Neural Network in 16 lines

[Yaroslav Bulatov]

Just for fun :)
http://yaroslav.hopto.org/russianwik...hp/neural-impl

Is there a more compact way?

Yaroslav

[pete]

bu*****@engr.orst.edu (Yaroslav Bulatov) wrote in
news:4d**************************@posting.google.c om:

Just for fun :)
http://yaroslav.hopto.org/russianwik...hp/neural-impl

Is there a more compact way?

Yaroslav

Here's the function from the link:

def train_smallest(data, weights, nu=1):
for it in range(1000):
for dp in data:
activations = [dp[0]+[1]]
for layer in weights: activations.append([sigmoid(innerproduct
(u,activations[-1])) for u in layer]+[1])
sigmas, new_weights = [],deepcopy(weights)
for i in range(len(weights))[::-1]:
sigma_row = []
for j, o in enumerate(activations[i+1][:-1]):
if not sigmas: err = dp[1][j]-o
else: err = innerproduct(sigmas[-1], [weights[i][k][j] for k in
range(len(weights[i+1]))])
sigma_row.append(o*(1-o)*err)
for k in range(len(weights[i][j])): new_weights[i][j][k]
+=nu*sigma_row[-1]*activations[i][k]
sigmas.append(sigma_row)
weights = new_weights
return weights

--------------------------------------------------------------------
And here's the whole program:

# Python implementation of feed-forward neural network

import Gnuplot
from math import *
from operator import mul
from copy import deepcopy
from Numeric import innerproduct

def sigmoid(x): return 1/(1+exp(-x))

# Trains Neural Network, returns
def train_smallest(data, weights, nu=1):
for it in range(1000):
for dp in data:
activations = [dp[0]+[1]]
for layer in weights: activations.append([sigmoid(innerproduct
(u,activations[-1])) for u in layer]+[1])
sigmas, new_weights = [],deepcopy(weights)
for i in range(len(weights))[::-1]:
sigma_row = []
for j, o in enumerate(activations[i+1][:-1]):
if not sigmas: err = dp[1][j]-o
else: err = innerproduct(sigmas[-1], [weights[i][k][j] for k in
range(len(weights[i+1]))])
sigma_row.append(o*(1-o)*err)
for k in range(len(weights[i][j])): new_weights[i][j][k]
+=nu*sigma_row[-1]*activations[i][k]
sigmas.append(sigma_row)
weights = new_weights
return weights

# graphs given neural network through gnuplot
def graphNN(weights):
g = Gnuplot.Gnuplot(debug=0)
g('set yrange [0:1]')

prev_row = ['x', 'y']

g('s(x) = 1/(1+exp(-x))')

# convert neural network to analytic form
for i, row in enumerate(weights):
new_row = []
for j, unit in enumerate(row):
name = "r%dc%d(x,y)" %(i, j)
new_row.append(name)
formula = ''
for k, weight in enumerate(unit):
if k>0: formula+='+'
if k < len(unit)-1:
formula+='%f*%s' % (weight, prev_row[k])
else: # bias unit
formula+='%f' % (weight)
g(name+'=s('+formula+')')
prev_row = new_row

g('splot[-2:2][-2:2][] %s' % (name,))
raw_input()

# XOR data
data = [[[1,1],[1]], [[-1,-1], [1]], [[1,-1],[0]], [[-1,1],[0]] ]

# Starting weights (leads to global optimum)
start_weights = [[[-1,-1, -1],[1,-1, -1]],[[1,1,0]]]

# Train the network
weights = train_smallest(data, start_weights)

# Visualize it
graphNN(weights)