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		Universit\"at Hamburg\\
		Department Informatik\\
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\section{Introduction}
\label{sec:introduction}

Autonomous robots need to adapt to new situations. They have a need to learn
for an entire life. In order to do this they need a second environmental feedback
loop that tells them when to learn.\cite{Toutounji2016}

The learning poses another problem as well. The previously learned weights
are usually largely forgotten, which is known as catastrophic forgetting.\cite{French1999},
\cite{McCloskey1989}

Since catastrophic forgetting is a key problem for autonomous learning, it is
crucial to overcome it. In this paper I will present some approaches for
learning in an autonomous setup to analyse which of them if any can overcome
catastrophic forgetting. Attempts to overcome that were made by
Kirkpatrick\cite{Kirkpatrick2017}, Velez\cite{Velez2017} and Shmelkov\cite{Shmelkov2017}.

In the context of this paper plasticity refers to synaptic plasticity as described
in Citri\cite{Citri2008}. The process of learning itself, changing the weights,
is already considered plasticity. It is important however that the weights can
be changed during the lifetime of the neural network. Ordinary neural networks
trained with backpropagation are not involving plasticity.

\section{Catastrophic Forgetting}
\label{sec:catastrophicforgetting}

This section presents the major research developments related to catastrophic
forgetting and explains what it actually is. It follows the review of French\cite{French1999}.

McCloskey and Cohen\cite{McCloskey1989} originally discovered the problem of
catastrophic forgetting, which was referred to as catastrophic interference. This
discovery of a fundamental limitation of the classic neural network was as
important as the work of Minsky and Papert\cite{Minsky1969} who described the
limitations of a perceptron twenty years prior. The key discovery of McCloskey
and Cohen was that previously learned patterns were completely forgotten after
a few training cycles of learning a new pattern. The reason behind this
behaviour was the real problem. They identified the single set of shared
weights as responsible for it.

If one thinks a few minutes about it this makes absolute sense. The classic
backpropagation algorithm works by modifying the weights that have contributed
the most to a bad outcome. When the set of targets is changing then the network
will perform badly for the new pattern. In order to rectify this the backpropagation
algorithm will change many of the weights so that the network is delivering a
good result for the new pattern. This on the other hand results in an increasingly
worse performance on previously learned patterns. If this worsening was gradual
it would still be unfortunate but understandable. It is called catastrophic
because this performance change is not gradual but rather abrupt. Even small
changes in the weights can have a huge impact on the output.

In fact catastrophic forgetting is only a very radical example of a more general
problem for all models of memory, the so called "stability-plasticity" problem\cite{Grossberg1982}.
This problem, sometimes called dilemma, basically puts up the question how to
design a system in such a way that it is both sensitive to new input and not
radically disrupted by it. In other words: That it can learn new things
without largely or completely forgetting already learned things.

Early attempts to alleviate or overcome catastrophic forgetting required a more
sparse representation. This means that not every weight is responsible for all
possible inputs. The downside is a worse ability to generalize to new input
and overall a worse ability to discriminate. In an extreme form this can
lead to catastrophic remembering\cite{Sharkey1995}.
The idea here is that a
network learns the function describing the inputs too well and therefore
loses its ability to differentiate between new and already learned input.
This can be understood well with the example given by French\cite{French1999},
where a network has the task to reproduce the input at the output. It can detect
a new input if the output is diverging by large margin. It has learned too well
if it learned the identity function and is therefore able to reproduce any
input perfectly at the output and hence loses the ability to detect new input.

Significant improvements were made by rehearsing previously learned input.
Robins\cite{Robins1995} found a way to rehearse prior input if it is no longer
available and called it "pseudo-patterns". The idea being that the weights
of the trained network resemble a function. A random input and the predicted
output together somewhat describe this function and are such a pattern. Robins
used a bunch of them interleaved with new input and the results were promising
as the forgetting became more gradual. This insight together with
the findings of McClelland\cite{McClelland1995} resulted in the development
of dual-network models.
In short one network would model and the hippocampus and be able to quickly learn new
information without disrupting previously learned regularities. This network
would then serve as teacher for the second network which models the neocortex
and is responsible for generalizing.

In the time between 1999 and 2018 more work was done with regards to catastrophic
forgetting. Most recently the work of Kirkpatrick\cite{Kirkpatrick2017},
Velez\cite{Velez2017} and Shmelkov\cite{Shmelkov2017} has to be named. The main
focus here was a brief introduction of catastrophic forgetting and therefore
these newest approaches will not be described here.

\section{Plasticity}
\label{sec:plasticity}

Plasticity can be realized by various approaches. Here three approaches are
presented, Modulated Random Search, Modulated Gaussian Walk and Diffusion based
neuromodulation.

\subsection{Modulated Random Search}
\label{subsec:mrs}

Does things.

\subsection{Modulated Gaussian Walk}
\label{subsec:mgw}

Does things more efficient.

\subsection{Localized learning}
\label{subsec:diffusion}

Velez describe another approach that employs
modularity for the learning. Essentially this results in task-specific localized
learning and functional modules for each subtask.

\section{Comparison regarding catastrophic forgetting}
\label{sec:comparison}

Modulated Random Search is not at all useful for overcoming catastrophic forgetting.
Modulated Gaussian Walk improves to that end.
Localized learning overcomes catastrophic forgetting for small
networks.

\section{Conclusion}
\label{sec:concl}

A second environmental feedback loop is important to tell autonomous systems
when to learn. But the method to learn is important as well to be any use
in a practical environment. A comparison has shown that localized learning
can overcome catastrophic forgetting for small networks.

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