours)
-0.72 0.02
0.02
BBB-JT"
1.52 0.04
83.93 1 0.04
16


Reviews:
[{"review_id": "SJlbynqTYS", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "** post rebuttal start **\n\nAfter reading reviews and authors' response, I decided not to change my score.\nI am happy with the author's response addressing my concerns (mainly about the fairness on the size of the model), so I recommend its acceptance. I believe it is a good addition to the community of continual learning.\n\n** post rebuttal end **\n\n\n- Summary:\nThis paper proposes to use a way to improve continual learning performance by taking \"Bayes-by-backprop\" method. They claim that the uncertainty can naturally be measured by estimating (log of) the standard deviation, and it is indeed useful to judge the importance of each learnable parameter. Experimental results on several benchmarks show that their method outperforms few state-of-the-art methods.\n\n\n- Decision and supporting arguments:\nWeak accept.\n\n1. The proposed method is simple but effective. However, It is still questionable whether \\sigma is the best measure of the weight importance. An ablation study with different choices of the importance measure (maybe \\mu can also be incorporated as well as \\sigma?) would be good to see.\n\n2. Survey and comparison with memory-based methods are limited. Though memory-based methods require some memory to keep the experience, the proposed method also requires additional memory for \\sigma; it essentially doubles the model capacity, assuming that \\sigma is solely for measuring the weight importance. In particular, when it comes to large-scale models, memory for storing some important experiences would be small compared to the memory to store the model.\nHere are some papers about recently proposed memory-based methods, which are not cited:\n\nCastro et al. End-to-End Incremental Learning. In ECCV, 2018.\nWu et al. Large Scale Incremental Learning. In CVPR, 2019.\nLee et al. Overcoming Catastrophic Forgetting with Unlabeled Data in the Wild. In ICCV, 2019.\n\n3. Comparison should include the model capacity as in Table 1(b). Again, compared to the conventional non-Bayesian model, half of the model capacity is used for computing \\sigma (uncertainty), I wonder it causes a performance drop when the model capacity is the same over all compared methods. If they used the same model architecture and just doubled the number of learnable parameters for \\sigma, then it is obviously unfair.\n\n\n- Comments:\n1. Pruning is not beneficial in terms of the performance. I hope to see some quantitative benefits obtained by introducing pruning. In Table 1(b), why doesn't pruning reduce the number of parameters?\n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "S1ewYgHaKr", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "**** Post Rebuttal ****\n\nI have read the author's response and other reviewers' comments. In light of comments by other reviewers, I am increasing the score. The paper reports decent empirical results in some challenging settings which might be useful to the continual learning community. \n\n**** End ****\n\nThe paper presents a simple yet effective way to avoid catastrophic forgetting in a continual learning setting. The proposed approach is referred to as UCB - \"Uncertainty Guided Bayesian Neural Networks\". The main idea of the approach is to weight the learning rate of each parameter in the neural network by the standard deviation of its posterior distribution. This leads to regularizing parameters that are \"important\" to tasks seen earlier and thus avoiding forgetting.  Results indicate an improvement over other baselines. However, I do not see any analysis of the method that explains this improvement. I do not recommend acceptance.\n\nCons:\n\n- My main concern with the paper is that it fails to justify the superiority of the method over other baselines. The numbers reported in the paper do seem good, but I don't see an explanation of why this is the case. What are the drawbacks of EWC, VCL or HAT that the proposed method solves? Why using uncertainty to define importance works better than using online VI in VCL or fisher information in EWC? There is no discussion in the paper about that. Without such a discussion it seems that the model was run a number of times and the best score was reported out of all those runs (especially because the improvement is only marginal). \n\n- I am not sure why weighting the learning rate would be a good idea? Having high uncertainty may increase the learning rate arbitrarily. Is there a constraint on the standard deviation? Does having a very high weight for learning rate not cause instability during optimization? I think the method would be very sensitive to the initialization of the standard deviation. \n\nOverall I think the idea of using uncertainties for continual learning is interesting. But from where it stands, I am not fully convinced that this method should do better than existing approaches.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I made a quick assessment of this paper.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "Byl4mBDl9B", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": null, "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": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The authors propose a novel method for continual learning with neural networks based on a Bayesian approach. The idea consists in working with Bayesian neural networks, using the Bayes by back-prop approach in which a factorized Gaussian variational distribution is used to approximate the true posterior. To address the continual learning setting, the authors propose to multiply the learning rate of the mean parameters in the posterior approximation by the corresponding standard deviation parameter in the posterior approximation, while the learning rate for the variance parameters in the posterior approximation is not changed. The authors also consider a version of his method which freezes the mean and variance variational parameters when the signal to noise ratio is high. The proposed method is evaluated in exhaustive experiments, showing state-of-the-art results.\n\nClarity:\n\nThe paper is clearly written and easy to read. The method proposed is well described and it would be easy to reproduce.\n\nQuality:\n\nThe proposed method is well justified and the experiments performed clearly illustrate the gains with respect to previous methods.\n\nNovelty:\n\nThe proposed method is novel up to my knowledge. The methodological contributions do not seem very sophisticated, but the experiments show that the proposed method, despite being very simple, works very well in practice.\n\nSignificance:\n\nThe experiments show that the proposed method achieves state of the art results when compared with a very large number of baselines. This indicates that the proposed method will be relevant to the community. In my opinion, this work is highly significant.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}]

Author rebuttal:

Meta-review: While prior work has shown the potential of using uncertainty to tackle catastrophic forgetting (e.g. by appropriate updates to the posterior), this paper goes further and proposes a strategy to adapt the learning rate based on the uncertainty. This is a very reasonable idea since, in practice, learning rate control is one of the simplest and most understood techniques to fight catastrophic forgetting. 
The overall approach ends up being a well-motivated strategy for controlling the learning rate of the parameters according to a notion of their "importance". Of course now the question is if this work uses a good proxy for "importance" so further ablation studies would help, but the current results already show a clear benefit. 

Decision: Accept (Poster)