user: text: Write a concise one-sentence TLDR summary of the scientific paper content below.

Title: OvA-INN: Continual Learning with Invertible Neural Networks

Paper content:
In the field of Continual Learning, the objective is to learn several tasks one after the other without access to the data from previous tasks.
Several solutions have been proposed to tackle this problem but they usually  assume that the user knows which of the tasks to perform at test time on a particular sample, or rely on small samples from previous data and most of them suffer of a substantial drop in accuracy when updated with batches of only one class at a time.
In this article, we propose a new method, OvA-INN, which is able to learn one class at a time and without storing any of the previous data.
To achieve this, for each class, we train a specific Invertible Neural Network to output the zero vector for its class.
At test time, we can predict the class of a sample by identifying which network outputs the vector with the smallest norm.
With this method, we show that we can take advantage of pretrained models by stacking an invertible network on top of a features extractor.
This way, we are able to outperform state-of-the-art approaches that rely on features learning for the Continual Learning of MNIST and CIFAR-100 datasets.
In our experiments, we are reaching 72% accuracy on CIFAR-100 after training our model one class at a time.
A typical Deep Learning workflow consists in gathering data, training a model on this data and finally deploying the model in the real world (Goodfellow et al., 2016) .
If one would need to update the model with new data, it would require to merge the old and new data and process a training from scratch on this new dataset.
Nevertheless, there are circumstances where this method may not apply.
For example, it may not be possible to store the old data because of privacy issues (health records, sensible data) or memory limitations (embedded systems, very large datasets).
In order to address those limitations, recent works propose a variety of approaches in a setting called Continual Learning (Parisi et al., 2018) .
In Continual Learning, we aim to learn the parameters w of a model on a sequence of datasets
with the inputs x j i ∈ X i and the labels y j i ∈ Y i , to predict p(y * |w, x * ) for an unseen pair (x * , y * ).
The training has to be done on each dataset, one after the other, without the possibility to reuse previous datasets.
The performance of a Continual Learning algorithm can then be measured with two protocols : multi-head or single-head.
In the multi-head scenario, the task identifier i is known at test time.
For evaluating performances on task i, the set of all possible labels is then Y = Y i .
Whilst in the single-head scenario, the task identifier is unknown, in that case we have Y = ∪ N i=1 Y i with N the number of tasks learned so far.
For example, let us say that the goal is to learn MNIST sequentially with two batches: using only the data from the first five classes and then only the data from the remaining five other classes.
In multi-head learning, one asks at test time to be able to recognize samples of 0-4 among the classes 0-4 and samples of 5-9 among classes 5-9.
On the other hand, in single-head learning, one can not assume from which batch a sample is coming from, hence the need to be able to recognize any samples of 0-9 among classes 0-9.
Although the former one has received the most attention from researchers, the last one fits better to the desiderata of a Continual Learning system as expressed in Farquhar & Gal (2018) and (van de Ven & Tolias, 2019) .
The single-head scenario is also notoriously harder than its multi-head counterpart (Chaudhry et al., 2018) and is the focus of the present work.
Updating the parameters with data from a new dataset exposes the model to drastically deteriorate its performance on previous data, a phenomenon known as catastrophic forgetting (McCloskey & Cohen, 1989) .
To alleviate this problem, researchers have proposed a variety of approaches such as storing a few samples from previous datasets (Rebuffi et al., 2017) , adding distillation regularization (Li & Hoiem, 2018) , updating the parameters according to their usefulness on previous datasets (Kirkpatrick et al., 2017) , using a generative model to produce samples from previous datasets (Kemker & Kanan, 2017) .
Despite those efforts toward a more realistic setting of Continual Learning, one can notice that, most of the time, results are proposed in the case of a sequence of batches of multiple classes.
This scenario often ends up with better accuracy (because the learning procedure highly benefits of the diversity of classes to find the best tuning of parameters) but it does not illustrate the behavior of those methods in the worst case scenario.
In fact, Continual Learning algorithms should be robust in the size of the batch of classes.
In this work, we propose to implement a method specially designed to handle the case where each task consists of only one class.
It will therefore be evaluated in the single-head scenario.
Our approach, named One-versus-All Invertible Neural Networks (OvA-INN), is based on an invertible neural network architecture proposed by Dinh et al. (2014) .
We use it in a One-versus-All strategy : each network is trained to make a prediction of a class and the most confident one on a sample is used to identify the class of the sample.
In contrast to most other methods, the training phase of each class can be independently executed from one another.
The contributions of our work are :
(i) a new approach for Continual Learning with one class per batch;
(ii) a neural architecture based on Invertible Networks that does not require to store any of the previous data;
(iii) state-of-the-art results on several tasks of Continual Learning for Computer Vision (CIFAR-100, MNIST) in this setting.
We start by reviewing the closest methods to our approach in Section 2, then explain our method in Section 3, analyse its performances in Section 4 and identify limitations and possible extensions in Section 5.
A limiting factor in our approach is the necessity to add a new network each time one wants to learn a new class.
This makes the memory and computational cost of OvA-INN linear with the number of classes.
Recent works in networks merging could alleviate the memory issue by sharing weights (Chou et al., 2018) or relying on weights superposition (Cheung et al., 2019) .
This being said, we showed that Ova-INN was able to achieve superior accuracy on CIFAR-100 class-by-class training than approaches reported in the literature, while using less parameters.
Another constraint of using Invertible Networks is to keep the size of the output equal to the size of the input.
When one wants to apply a features extractor with a high number of output channels, it can have a very negative impact on the memory consumption of the invertible layers.
Feature Selection or Feature Aggregation techniques may help to alleviate this issue (Tang et al., 2014) .
Finally, we can notice that our approach is highly dependent on the quality of the pretrained features extractor.
In our CIFAR-100, we had to rescale the input to make it compatible with ResNet.
Nonetheless, recent research works show promising results in training features extractors in very efficient ways (Asano et al., 2019) .
Because it does not require to retrain its features extractor, we can foresee better performance in class-by-class learning with OvA-INN as new and more efficient features extractors are discovered.
As a future research direction, one could try to incorporate our method in a Reinforcement Learning scenario where various situations can be learned separately in a first phase (each situation with its own Invertible Network).
Then during a second phase where any situation can appear without the agent explicitly told in which situation it is in, the agent could rely on previously trained Invertible Networks to improve its policy.
This setting is closely related to Options in Reinforcement Learning.
Also, in a regression setting, one can add a fully connected layer after an intermediate layer of an Invertible Network and use it to predict the output for the trained class.
At test time, one only need to read the output from the regression layer of the Invertible Network that had the highest confidence.
In this paper, we proposed a new approach for the challenging problem of single-head Continual Learning without storing any of the previous data.
On top of a fixed pretrained neural network, we trained for each class an Invertible Network to refine the extracted features and maximize the loglikelihood on samples from its class.
This way, we show that we can predict the class of a sample by running each Invertible Network and identifying the one with the highest log-likelihood.
This setting allows us to take full benefit of pretrained models, which results in very good performances on the class-by-class training of CIFAR-100 compared to prior works.
channels with 5 × 5 kernel, a fully-connected layer with 100 channels applied on an input of size 7 × 7 and a final layer of 10 channels :
S iCaRL,MNIST = 28 × 28 × 800 + (5 × 5 + 1) × 32 + (5 × 5 + 1) × 64 + (7 × 7 × 64 + 1) × 100 + (100 + 1) × 10 = 944406

assistant: text: We propose to train an Invertible Neural Network for each class to perform class-by-class Continual Learning.