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Title: Differentiable Hebbian Consolidation for Continual Learning

Paper content:
Continual learning is the problem of sequentially learning new tasks or knowledge while protecting previously acquired knowledge.
However, catastrophic forgetting poses a grand challenge for neural networks performing such learning process.
Thus, neural networks that are deployed in the real world often struggle in scenarios where the data distribution is non-stationary (concept drift), imbalanced, or not always fully available, i.e., rare edge cases.
We propose a Differentiable Hebbian Consolidation model which is composed of a Differentiable Hebbian Plasticity (DHP) Softmax layer that adds a rapid learning plastic component (compressed episodic memory) to the fixed (slow changing) parameters of the softmax output layer; enabling learned representations to be retained for a longer timescale.
We demonstrate the flexibility of our method by integrating well-known task-specific synaptic consolidation methods to penalize changes in the slow weights that are important for each target task.
We evaluate our approach on the Permuted MNIST, Split MNIST and Vision Datasets Mixture benchmarks, and introduce an imbalanced variant of Permuted MNIST --- a dataset that combines the challenges of class imbalance and concept drift.
Our proposed model requires no additional hyperparameters and outperforms comparable baselines by reducing forgetting.
A key aspect of human intelligence is the ability to continually adapt and learn in dynamic environments, a characteristic which is challenging to embed into artificial intelligence.
Recent advances in machine learning (ML) have shown tremendous improvements in various problems, by learning to solve one complex task very well, through extensive training on large datasets with millions of training examples or more.
However, most of the ML models that are used during deployment in the real-world are exposed to non-stationarity where the distributions of acquired data changes over time.
Therefore, after learning is complete, and these models are further trained with new data, responding to distributional changes, performance degrades with respect to the original data.
This phenomenon known as catastrophic forgetting or catastrophic interference (McCloskey & Cohen, 1989; French, 1999 ) presents a crucial problem for deep neural networks (DNNs) that are tasked with continual learning (Ring, 1994) , also called lifelong learning (Thrun & Mitchell, 1995; Thrun, 1998) .
In continual learning, the goal is to adapt and learn consecutive tasks without forgetting how to perform well on previously learned tasks, enabling models that are scalable and efficient over long timescales.
In most supervised learning methods, DNN architectures require independent and identically distributed (iid) samples from a stationary training distribution.
However, for ML systems in realworld applications that require continual learning, the iid assumption is easily violated when: (1) There is concept drift in the training data distribution.
(2) There are imbalanced class distributions and concept drift occuring simultaneously.
(3) Data representing all scenarios in which the learner is expected to perform are not initially available.
In such situations, learning systems face the "stability-plasticity dilemma" which is a well-known problem for artificial and biological neural networks (Carpenter & Grossberg, 1987; Abraham & Robins, 2005) .
This presents a continual learning challenge for an ML system where the model needs to provide a balance between its plasticity (to integrate new knowledge) and stability (to preserve existing knowledge).
In biological neural networks, synaptic plasticity has been argued to play an important role in learning and memory (Howland & Wang, 2008; Takeuchi et al., 2013; Bailey et al., 2015) and two major theories have been proposed to explain a human's ability to perform continual learning.
The first theory is inspired by synaptic consolidation in the mammalian neocortex (Benna & Fusi, 2016) where a subset of synapses are rendered less plastic and therefore preserved for a longer timescale.
The general idea for this approach is to consolidate and preserve synaptic parameters that are considered important for the previously learned tasks.
This is normally achieved through task-specific updates of synaptic weights in a neural network.
The second is the complementary learning system (CLS) theory (McClelland et al., 1995; Kumaran et al., 2016) , which suggests that humans extract highlevel structural information and store it in different brain areas while retaining episodic memories.
Recent work on differentiable plasticity has shown that neural networks with "fast weights" that leverage Hebbian learning rules (Hebb, 1949) can be trained end-to-end through backpropagation and stochastic gradient descent (SGD) to optimize the standard "slow weights", as well as also the amount of plasticity in each synaptic connection (Miconi, 2016; Miconi et al., 2018) .
These works use slow weights to refer to the weights normally used to train vanilla neural networks, which are updated slowly and are often associated with long-term memory.
The fast weights represent the weights that are superimposed on the slow weights and change quickly from one time step to the next based on input representations.
These fast weights behave as a form of short-term memory that enable "reactivation" of long-term memory traces in the slow weights.
Miconi et al. (2018) showed that simple plastic networks with learned plasticity outperform networks with uniform plasticity on various problems.
Moreover, there have been several approaches proposed recently for overcoming the catastrophic forgetting problem in fixed-capacity models by dynamically adjusting the plasticity of each synapse based on its importance for retaining past memories (Parisi et al., 2019) .
Here, we extend the work on differentiable plasticity to the task-incremental continual learning setting (van de Ven & Tolias, 2019) , where tasks arrive in a batch-like fashion, and have clear boundaries.
We develop a Differentiable Hebbian Consolidation 1 model that is capable of adapting quickly to changing environments as well as consolidating previous knowledge by selectively adjusting the plasticity of synapses.
We modify the traditional softmax layer and propose to augment the slow weights in the final fully-connected (FC) layer (softmax output layer) with a set of plastic weights implemented using Differentiable Hebbian Plasticity (DHP).
Furthermore, we demonstrate the flexibility of our model by combining it with recent task-specific synaptic consolidation based approaches to overcoming catastrophic forgetting such as elastic weight consolidation (Kirkpatrick et al., 2017; Schwarz et al., 2018) , synaptic intelligence (Zenke et al., 2017b) and memory aware synapses (Aljundi et al., 2018) .
Our model unifies core concepts from Hebbian plasticity, synaptic consolidation and CLS theory to enable rapid adaptation to new unseen data, while consolidating synapses and leveraging compressed episodic memories in the softmax layer to remember previous knowledge and mitigate catastrophic forgetting.
We test our proposed method on established benchmark problems including the Permuted MNIST (Goodfellow et al., 2013) , Split MNIST (Zenke et al., 2017b) and Vision Datasets Mixture (Ritter et al., 2018) benchmarks.
We also introduce the Imbalanced Permuted MNIST problem and show that plastic networks with task-specific synaptic consolidation methods outperform networks with uniform plasticity.

assistant: text: Hebbian plastic weights can behave as a compressed episodic memory storage in neural networks and with the combination of task-specific synaptic consolidation can improve the ability to alleviate catastrophic forgetting in continual learning.