  Continual learning algorithms strive to acquire new knowledge while
preserving prior information. Often, these algorithms emphasise stability and
restrict network updates upon learning new tasks. In many cases, such
restrictions come at a cost to the model's plasticity, i.e. the model's ability
to adapt to the requirements of a new task. But is all change detrimental?
Here, we approach this question by proposing that activation spaces in neural
networks can be decomposed into two subspaces: a readout range in which change
affects prior tasks and a null space in which change does not alter prior
performance. Based on experiments with this novel technique, we show that,
indeed, not all activation change is associated with forgetting. Instead, only
change in the subspace visible to the readout of a task can lead to decreased
stability, while restricting change outside of this subspace is associated only
with a loss of plasticity. Analysing various commonly used algorithms, we show
that regularisation-based techniques do not fully disentangle the two spaces
and, as a result, restrict plasticity more than need be. We expand our results
by investigating a linear model in which we can manipulate learning in the two
subspaces directly and thus causally link activation changes to stability and
plasticity. For hierarchical, nonlinear cases, we present an approximation that
enables us to estimate functionally relevant subspaces at every layer of a deep
nonlinear network, corroborating our previous insights. Together, this work
provides novel means to derive insights into the mechanisms behind stability
and plasticity in continual learning and may serve as a diagnostic tool to
guide developments of future continual learning algorithms that stabilise
inference while allowing maximal space for learning.
