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Title: Variational Continual Learning

Paper content:
This paper develops variational continual learning (VCL), a simple but general framework for continual learning that fuses online variational inference (VI) and recent advances in Monte Carlo VI for neural networks.
The framework can successfully train both deep discriminative models and deep generative models in complex continual learning settings where existing tasks evolve over time and entirely new tasks emerge.
Experimental results show that VCL outperforms state-of-the-art continual learning methods on a variety of tasks, avoiding catastrophic forgetting in a fully automatic way.
Continual learning (also called life-long learning and incremental learning) is a very general form of online learning in which data continuously arrive in a possibly non i.i.d. way, tasks may change over time (e.g. new classes may be discovered), and entirely new tasks can emerge BID43 BID47 BID39 .
What is more, continual learning systems must adapt to perform well on the entire set of tasks in an incremental way that avoids revisiting all previous data at each stage.
This is a key problem in machine learning since real world tasks continually evolve over time (e.g. they suffer from covariate and dataset shift) and the size of datasets often prohibits frequent batch updating.
Moreover, practitioners are often interested in solving a set of related tasks that benefit from being handled jointly in order to leverage multi-task transfer.
Continual learning is also of interest to cognitive science, being an intrinsic human ability.The ubiquity of deep learning means that it is important to develop deep continual learning methods.
However, it is challenging to strike a balance between adapting to recent data and retaining knowledge from old data.
Too much plasticity leads to the infamous catastrophic forgetting problem BID34 BID36 BID13 and too much stability leads to an inability to adapt.
Recently there has been a resurgence of interest in this area.
One approach trains individual models on each task and then carries out a second stage of training to combine them BID28 .
A more elegant and more flexible approach maintains a single model and uses a single type of regularized training that prevents drastic changes in the parameters which have a large influence on prediction, but allows other parameters to change more freely BID29 BID26 BID50 .
The approach developed here follows this venerable work, but is arguably more principled, extensible and automatic.
This paper is built on the observation that there already exists an extremely general framework for continual learning: Bayesian inference.
Critically, Bayesian inference retains a distribution over model parameters that indicates the plausibility of any setting given the observed data.
When new data arrive, we combine what previous data have told us about the model parameters (the previous posterior) with what the current data are telling us (the likelihood).
Multiplying and renormalizing yields the new posterior, from which point we can recurse.
Critically, the previous posterior constrains parameters that strongly influence prediction, preventing them from changing drastically, but it allows other parameters to change.
The wrinkle is that exact Bayesian inference is typically intractable and so approximations are required.
Fortunately, there is an extensive literature on approximate inference for neural networks.
We merge online variational inference (VI) BID11 BID42 BID4 with Monte Carlo VI for neural networks BID3 to yield variational continual learning (VCL).
In addition, we extend VCL to include a small episodic memory by combining VI with the coreset data summarization method BID0 BID19 .
We demonstrate that the framework is general, applicable to both deep discriminative models and deep generative models, and that it yields excellent performance.
Approximate Bayesian inference provides a natural framework for continual learning.
Variational Continual Learning (VCL), developed in this paper, is an approach in this vein that extends online variational inference to handle more general continual learning tasks and complex neural network models.
VCL can be enhanced by including a small episodic memory that leverages coreset algorithms from statistics and connects to message-scheduling in variational message passing.
We demonstrated how the VCL framework can be applied to both discriminative and generative models.
Experimental results showed state-of-the-art performance when compared to previous continual learning approaches, even though VCL has no free parameters in its objective function.
Future work should explore alternative approximate inference methods using the same framework and also develop more sophisticated episodic memories.
Finally, we note that VCL is ideally suited for efficient model refinement in sequential decision making problems, such as reinforcement learning and active learning.
DISPLAYFORM0 Figure 6: Generated images from each of the generators after training.
Each of the columns shows the images generated from a specific task's generator, and each of the lines shows the generations from generators of all trained tasks.
Clearly the naive approach suffers from catastrophic forgetting, while other approaches successfully remember previous tasks.

assistant: text: This paper develops a principled method for continual learning in deep models.