Paper:
Gradient Episodic Memory for Continual Learning
One major obstacle towards AI is the poor ability of models to solve new problems quicker, and without forgetting previously acquired knowledge. To better understand this issue, we study the problem of continual learning, where the model observes, once and one by one, examples concerning a sequence of tasks. First, we propose a set of metrics to evaluate models learning over a continuum of data. These metrics characterize models not only by their test accuracy, but also in terms of their ability to transfer knowledge across tasks. Second, we propose a model for continual learning, called Gradient Episodic Memory (GEM) that alleviates forgetting, while allowing beneficial transfer of knowledge to previous tasks. Our experiments on variants of the MNIST and CIFAR-100 datasets demonstrate the strong performance of GEM when compared to the state-of-the-art.

Review:
The authors of the manuscript consider the continuum learning setting, where the learner observes a stream of data points from training, which are ordered according to the tasks they belong to, i.e. the learner encounters any data from the next task only after it has observed all the training data for the current one. The authors propose a set of three metrics for evaluation performance of learning algorithms in this setting, which reflect their ability to transfer information to new tasks and not forget information about the earlier tasks. Could the authors, please, comment on the difference between continuum and lifelong learning (the corresponding sentence in line 254 seems incomplete)?
The authors also propose a learning method, termed Gradient of Episodic Memory (GEM). The idea of the method is to keep a set of examples from every observed task and make sure that at each update stage the loss on the observed tasks does not increase. It seems like there are some typos in eq. (6), because in its current form I don’t see how it captures this idea.
GEM is evaluated on a set of real-world datasets against a set of state-of-the-art baselines. I have a few questions regarding this evaluation:
1. comparison to icarl: if I understand correctly, icarl solves a multi-class classification problem with new classes being added over time, i.e. by the end of training on CIFAR-100 it would be able to solve a full 100-classes problem, while GEM would solve only any of 20 5-classes problems. How was the evaluation of icarl performed in this experiment? Was it ever given a hint which of 5 classes to look at?
2. it also seems from table 1 that the results in figure 1 for GEM and icarl were obtained for different memory sizes. If this is true, could the authors comment on why?
3. on MNIST rotations task multi-task method has less negative transfer than GEM, but its accuracy is lower. Could the authors, please, comment on why? Or these differences are non-significant? 
4. It would be very interesting to see performance of baseline (multi-task for MNIST and/or multi-class for CIFAR) that gets all the data in a batch, to evaluate the gap that remains there between continuum learning methods, like GEM, and standard batch learning.
5. were the architectures, used for baseline methods (multi-task and icarl), the same as for GEM?