Furthermore, we derived an STDP-like online learning rule by considering an approximation of Bayesian ICA with sequence sampling.

With these learning rules , the lateral connections successfully learn a mutual inhibition structure (Fig 5D); however, this learning is achievable only when the learning of a hidden external structure is possible from the random lateral connections (magenta lines in Fig 5B and 5C; note that orange points are hidden by magenta points because they show similar behaviors in noisy cases), which means either when crosstalk noise is low or two sources have similar amplitudes.

In addition, local minima are often unavoidable for online learning rules .

In this approximation, the learning rule of the estimated response probability matriX Q obeys where Y is the sampled sequence, and pik(Y1‘k'1) is the sample based approximation of pik in the previous equation.

Additionally, while we focused primarily on evolution specifying modular architectures, those architectures could also emerge via intra-life learning rules that lead to modular neural architectures.

More generally, exploring the degree to which evolution encodes learning rules that lead to modular architectures, as opposed to hard coding modular architectures, is an interesting area for future research.

The result is a Hebbian learning rule that is regulated by the inputs from neuromodulatory neurons, allowing the learning rate of specific connections to be increased or decreased in specific circumstances.