plomlompom.com Git - plomrogue2-experiments/blob - neural/single_neuron_with_backprop.py

   1 import random
   2
   3 def sigmoid(x):
   4     import math
   5     return 1 / (1 + math.exp(-x))
   6
   7 def d_sigmoid(x):
   8     return sigmoid(x) * (1 - sigmoid(x))
   9
  10 def result(inputs):
  11     end_node['inputs'] = inputs[:]
  12     s = 0
  13     for i in range(len(inputs)):
  14         s += inputs[i] * end_node['weights'][i]
  15     end_node['weighted_biased_input'] = s + end_node['bias']
  16     end_node['sigmoid_output'] = sigmoid(end_node['weighted_biased_input'])
  17     return end_node['sigmoid_output']
  18
  19 def backprop(end_result, target, cost):
  20     d_cost_over_sigmoid_output = 2*(end_result - target)
  21     for i in range(len(end_node['weights'])):
  22         d_weighted_biased_input_over_weight = end_node['inputs'][i]
  23         d_sigmoid_output_over_weighted_biased_input = d_sigmoid(end_node['weighted_biased_input'])
  24         d_cost_over_weight = d_cost_over_sigmoid_output * d_sigmoid_output_over_weighted_biased_input * d_weighted_biased_input_over_weight
  25         end_node['weights'][i] -= d_cost_over_weight
  26     d_cost_over_bias = d_cost_over_sigmoid_output
  27     end_node['bias'] -= d_cost_over_bias
  28
  29 # identity
  30 training_set = [((0,), 0),
  31                 ((1,), 1)]
  32
  33 # NOT
  34 #training_set = [((0,), 1),
  35 #                ((1,), 0)]
  36
  37 # AND
  38 #training_set = [((0,0), 0),
  39 #                ((1,0), 0),
  40 #                ((0,1), 0),
  41 #                ((1,1), 1)]
  42
  43 # OR
  44 #training_set = [((0,0), 0),
  45 #                ((1,0), 1),
  46 #                ((0,1), 1),
  47 #                ((1,1), 1)]
  48
  49 # NOT (with one irrelevant column)
  50 #training_set = [((0,0), 1),
  51 #                ((1,0), 0),
  52 #                ((0,1), 1),
  53 #                ((1,1), 0)]
  54
  55 # XOR (will fail)
  56 #training_set = [((0,0), 0),
  57 #                ((1,0), 1),
  58 #                ((0,1), 1),
  59 #                ((1,1), 0)]
  60
  61 # 1 if above f(x)=x line, else 0
  62 #training_set = [((0,1), 1),
  63 #                ((2,3), 1),
  64 #                ((1,1), 0),
  65 #                ((2,2), 0)]
  66
  67 # 1 if above f(x)=x**2, else 0 (will fail: no linear separability)
  68 #training_set = [((2,4), 0),
  69 #                ((2,5), 1),
  70 #                ((3,9), 0),
  71 #                ((3,10), 1)]
  72
  73 end_node = {'weights': [random.random() for i in range(len(training_set[0][0]))],
  74             'bias': random.random()}
  75 n_training_runs = 100
  76 for i in range(n_training_runs):
  77     print()
  78     for element in training_set:
  79         inputs = element[0]
  80         target = element[1]
  81         result_ = result(inputs)
  82         cost = (result_ - target)**2
  83         formatted_weights = []
  84         for w in end_node['weights']:
  85             formatted_weights += ['%1.3f' % w]
  86         print("inputs %s target %s result %0.9f cost %0.9f weights [%s] bias %1.3f" % (inputs, target, result_, cost, ','.join(formatted_weights), end_node['bias']))
  87         backprop(result_, target, cost)