import numpy as np from copy import deepcopy as copy class AIlib: def sigmoid(x): return 1/(1 + np.exp(-x)) def correctFunc(inp: np.array): # generates the correct answer for the AI # basically invert the rgb values return np.asarray([1.0 - inp[0], 1.0 - inp[1], 1.0 - inp[2]]) # cost function, lower -> good, higher -> bad, bad bot, bad def calcCost(predicted: np.array, correct: np.array): costSum = 0 maxLen = len(correct) for i in range(maxLen): costSum += abs((predicted[i] - correct[i])) return costSum / maxLen def getThinkCost(inp: np.array, predicted: np.array): corr = AIlib.correctFunc(inp) return AIlib.calcCost(predicted, corr) # generate a matrix with x, y dimensions with random values from min-max in it def genRandomMatrix(x: int, y: int, min: float = 0.0, max: float = 1.0): # apply ranger with * and - mat = np.random.rand(x, y) - 0.25 return mat def think(inp: np.array, obj, layerIndex: int = 0): # recursive thinking, hehe maxLayer = len(obj.weights) - 1 # dot multiply the input and the weights weightedLayer = np.dot(inp, obj.weights[layerIndex]) layer = AIlib.sigmoid( np.add(weightedLayer, obj.bias[layerIndex])) # add the biases if(layerIndex < maxLayer): return AIlib.think(layer, obj, layerIndex + 1) else: out = np.squeeze(np.asarray(layer)) return out def propDer(dCost, dProp): # Calculate the partial derivative for that prop return dCost / dProp def compareAIobjects(inp, obj1, obj2): # Compare the two instances res1 = AIlib.think(inp, obj1) cost1 = AIlib.getThinkCost(inp, res1) # get the cost res2 = AIlib.think(inp, obj2) cost2 = AIlib.getThinkCost(inp, res2) # get the second cost # Actually calculate stuff dCost = cost2 - cost1 return dCost, cost1 def compareInstanceWeight(obj, inp, theta: float, layerIndex: int, neuronIndex_X: int, neuronIndex_Y: int): # Create new a instance of the object obj2 = copy(obj) # annoying way to create a new instance of the object # mutate the second objects neuron obj2.weights[layerIndex][neuronIndex_X][neuronIndex_Y] += theta # compare the two and get the dCost with respect to the weights dCost, curCost = AIlib.compareAIobjects(inp, obj, obj2) return dCost, curCost def compareInstanceBias(obj, inp, theta: float, layerIndex: int, biasIndex: int): obj2 = copy(obj) # do the same thing for the bias obj2.bias[layerIndex][0][biasIndex] += theta dCost, curCost = AIlib.compareAIobjects(inp, obj, obj2) return dCost, curCost def getChangeInCost(obj, inp, theta, layerIndex): mirrorObj = copy(obj) # Fill the buffer with None so that the dCost can replace it later # fill it with a placeholder dCost_W = np.zeros(shape=mirrorObj.weights[layerIndex].shape) dCost_B = np.zeros(shape=mirrorObj.bias[layerIndex].shape) # Get the cost change for the weights weightLenX = len(dCost_W) weightLenY = len(dCost_W[0]) for x in range(weightLenX): # get the dCost for each x,y for y in range(weightLenY): dCost_W[x][y], curCostWeight = AIlib.compareInstanceWeight( obj, inp, theta, layerIndex, x, y) # Get the cost change for the biases biasLenY = len(dCost_B[0]) for index in range(biasLenY): dCost_B[0][index], curCostBias = AIlib.compareInstanceBias( obj, inp, theta, layerIndex, index) return dCost_W, dCost_B, (curCostBias + curCostWeight)/2 # Calculate the gradient for that prop def gradient(inp: np.array, obj, theta: float, maxLayer: int, layerIndex: int = 0, grads=None, obj1=None, obj2=None): # Check if grads exists, if not create the buffer if(not grads): grads = [None] * (maxLayer+1) dCost_W, dCost_B, meanCurCost = AIlib.getChangeInCost( obj, inp, theta, layerIndex) # Calculate the gradient for the layer weightDer = AIlib.propDer(dCost_W, theta) biasDer = AIlib.propDer(dCost_B, theta) # Append the gradients to the list grads[layerIndex] = { "weight": weightDer, "bias": biasDer } newLayer = layerIndex + 1 if(newLayer <= maxLayer): return AIlib.gradient(inp, obj, theta, maxLayer, newLayer, grads, obj1, obj2) else: return grads, meanCurCost def mutateProps(inpObj, maxLen: int, gradient: list): obj = copy(inpObj) for i in range(maxLen): obj.weights[i] -= obj.learningrate * \ gradient[i]["weight"] # mutate the weights obj.bias[i] -= obj.learningrate * gradient[i]["bias"] return obj def learn(inputNum: int, targetCost: float, obj, theta: float, curCost: float = None): # Calculate the derivative for: # Cost in respect to weights # Cost in respect to biases # i.e. : W' = W - lr * gradient (respect to W in layer i) = W - lr*[ dC / dW[i] ... ] # So if we change all the weights with i.e. 0.01 = theta, then we can derive the gradient with math and stuff inp = np.asarray(np.random.rand(1, inputNum))[ 0] # create a random learning sample # targetCost is the target for the cost function while(not curCost or curCost > targetCost): maxLen = len(obj.bias) grads, curCost = AIlib.gradient(inp, obj, theta, maxLen - 1) # mutate the props for next round obj = AIlib.mutateProps(obj, maxLen, grads) print(f"Cost: {curCost}") print("DONE\n") print(obj.weights) print(obj.bias)