From: Christian Heller Date: Mon, 13 May 2019 03:27:11 +0000 (+0200) Subject: Add basic neural networking experiments. X-Git-Url: https://plomlompom.com/repos/%7B%7Bdb.prefix%7D%7D/%7B%7B%20web_path%20%7D%7D/decks/index.html?a=commitdiff_plain;h=1b80c5b27b73e55b25251e002c4e545ecc5ae298;p=plomrogue2-experiments Add basic neural networking experiments. --- diff --git a/neural/simple_perceptron.py b/neural/simple_perceptron.py new file mode 100755 index 0000000..8af59f3 --- /dev/null +++ b/neural/simple_perceptron.py @@ -0,0 +1,83 @@ +def step(x): + step = 0 # If 0.5, we need no bias for AND and OR; if 0, none for NOT. + # With learning, the bias will slowly balance any choice. + if x >= step: + return 1 + else: + return 0 + +def result(inputs): + s = 0 + perceptron['inputs'] = inputs[:] + for i in range(len(inputs)): + s += inputs[i] * perceptron['weights'][i] + return step(s + perceptron['bias']) + +# identity +#training_set = [((0,), 0), +# ((1,), 1)] + +# NOT +#training_set = [((0,), 1), +# ((1,), 0)] + +# AND +#training_set = [((0,0), 0), +# ((1,0), 0), +# ((0,1), 0), +# ((1,1), 1)] + +# OR +#training_set = [((0,0), 0), +# ((1,0), 1), +# ((0,1), 1), +# ((1,1), 1)] + +# NOT (with one irrelevant column) +#training_set = [((0,0), 1), +# ((1,0), 0), +# ((0,1), 1), +# ((1,1), 0)] + +# XOR (will fail, as Minsky/Papert say) +#training_set = [((0,0), 0), +# ((1,0), 1), +# ((0,1), 1), +# ((1,1), 0)] + +# 1 if above f(x)=x line, else 0 +training_set = [((0,1), 1), + ((2,3), 1), + ((1,1), 0), + ((2,2), 0)] + +# 1 if above f(x)=x**2, else 0 (will fail: no linear separability) +#training_set = [((2,4), 0), +# ((2,5), 1), +# ((3,9), 0), +# ((3,10), 1)] + +perceptron = {'weights': [0 for i in range(len(training_set[0][0]))], + 'bias': 0} +adaption_size = 0.1 + +for i in range(100): + print() + go_on = False + for element in training_set: + inputs = element[0] + target = element[1] + result_ = result(inputs) + print("inputs %s target %s result %s correctness %5s weights %s bias %s" % (inputs, target, result_, target==result_, perceptron['weights'], perceptron['bias'])) + if target != result_: + go_on=True + perceptron['bias'] += adaption_size * (target - result_) + for i in range(len(perceptron['weights'])): + perceptron['weights'][i] += adaption_size * (target - result_) * perceptron['inputs'][i] + if not go_on: + break +print() +if go_on: + print('COULD NOT SOLVE.') +else: + print('SUCCESS') diff --git a/neural/single_neuron_with_backprop.py b/neural/single_neuron_with_backprop.py new file mode 100755 index 0000000..f438c7e --- /dev/null +++ b/neural/single_neuron_with_backprop.py @@ -0,0 +1,87 @@ +import random + +def sigmoid(x): + import math + return 1 / (1 + math.exp(-x)) + +def d_sigmoid(x): + return sigmoid(x) * (1 - sigmoid(x)) + +def result(inputs): + end_node['inputs'] = inputs[:] + s = 0 + for i in range(len(inputs)): + s += inputs[i] * end_node['weights'][i] + end_node['weighted_biased_input'] = s + end_node['bias'] + end_node['sigmoid_output'] = sigmoid(end_node['weighted_biased_input']) + return end_node['sigmoid_output'] + +def backprop(end_result, target, cost): + d_cost_over_sigmoid_output = 2*(end_result - target) + for i in range(len(end_node['weights'])): + d_weighted_biased_input_over_weight = end_node['inputs'][i] + d_sigmoid_output_over_weighted_biased_input = d_sigmoid(end_node['weighted_biased_input']) + d_cost_over_weight = d_cost_over_sigmoid_output * d_sigmoid_output_over_weighted_biased_input * d_weighted_biased_input_over_weight + end_node['weights'][i] -= d_cost_over_weight + d_cost_over_bias = d_cost_over_sigmoid_output + end_node['bias'] -= d_cost_over_bias + +# identity +training_set = [((0,), 0), + ((1,), 1)] + +# NOT +#training_set = [((0,), 1), +# ((1,), 0)] + +# AND +#training_set = [((0,0), 0), +# ((1,0), 0), +# ((0,1), 0), +# ((1,1), 1)] + +# OR +#training_set = [((0,0), 0), +# ((1,0), 1), +# ((0,1), 1), +# ((1,1), 1)] + +# NOT (with one irrelevant column) +#training_set = [((0,0), 1), +# ((1,0), 0), +# ((0,1), 1), +# ((1,1), 0)] + +# XOR (will fail) +#training_set = [((0,0), 0), +# ((1,0), 1), +# ((0,1), 1), +# ((1,1), 0)] + +# 1 if above f(x)=x line, else 0 +#training_set = [((0,1), 1), +# ((2,3), 1), +# ((1,1), 0), +# ((2,2), 0)] + +# 1 if above f(x)=x**2, else 0 (will fail: no linear separability) +#training_set = [((2,4), 0), +# ((2,5), 1), +# ((3,9), 0), +# ((3,10), 1)] + +end_node = {'weights': [random.random() for i in range(len(training_set[0][0]))], + 'bias': random.random()} +n_training_runs = 100 +for i in range(n_training_runs): + print() + for element in training_set: + inputs = element[0] + target = element[1] + result_ = result(inputs) + cost = (result_ - target)**2 + formatted_weights = [] + for w in end_node['weights']: + formatted_weights += ['%1.3f' % w] + 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'])) + backprop(result_, target, cost)