nengolib.signal.pes_learning_rate

nengolib.signal.pes_learning_rate(epsilon, activities, t, dt=0.001)

Determine the ideal learning rate for PES without noise or filtering.

This function returns a learning_rate for use in the PES rule, such that after t seconds (with a simulation timestep of dt) a constant input will have error equal to epsilon times the initial error. [1]

Parameters:

epsilon : float

The desired approximation factor. The resulting error will be epsilon times the initial error after time t. If you want the error to be at most some constant, then divide epsilon by the largest possible initial error (usually no more than 2, when the radius is 1).

activities : (n,) array_like

An array of n activity rates. Less activity (small \(||a||\)) need a higher learning rate. Pick the activities with the smallest \(||a||\) that you want to learn within epsilon, or make it the average firing rate of each neuron.

t : float

The amount of simulation time (in seconds) required to obtain the desired error.

dt : float, optional

The simulation timestep, defaults to 0.001 seconds.

Returns:

learning_rate : float

The learning rate to provide to the PES rule.

gamma : float

The rate of convergence, such that the error is the initial error multiplied by \(\gamma^k\) on the k’th timestep.

References

[1]	Aaron R. Voelker. A solution to the dynamics of the prescribed error sensitivity learning rule. Technical Report, Centre for Theoretical Neuroscience, Waterloo, ON, 10 2015. doi:10.13140/RG.2.1.3048.0084. [URL]