  Hebbian synaptic plasticity inevitably leads to interference and forgetting
when different, overlapping memory patterns are sequentially stored in the same
network. Recent work on artificial neural networks shows that an
information-geometric approach can be used to protect important weights to slow
down forgetting. This strategy however is biologically implausible as it
requires knowledge of the history of previously learned patterns. In this work,
we show that a purely local weight consolidation mechanism, based on estimating
energy landscape curvatures from locally available statistics, prevents pattern
interference. Exploring a local calculation of energy curvature in the
sparse-coding limit, we demonstrate that curvature-aware learning rules reduce
forgetting in the Hopfield network. We further show that this method connects
information-geometric global learning rules based on the Fisher information to
local spike-dependent rules accessible to biological neural networks. We
conjecture that, if combined with other learning procedures, it could provide a
building-block for content-aware learning strategies that use only quantities
computable in biological neural networks to attenuate pattern interference and
catastrophic forgetting. Additionally, this work clarifies how global
information-geometric structure in a learning problem can be exposed in local
model statistics, building a deeper theoretical connection between the
statistics of single units in a network, and the global structure of the
collective learning space.
