Hebbian Crosstalk and Input Segregation
  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. 
Anca Radulescu, Paul Adams
q-bio.NC math.DS