Figure 3
From: Efficient dendritic learning as an alternative to synaptic plasticity hypothesis
Biological mechanism for self-emergence of input crosses. (a) Zoom-in on three inputs (i.e., \(I_{1} , I_{2} , I_{3} )\) dendritic segment, with nonlinear amplification \(A\left( I \right) = I + I^{2}\), resulting in input crosses. (b) Combining all synaptic influx inputs \(I\left( {\left\{ {I_{k} } \right\}} \right)\) results in higher-order input crosses. (c) Equivalence between one amplified dendrite, \(f\left( I \right) = 3I\) (left) and where amplification is shifted to its synapses (larger green-circles, right). (d) Log–log scale of optimized test errors for the architecture presented in Fig. 2c with additional 10,000 input crosses trained over 15, 30, 60 and 90 examples/digit and a power-law fit (line), and without input crosses (circles). Standard deviation obtained from 10 samples with different initial conditions, i.e. weights and examples. (e) Hebbian learning identifier for a digit, consisting of a committee of seven perceptrons, each with 10,000 input crosses of order 3 (green background).
