Tag Archives: absolute value

Nengo scripting: absolute value

To just get the code you can copy / paste from below or get the code from my github: absolute_value.py

This is a simple script for performing the absolute value function in Nengo. The most efficient way I’ve found to implement this is to use two separate populations for each dimension of the input signal, one to represent the signal when it’s greater than zero and simply relay it to the output node, and one to represent the signal when it’s less than zero, and project x * -1 to the output node. Here’s the code, and I’ll step through it below.

def make_abs_val(name, neurons, dimensions, intercept=[0]):
    def mult_neg_one(x):
        return x[0] * -1 

    abs_val = nef.Network(name)

    abs_val.make('input', neurons=1, dimensions=dimensions, mode='direct') # create input relay
    abs_val.make('output', neurons=1, dimensions=dimensions, mode='direct') # create output relay
    
    for d in range(dimensions): # create a positive and negative population for each dimension in the input signal
        abs_val.make('abs_pos%d'%d, neurons=neurons, dimensions=1, encoders=[[1]], intercept=intercept)
        abs_val.make('abs_neg%d'%d, neurons=neurons, dimensions=1, encoders=[[-1]], intercept=intercept)

        abs_val.connect('input', 'abs_pos%d'%d, index_pre=d)
        abs_val.connect('input', 'abs_neg%d'%d, index_pre=d)
    
        abs_val.connect('abs_pos%d'%d, 'output', index_post=d)
        abs_val.connect('abs_neg%d'%d, 'output', index_post=d, func=mult_neg_one)

    return abs_val.network

First off, the function takes in parameters specifying the number of dimensions, the number of neurons for each population generated, a name, and optionally an intercept value. I’ll come back to why the intercept value is an option in a bit.

Inside the make_abs_val function another function that multiplies the first dimension of its input by -1 is specified. This mult_neg_one function is going to be used by our population representing negative values of the input signal.

Next, we create the network and call it abs_val. Input and output relay nodes are then created, with one neuron, of the specified dimension number, and the populations are set to direct mode. These are the populations that will be connected to from populations outside of the abs_val network.

Now there is a loop for each dimension of the input signal. Inside, two populations are created, where the only difference is their encoder values. Their intercepts specify the start of the range of values they represent. The default is 0, so when it’s not specified these populations will represent values from 0 to 1 (1 is the default end value of the range). For abs_neg, the encoders=[[-1]] line changes the range of values represented from (0,1) to (-1,0). Now we have two populations for dimension d, one that represents only positive values (between 0 and 1), and one that represents only negative values (between -1 and 0). And we’re almost done!

The only thing left to do is to hook up the populations to the input and output appropriately and incorporate the mult_neg_one function into the connection between each of the abs_neg populations and the output relay node. We want each set of populations representing a single dimension to receive and project back into the appropriate dimension of the output relay function, so we employ the index_pre and index_post parameters. Because we want each set to receive only dimension d from the input, on that connection specification we set index_pre=d. When setting up the projections to the output relay node, we similarly only want each population to project to the appropriate output dimension d, so we set index_post=d.

By default, the connect call sets up a communication channel, that is to say no computation is performed on the signal passed from the pre to the post population. This is what we want for abs_pos population, but for the abs_neg population we want the mult_neg_one function to be applied, so that any negative values are multiplied by -1, and give us positive values. This can be done by using the func parameter, and so we call it and set it func=mult_neg_one. Now the connection from abs_neg to the output node will be transformed by the mult_neg_one function.

And that’s it! Here is a script that gets it running (which can also be found on my github: absolute_value.py):

import nef
import random

# constants / parameter setup etc
N = 50 # number of neurons
D = 3 # number of dimensions

def make_abs_val(name, neurons, dimensions, intercept=[0]):
    def mult_neg_one(x):
        return x[0] * -1 

    abs_val = nef.Network(name)

    abs_val.make('input', neurons=1, dimensions=dimensions, mode='direct') # create input relay
    abs_val.make('output', neurons=1, dimensions=dimensions, mode='direct') # create output relay
    
    for d in range(dimensions): # create a positive and negative population for each dimension in the input signal
        abs_val.make('abs_pos%d'%d, neurons=neurons, dimensions=1, encoders=[[1]], intercept=intercept)
        abs_val.make('abs_neg%d'%d, neurons=neurons, dimensions=1, encoders=[[-1]], intercept=intercept)

        abs_val.connect('input', 'abs_pos%d'%d, index_pre=d)
        abs_val.connect('input', 'abs_neg%d'%d, index_pre=d)
    
        abs_val.connect('abs_pos%d'%d, 'output', index_post=d)
        abs_val.connect('abs_neg%d'%d, 'output', index_post=d, func=mult_neg_one)

    return abs_val.network

net = nef.Network('network')

# Create absolute value subnetwork and add it to net
net.add(make_abs_val(name='abs_val', dimensions=D, neurons=N))

# Create function input
net.make_input('input', values=[random.random() for d in range(D)])

# Connect things up
net.connect('input', 'abs_val.input')

# Add it all to the Nengo world
net.add_to_nengo()

And here’s a picture of it running.

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