Representational Drift as a Result of Implicit Regularization

Recent studies show that, even in constant environments, the tuning of single neurons
to outside world variables gradually changes over time in a variety of brain regions [1, 2, 3, 4, 5]. This
phenomenon, termed representational drift, has changed the way we think about the stability of
memory and perception, but its driving forces and properties are still mostly unknown. We combine
data analysis and modeling to show that implicit regularization can partially explain drift. We train an
artificial neural network on a predictive coding task. We continue training in the presence of noise
after good performance is obtained. We find that neurons become tuned to position early in training,
but that the tuning slowly changes as training continues. Specifically, the network is spontaneously
and slowly converging to a sparse solution, while maintaining a good representation of the
environment. Recent results from the machine learning community offer an analytical explanation to
this process [7]. Intuitively, when a learning system is perturbed by noise during learning it will aspire
to be robust to that type of noise by slowly minimizing an implicit regularizer. We then analyze data
from an experimental paradigm in which drift was demonstrated, and observe similar trends. Drift is
relative to time spent in a specific context, it results in a slow sparsification process, and the overall
decoding error remains constant. We conclude that learning of a given stimulus or environment is
divided into three phases: a short transient of familiarity with the environment in which
representations form, a long transient of implicit regularization in which representations change in a
specific direction, and a steady state of null drift in which representations change randomly.