How Neurons do Differentiation

Today I learned…

…how neural networks (think brains) can do differentiation by using temporal inhibition – i.e. by using a delayed signal. In the figure below, the node α will send a signal to two nodes. One of them – β – will pass on an inhibitory signal of the same strength as its input signal, but with a delay. Thus, when β’s signal gets sent to the final node, α will at the same time be sending its “next” output signal to the final node.

Differentiation by using delayed inhibition. Solid lines indicate excitatory signals and the dotted line an inhibitory signal.

“Differentiation” by using delayed inhibition. Solid lines indicate excitatory signals and the dotted line an inhibitory signal.

Therefore, the final node will receive two signals: the current output of α and the inverted previous output of α. If the final node sums these together its output will therefore be α’s current value minus its old value – i.e. positive if α’s output signal is increasing and negative if it is decreasing. Simple and beautiful!

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