  Purpose: We previously proposed that Hebbian adjustments that are
incompletely synapse specific ("crosstalk") might be analogous to genetic
mutations. We analyze aspects of the effect of crosstalk in Hebbian learning
using the classical Oja model.
  Methods: In previous work we showed that crosstalk leads to learning of the
principal eigenvector of EC (the input covariance matrix pre-multiplied by an
error matrix that describes the crosstalk pattern), and found that with
positive input correlations increasing crosstalk smoothly degrades performance.
However, the Oja model requires negative input correlations to account for
biological ocular segregation. Although this assumption is biologically
somewhat implausible, it captures features that are seen in more complex
models. Here, we analyze how crosstalk would affect such segregation.
  Results: We show that for statistically unbiased inputs crosstalk induces a
bifurcation from segregating to non-segregating outcomes at a critical value
which depends on correlations. We also investigate the behavior in the vicinity
of this critical state and for weakly biased inputs.
  Conclusions: Our results show that crosstalk can induce a bifurcation under
special conditions even in the simplest Hebbian models and that even the low
levels of crosstalk observed in the brain could prevent normal development.
However, during learning pairwise input statistics are more complex and
crosstalk-induced bifurcations may not occur in the Oja model. Such
bifurcations would be analogous to "error catastrophes" in genetic models, and
we argue that they are usually absent for simple linear Hebbian learning
because such learning is only driven by pairwise correlations.
