Hebbian learning from higher-order correlations requires crosstalk minimization

Activity-dependent synaptic plasticity should be extremely connection specific, though experiments have shown it is not, and biophysics suggests it cannot be. Extreme specificity (near-zero "crosstalk") might be essential for unsupervised learning from higher-order correlations, especially when a neuron has many inputs. It is well known that a normalized nonlinear Hebbian rule can learn "unmixing" weights from inputs generated by linearly combining independently fluctuating nonGaussian sources using an orthogonal mixing matrix. We previously reported that even if the matrix is only approximately orthogonal, a nonlinear-specific Hebbian rule can usually learn almost correct unmixing weights (Cox and Adams in Front Comput Neurosci 3: doi: 10.3389/neuro.10.011.2009 2009). We also reported simulations that showed that as crosstalk increases from zero, the learned weight vector first moves slightly away from the crosstalk-free direction and then, at a sharp threshold level of inspecificity, jumps to a completely incorrect direction. Here, we report further numerical experiments that show that above this threshold, residual learning is driven instead almost entirely by second-order input correlations, as occurs using purely Gaussian sources or a linear rule, and any amount of crosstalk. Thus, in this "ICA" model learning from higher-order correlations, required for unmixing, requires high specificity. We compare our results with a recent mathematical analysis of the effect of crosstalk for exactly orthogonal mixing, which revealed that a second, even lower, threshold, exists below which successful learning is impossible unless weights happen to start close to the correct direction. Our simulations show that this also holds when the mixing is not exactly orthogonal. These results suggest that if the brain uses simple Hebbian learning, it must operate with extraordinarily accurate synaptic plasticity to ensure powerful high-dimensional learning. Synaptic crowding would preclude this when inputs are numerous, and we propose that the neocortex might be distinguished by special circuitry that promotes extreme specificity for high-dimensional nonlinear learning.