I am looking for good papers on the possibility that dendritic trees may compute derivatives of functions but haven’t found anything so far. Such computations may be very useful for both learning and closed-loop control. Are there papers I have overlooked?
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For concreteness, I think dendritic trees may compute the partial derivatives of functions using an algorithm similar to the Cauchy Integral Formula for derivatives. It can be implemented on any binary tree where a large number of local computations occur in parallel.
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For a large number of functions(ex. polynomials, sigmoid, trigonometric) we have geometric convergence in error. I think any proposed algorithm must scale very well with the dimension of the input to the dendritic tree. Very fast convergence implies robustness.
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I am a synapse somewhere in a neuron. I participate locally in potential NMDA spikes. My influence on the soma may be shunted at times. etc. A spike has just happened. Can I know if it would have happened without me. Iwould the spike have been more likely if I had a larger weight
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This version makes sense.
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